Beyond computational difficulties: Survey of the two decades from the elaboration to the extensive application of the Hartree-Fock method

NASA Astrophysics Data System (ADS)

Martinez, Jean-Philippe

2017-11-01

The Hartree-Fock method, one of the first applications of the new quantum mechanics in the frame of the many-body problem, had been elaborated by Rayner Douglas Hartree in 1928 and Vladimir Fock in 1930. Promptly, the challenge of tedious computations was being discussed and it is well known that the application of the method benefited greatly from the development of computers from the mid-to-late 1950s. However, the years from 1930 to 1950 were by no means years of stagnation, as the method was the object of several considerations related to its mathematical formulation, possible extension, and conceptual understanding. Thus, with a focus on the respective attitudes of Hartree and Fock, in particular with respect to the concept of quantum exchange, the present work puts forward some mathematical and conceptual clarifications, which played an important role for a better understanding of the many-body problem in quantum mechanics.

A finite-temperature Hartree-Fock code for shell-model Hamiltonians

NASA Astrophysics Data System (ADS)

Bertsch, G. F.; Mehlhaff, J. M.

2016-10-01

The codes HFgradZ.py and HFgradT.py find axially symmetric minima of a Hartree-Fock energy functional for a Hamiltonian supplied in a shell model basis. The functional to be minimized is the Hartree-Fock energy for zero-temperature properties or the Hartree-Fock grand potential for finite-temperature properties (thermal energy, entropy). The minimization may be subjected to additional constraints besides axial symmetry and nucleon numbers. A single-particle operator can be used to constrain the minimization by adding it to the single-particle Hamiltonian with a Lagrange multiplier. One can also constrain its expectation value in the zero-temperature code. Also the orbital filling can be constrained in the zero-temperature code, fixing the number of nucleons having given Kπ quantum numbers. This is particularly useful to resolve near-degeneracies among distinct minima.

Restricted Closed Shell Hartree Fock Roothaan Matrix Method Applied to Helium Atom Using Mathematica

ERIC Educational Resources Information Center

Acosta, César R.; Tapia, J. Alejandro; Cab, César

2014-01-01

Slater type orbitals were used to construct the overlap and the Hamiltonian core matrices; we also found the values of the bi-electron repulsion integrals. The Hartree Fock Roothaan approximation process starts with setting an initial guess value for the elements of the density matrix; with these matrices we constructed the initial Fock matrix.…

Improvement of one-nucleon removal and total reaction cross sections in the Liège intranuclear-cascade model using Hartree-Fock-Bogoliubov calculations

NASA Astrophysics Data System (ADS)

Rodríguez-Sánchez, Jose Luis; David, Jean-Christophe; Mancusi, Davide; Boudard, Alain; Cugnon, Joseph; Leray, Sylvie

2017-11-01

The prediction of one-nucleon-removal cross sections by the Liège intranuclear-cascade model has been improved using a refined description of the matter and energy densities in the nuclear surface. Hartree-Fock-Bogoliubov calculations with the Skyrme interaction are used to obtain a more realistic description of the radial-density distributions of protons and neutrons, as well as the excitation-energy uncorrelation at the nuclear surface due to quantum effects and short-range correlations. The results are compared with experimental data covering a large range of nuclei, from carbon to uranium, and projectile kinetic energies. We find that the new approach is in good agreement with experimental data of one-nucleon-removal cross sections covering a broad range in nuclei and energies. The new ingredients also improve the description of total reaction cross sections induced by protons at low energies, the production cross sections of heaviest residues close to the projectile, and the triple-differential cross sections for one-proton removal. However, other observables such as quadruple-differential cross sections of coincident protons do not present any sizable sensitivity to the new approach. Finally, the model is also tested for light-ion-induced reactions. It is shown that the new parameters can give a reasonable description of the nucleus-nucleus total reaction cross sections at high energies.

A finite difference Hartree-Fock program for atoms and diatomic molecules

NASA Astrophysics Data System (ADS)

Kobus, Jacek

2013-03-01

. The lowest energy eigenstates of a given irreducible representation and spin can be obtained. The program can be used to perform one-particle calculations with (smooth) Coulomb and Krammers-Henneberger potentials and also DFT-type calculations using LDA or B88 exchange functionals and LYP or VWN correlations ones or the self-consistent multiplicative constant method. Solution method: Single-particle two-dimensional numerical functions (orbitals) are used to construct an antisymmetric many-electron wave function of the restricted open-shell Hartree-Fock model. The orbitals are obtained by solving the Hartree-Fock equations as coupled two-dimensional second-order (elliptic) partial differential equations (PDEs). The Coulomb and exchange potentials are obtained as solutions of the corresponding Poisson equations. The PDEs are discretized by the eighth-order central difference stencil on a two-dimensional single grid, and the resulting large and sparse system of linear equations is solved by the (multicolour) successive overrelaxation ((MC)SOR) method. The self-consistent-field iterations are interwoven with the (MC)SOR ones and orbital energies and normalization factors are used to monitor the convergence. The accuracy of solutions depends mainly on the grid and the system under consideration, which means that within double precision arithmetic one can obtain orbitals and energies having up to 12 significant figures. If more accurate results are needed, quadruple-precision floating-point arithmetic can be used. Reasons for new version: Additional features, many modifications and corrections, improved convergence rate, overhauled code and documentation. Summary of revisions: see ChangeLog found in tar.gz archive Restrictions: The present version of the program is restricted to 60 orbitals. The maximum grid size is determined at compilation time. Unusual features: The program uses two C routines for allocating and deallocating memory. Several BLAS (Basic Linear Algebra

Qualitative breakdown of the unrestricted Hartree-Fock energy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mori-Sánchez, Paula, E-mail: paula.mori@uam.es; Cohen, Aron J., E-mail: ajc54@cam.ac.uk

2014-10-28

The stretching of closed-shell molecules is a qualitative problem for restricted Hartree-Fock that is usually circumvented by the use of unrestricted Hartree-Fock (UHF). UHF is well known to break the spin symmetry at the Coulson-Fischer point, leading to a discontinuous derivative in the potential energy surface and incorrect spin density. However, this is generally not considered as a major drawback. In this work, we present a set of two electron molecules which magnify the problem of symmetry breaking and lead to drastically incorrect potential energy surfaces with UHF. These molecules also fail with unrestricted density-functional calculations where a functional suchmore » as B3LYP gives both symmetry breaking and an unphysically low energy due to the delocalization error. The implications for density functional theory are also discussed.« less

Computational Nuclear Physics and Post Hartree-Fock Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lietz, Justin; Sam, Novario; Hjorth-Jensen, M.

We present a computational approach to infinite nuclear matter employing Hartree-Fock theory, many-body perturbation theory and coupled cluster theory. These lectures are closely linked with those of chapters 9, 10 and 11 and serve as input for the correlation functions employed in Monte Carlo calculations in chapter 9, the in-medium similarity renormalization group theory of dense fermionic systems of chapter 10 and the Green's function approach in chapter 11. We provide extensive code examples and benchmark calculations, allowing thereby an eventual reader to start writing her/his own codes. We start with an object-oriented serial code and end with discussions onmore » strategies for porting the code to present and planned high-performance computing facilities.« less

Axially deformed solution of the Skyrme-Hartree-Fock-Bogoliubov equations using the transformed harmonic oscillator basis (II) HFBTHO v2.00d: A new version of the program

NASA Astrophysics Data System (ADS)

Stoitsov, M. V.; Schunck, N.; Kortelainen, M.; Michel, N.; Nam, H.; Olsen, E.; Sarich, J.; Wild, S.

2013-06-01

We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogoliubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas. Program summaryProgram title: HFBTHO v2.00d Catalog identifier: ADUI_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 167228 No. of bytes in distributed program, including test data, etc.: 2672156 Distribution format: tar.gz Programming language: FORTRAN-95. Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT5, Cray XE6. Operating system: UNIX, LINUX, WindowsXP. RAM: 200 Mwords Word size: 8 bits Classification: 17.22. Does the new version supercede the previous version?: Yes Catalog identifier of previous version: ADUI_v1_0 Journal reference of previous version: Comput. Phys. Comm. 167 (2005) 43 Nature of problem: The solution of self-consistent mean-field equations for weakly-bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasi-particle wave functions. In the present implementation, this is achieved by using the single-particle wave functions

Superdeformed bands in neutron-rich sulfur isotopes suggested by cranked Skyrme-Hartree-Fock calculations

NASA Astrophysics Data System (ADS)

Inakura, T.; Mizutori, S.; Yamagami, M.; Matsuyanagi, K.

2003-12-01

On the basis of the cranked Skyrme-Hartree-Fock calculations in the three-dimensional coordinate-mesh representation, we suggest that, in addition to the well-known candidate 32S, the neutron-rich nucleus 36S and the drip-line nuclei, 48S and 50S, are also good candidates for finding superdeformed rotational bands in sulfur isotopes. Calculated density distributions for the superdeformed states in 48S and 50S exhibit superdeformed neutron skins.

Skyrme-Hartree-Fock calculation on He, Li, and Be isotopes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shen, Y.; Ren, Z.

1996-09-01

The ground-state properties of He, Li, and Be nuclei are investigated by the Skyrme-Hartree-Fock approach with new force parameters SKI4 of Reinhard and Flocard [Nucl. Phys. A {bold 584}, 467 (1995)] plus a density-dependent pairing correlation. Calculations show that the Skyrme-Hartree-Fock model with above force parameters provides a good description on the binding energy and radii of He, Li, and Be isotopes. It also succeeds in reproducing neutron halos in nuclei {sup 6}He, {sup 8}He, {sup 11}Li, and {sup 14}Be. A detailed discussion on numerical results is provided and an explanation for the above success is given. {copyright} {ital 1996more » The American Physical Society.}« less

Structure factors for tunneling ionization rates of molecules: General Hartree-Fock-based integral representation

NASA Astrophysics Data System (ADS)

Madsen, Lars Bojer; Jensen, Frank; Dnestryan, Andrey I.; Tolstikhin, Oleg I.

2017-07-01

In the leading-order approximation of the weak-field asymptotic theory (WFAT), the dependence of the tunneling ionization rate of a molecule in an electric field on its orientation with respect to the field is determined by the structure factor of the ionizing molecular orbital. The WFAT yields an expression for the structure factor in terms of a local property of the orbital in the asymptotic region. However, in general quantum chemistry approaches molecular orbitals are expanded in a Gaussian basis which does not reproduce their asymptotic behavior correctly. This hinders the application of the WFAT to polyatomic molecules, which are attracting increasing interest in strong-field physics. Recently, an integral-equation approach to the WFAT for tunneling ionization of one electron from an arbitrary potential has been developed. The structure factor is expressed in an integral form as a matrix element involving the ionizing orbital. The integral is not sensitive to the asymptotic behavior of the orbital, which resolves the difficulty mentioned above. Here, we extend the integral representation for the structure factor to many-electron systems treated within the Hartree-Fock method and show how it can be implemented on the basis of standard quantum chemistry software packages. We validate the methodology by considering noble-gas atoms and the CO molecule, for which accurate structure factors exist in the literature. We also present benchmark results for CO2 and for NH3 in the pyramidal and planar geometries.

Hyperfine coupling constants of the nitrogen and phosphorus atoms: A challenge for exact-exchange density-functional and post-Hartree-Fock methods

NASA Astrophysics Data System (ADS)

Kaupp, Martin; Arbuznikov, Alexei V.; Heßelmann, Andreas; Görling, Andreas

2010-05-01

The isotropic hyperfine coupling constants of the free N(S4) and P(S4) atoms have been evaluated with high-level post-Hartree-Fock and density-functional methods. The phosphorus hyperfine coupling presents a significant challenge to both types of methods. With large basis sets, MP2 and coupled-cluster singles and doubles calculations give much too small values for the phosphorus atom. Triple excitations are needed in coupled-cluster calculations to achieve reasonable agreement with experiment. None of the standard density functionals reproduce even the correct sign of this hyperfine coupling. Similarly, the computed hyperfine couplings depend crucially on the self-consistent treatment in exact-exchange density-functional theory within the optimized effective potential (OEP) method. Well-balanced auxiliary and orbital basis sets are needed for basis-expansion exact-exchange-only OEP approaches to come close to Hartree-Fock or numerical OEP data. Results from the localized Hartree-Fock and Krieger-Li-Iafrate approximations deviate notably from exact OEP data in spite of very similar total energies. Of the functionals tested, only full exact-exchange methods augmented by a correlation functional gave at least the correct sign of the P(S4) hyperfine coupling but with too low absolute values. The subtle interplay between the spin-polarization contributions of the different core shells has been analyzed, and the influence of even very small changes in the exchange-correlation potential could be identified.

Axial deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator Basis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perez, R. Navarro; Schunck, N.; Lasseri, R.

2017-03-09

HFBTHO is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the nuclear energy Density Functional Theory (DFT), where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton densities. In HFBTHO, the energy density derives either from the zero-range Dkyrme or the finite-range Gogny effective two-body interaction between nucleons. Nuclear superfluidity is treated at the Hartree-Fock-Bogoliubov (HFB) approximation, and axial-symmetry of the nuclear shape is assumed. This version is the 3rd release ofmore » the program; the two previous versions were published in Computer Physics Communications [1,2]. The previous version was released at LLNL under GPL 3 Open Source License and was given release code LLNL-CODE-573953.« less

Constrained-pairing mean-field theory. IV. Inclusion of corresponding pair constraints and connection to unrestricted Hartree-Fock theory.

PubMed

Tsuchimochi, Takashi; Henderson, Thomas M; Scuseria, Gustavo E; Savin, Andreas

2010-10-07

Our previously developed constrained-pairing mean-field theory (CPMFT) is shown to map onto an unrestricted Hartree-Fock (UHF) type method if one imposes a corresponding pair constraint to the correlation problem that forces occupation numbers to occur in pairs adding to one. In this new version, CPMFT has all the advantages of standard independent particle models (orbitals and orbital energies, to mention a few), yet unlike UHF, it can dissociate polyatomic molecules to the correct ground-state restricted open-shell Hartree-Fock atoms or fragments.

Positron and electron energy bands in several ionic crystals using restricted Hartree-Fock method

NASA Astrophysics Data System (ADS)

Kunz, A. B.; Waber, J. T.

1981-08-01

Using a restricted Hartree-Fock formalism and suitably localized and symmetrized wave functions, both the positron and electron energy bands were calculated for NaF, MgO and NiO. The lowest positron state at Γ 1 lies above the vacuum level and negative work functions are predicted. Positron annihilation rates were calculated and found to be in good agreement with measured lifetimes.

a HARTREE-FOCK Nuclear Mass Table

NASA Astrophysics Data System (ADS)

Goriely, S.; Tondeur, F.; Pearson, J. M.

2001-03-01

We present the first complete nuclear mass table, HFBCS-1, to be based on the Hartree-Fock-BCS method. The force used, MSk7, is a 10-parameter Skyrme force, along with a 4-parameter δ-function pairing force and a 2-parameter phenomenological Wigner term. Our tabulation presents 9200 nuclei, including all those lying between the drip lines over the range Z, N≥8 and Z≤120. The root-mean-square error of our fit to the 1888 nuclei in this range for which measured masses are given in the 1995 Audi-Wapstra compilation is 0.738 MeV. In addition to the calculated masses, we show the calculated neutron- and proton-separation energies, and beta-decay energies. We also give for each nucleus in the table the calculated values for the deformation parameters and deformation energy (with axial and left-right symmetry assumed), and for the charge radius.

Hartree-Fock studies of hypernuclear properties

NASA Astrophysics Data System (ADS)

Lanskoy, D. E.

1998-08-01

The Skyrme-Hartree-Fock approach is approved as a powerful tool to reproduce general properties of Λ hypernuclear spectra [1-4] and to relate hypernuclear observables to effective interaction features. In this contribution, we consider briefly some less common hypernuclear systems, which appear to be quite sensitive to details of the relevant interactions. Particularly, we address possible manifestations of the polarization of a hypernuclear core (i.e. core distortion due to hyperon addition), which is driven in terms of the Skyrme force mainly by counterbalance between the two-body ΛN force and the three-body ΛNN (or density-dependent ΛN) one.

Non-plane-wave Hartree-Fock states and nuclear homework potentials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gutierrez, G.; Plastino, A.; de Llano, M.

1979-12-01

It is shown that non-plane-wave single-particle Hartree-Fock orbitals giving rise to a ''spin-density-wave-like'' structure give lower energy than plane waves beyond a certain relatively low density in both nuclear and neutron matter with homework pair potentials v/sub 1/ and v/sub 2/.

Influence of the Dirac-Hartree-Fock starting potential on the parity-nonconserving electric-dipole-transition amplitudes in cesium and thallium

NASA Technical Reports Server (NTRS)

Perger, W. F.; Das, B. P.

1987-01-01

The parity-nonconserving electric-dipole-transition amplitudes for the 6s1/2-7s1/2 transition in cesium and the 6p1/2-7p1/2 transition in thallium have been calculated by the Dirac-Hartree-Fock method. The effects of using different Dirac-Hartree-Fock atomic core potentials are examined and the transition amplitudes for both the length and velocity gauges are given. It is found that the parity-nonconserving transition amplitudes exhibit a greater dependence on the starting potential for thallium than for cesium.

Near Hartree-Fock quality GTO basis sets for the first- and third-row atoms

NASA Technical Reports Server (NTRS)

Partridge, Harry

1989-01-01

Energy-optimized Gaussian-type-orbital (GTO) basis sets of accuracy approaching that of numerical Hartree-Fock computations are compiled for the elements of the first and third rows of the periodic table. The methods employed in calculating the sets are explained; the applicability of the sets to electronic-structure calculations is discussed; and the results are presented in tables and briefly characterized.

Quantum supercharger library: hyper-parallelism of the Hartree-Fock method.

PubMed

Fernandes, Kyle D; Renison, C Alicia; Naidoo, Kevin J

2015-07-05

We present here a set of algorithms that completely rewrites the Hartree-Fock (HF) computations common to many legacy electronic structure packages (such as GAMESS-US, GAMESS-UK, and NWChem) into a massively parallel compute scheme that takes advantage of hardware accelerators such as Graphical Processing Units (GPUs). The HF compute algorithm is core to a library of routines that we name the Quantum Supercharger Library (QSL). We briefly evaluate the QSL's performance and report that it accelerates a HF 6-31G Self-Consistent Field (SCF) computation by up to 20 times for medium sized molecules (such as a buckyball) when compared with mature Central Processing Unit algorithms available in the legacy codes in regular use by researchers. It achieves this acceleration by massive parallelization of the one- and two-electron integrals and optimization of the SCF and Direct Inversion in the Iterative Subspace routines through the use of GPU linear algebra libraries. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Koopmans' theorem in the Hartree-Fock method. General formulation

NASA Astrophysics Data System (ADS)

Plakhutin, Boris N.

2018-03-01

This work presents a general formulation of Koopmans' theorem (KT) in the Hartree-Fock (HF) method which is applicable to molecular and atomic systems with arbitrary orbital occupancies and total electronic spin including orbitally degenerate (OD) systems. The new formulation is based on the full set of variational conditions imposed upon the HF orbitals by the variational principle for the total energy and the conditions imposed by KT on the orbitals of an ionized electronic shell [B. N. Plakhutin and E. R. Davidson, J. Chem. Phys. 140, 014102 (2014)]. Based on these conditions, a general form of the restricted open-shell HF method is developed, whose eigenvalues (orbital energies) obey KT for the whole energy spectrum. Particular attention is paid to the treatment of OD systems, for which the new method gives a number of unexpected results. For example, the present method gives four different orbital energies for the triply degenerate atomic level 2p in the second row atoms B to F. Based on both KT conditions and a parallel treatment of atoms B to F within a limited configuration interaction approach, we prove that these four orbital energies, each of which is triply degenerate, are related via KT to the energies of different spin-dependent ionization and electron attachment processes (2p)N → (2p ) N ±1. A discussion is also presented of specific limitations of the validity of KT in the HF method which arise in OD systems. The practical applicability of the theory is verified by comparing KT estimates of the ionization potentials I2s and I2p for the second row open-shell atoms Li to F with the relevant experimental data.

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. I. General formalism and application to open-shell states.

PubMed

Miranda, R P; Fisher, A J; Stella, L; Horsfield, A P

2011-06-28

The solution of the time-dependent Schrödinger equation for systems of interacting electrons is generally a prohibitive task, for which approximate methods are necessary. Popular approaches, such as the time-dependent Hartree-Fock (TDHF) approximation and time-dependent density functional theory (TDDFT), are essentially single-configurational schemes. TDHF is by construction incapable of fully accounting for the excited character of the electronic states involved in many physical processes of interest; TDDFT, although exact in principle, is limited by the currently available exchange-correlation functionals. On the other hand, multiconfigurational methods, such as the multiconfigurational time-dependent Hartree-Fock (MCTDHF) approach, provide an accurate description of the excited states and can be systematically improved. However, the computational cost becomes prohibitive as the number of degrees of freedom increases, and thus, at present, the MCTDHF method is only practical for few-electron systems. In this work, we propose an alternative approach which effectively establishes a compromise between efficiency and accuracy, by retaining the smallest possible number of configurations that catches the essential features of the electronic wavefunction. Based on a time-dependent variational principle, we derive the MCTDHF working equation for a multiconfigurational expansion with fixed coefficients and specialise to the case of general open-shell states, which are relevant for many physical processes of interest.

Projected Hartree-Fock theory as a polynomial of particle-hole excitations and its combination with variational coupled cluster theory

NASA Astrophysics Data System (ADS)

Qiu, Yiheng; Henderson, Thomas M.; Scuseria, Gustavo E.

2017-05-01

Projected Hartree-Fock theory provides an accurate description of many kinds of strong correlations but does not properly describe weakly correlated systems. Coupled cluster theory, in contrast, does the opposite. It therefore seems natural to combine the two so as to describe both strong and weak correlations with high accuracy in a relatively black-box manner. Combining the two approaches, however, is made more difficult by the fact that the two techniques are formulated very differently. In earlier work, we showed how to write spin-projected Hartree-Fock in a coupled-cluster-like language. Here, we fill in the gaps in that earlier work. Further, we combine projected Hartree-Fock and coupled cluster theory in a variational formulation and show how the combination performs for the description of the Hubbard Hamiltonian and for several small molecular systems.

Hartree-Fock limit values of multipole moments, polarizabilities, and hyperpolarizabilities for atoms and diatomic molecules

NASA Astrophysics Data System (ADS)

Kobus, Jacek

2015-02-01

Recently it has been demonstrated that the finite difference Hartree-Fock method can be used to deliver highly accurate values of electric multipole moments together with polarizabilities αz z,Az ,z z , and hyperpolarizabilities βz z z, γz z z,Bz z ,z z , for the ground states of various atomic and diatomic systems. Since these results can be regarded as de facto Hartree-Fock limit values their quality is of the utmost importance. This paper reexamines the use of the finite field method to calculate these electric properties, discusses its accuracy, and presents an updated list of the properties for the following atoms and diatomic molecules: H-, He, Li, Li+,Li2 +,Li-,Be2 + , Be, B+,C2 + , Ne, Mg2 +, Mg, Al+,Si2 + , Ar, K+,Ca2 +,Rb+,Sr2 +,Zr4 +,He2 , Be2,N2,F2,O2 , HeNe, LiH2 +, LiCl, LiBr, BH, CO, FH, NaCl, and KF. The potential energy curves and the dependence of the electric properties on the internuclear distance is also studied for He2,LiH+,Be2 , and HeNe systems.

Second-Order Moller-Plesset Perturbation Theory for Molecular Dirac-Hartree-Fock Wave Functions

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.; Arnold, James O. (Technical Monitor)

1994-01-01

Moller-Plesset perturbation theory is developed to second order for a selection of Kramers restricted Dirac-Hartree-Fock closed and open-shell reference wave functions. The open-shell wave functions considered are limited to those with no more than two electrons in open shells, but include the case of a two-configuration SCF reference. Denominator shifts are included in the style of Davidson's OPT2 method. An implementation which uses unordered integrals with labels is presented, and results are given for a few test cases.

Equilibration in the time-dependent Hartree-Fock approach probed with the Wigner distribution function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Loebl, N.; Maruhn, J. A.; Reinhard, P.-G.

2011-09-15

By calculating the Wigner distribution function in the reaction plane, we are able to probe the phase-space behavior in the time-dependent Hartree-Fock scheme during a heavy-ion collision in a consistent framework. Various expectation values of operators are calculated by evaluating the corresponding integrals over the Wigner function. In this approach, it is straightforward to define and analyze quantities even locally. We compare the Wigner distribution function with the smoothed Husimi distribution function. Different reaction scenarios are presented by analyzing central and noncentral {sup 16}O +{sup 16}O and {sup 96}Zr +{sup 132}Sn collisions. Although we observe strong dissipation in the timemore » evolution of global observables, there is no evidence for complete equilibration in the local analysis of the Wigner function. Because the initial phase-space volumes of the fragments barely merge and mean values of the observables are conserved in fusion reactions over thousands of fm/c, we conclude that the time-dependent Hartree-Fock method provides a good description of the early stage of a heavy-ion collision but does not provide a mechanism to change the phase-space structure in a dramatic way necessary to obtain complete equilibration.« less

Polyatomic molecular Dirac-Hartree-Fock calculations with Gaussian basis sets

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.; Faegri, Knut, Jr.; Taylor, Peter R.

1990-01-01

Numerical methods have been used successfully in atomic Dirac-Hartree-Fock (DHF) calculations for many years. Some DHF calculations using numerical methods have been done on diatomic molecules, but while these serve a useful purpose for calibration, the computational effort in extending this approach to polyatomic molecules is prohibitive. An alternative more in line with traditional quantum chemistry is to use an analytical basis set expansion of the wave function. This approach fell into disrepute in the early 1980's due to problems with variational collapse and intruder states, but has recently been put on firm theoretical foundations. In particular, the problems of variational collapse are well understood, and prescriptions for avoiding the most serious failures have been developed. Consequently, it is now possible to develop reliable molecular programs using basis set methods. This paper describes such a program and reports results of test calculations to demonstrate the convergence and stability of the method.

The generator coordinate Dirac-Fock method for open-shell atomic systems

NASA Astrophysics Data System (ADS)

Malli, Gulzari L.; Ishikawa, Yasuyuki

1998-11-01

Recently we developed generator coordinate Dirac-Fock and Dirac-Fock-Breit methods for closed-shell systems assuming finite nucleus and have reported Dirac-Fock and Dirac-Fock-Breit energies for the atoms He through Nobelium (Z=102) [see Refs. Reference 10Reference 11Reference 12Reference 13]. In this paper, we generalize our earlier work on closed-shell systems and develop a generator coordinate Dirac-Fock method for open-shell systems. We present results for a number of representative open-shell heavy atoms (with nuclear charge Z>80) including the actinide and superheavy transactinide (with Z>103) atomic systems: Fr (Z=87), Ac (Z=89), and Lr (Z=103) to E113 (eka-thallium, Z=113). The high accuracy obtained in our open-shell Dirac-Fock calculations is similar to that of our closed-shell calculations, and we attribute it to the fact that the representation of the relativistic dynamics of an electron in a spherical ball finite nucleus near the origin in terms of our universal Gaussian basis set is as accurate as that provided by the numerical finite difference method. The DF SCF energies calculated by Desclaux [At. Data. Nucl. Data Tables 12, 311 (1973)] (apart from a typographic error for Fr pointed out here) are higher than those reported here for atoms of some of the superheavy transactinide elements by as much as 5 hartrees (136 eV). We believe that this is due to the use by Desclaux of much larger atomic masses than the currently accepted values for these elements.

A multireference perturbation method using non-orthogonal Hartree-Fock determinants for ground and excited states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yost, Shane R.; Kowalczyk, Tim; Van Voorhis, Troy, E-mail: tvan@mit.edu

2013-11-07

In this article we propose the ΔSCF(2) framework, a multireference strategy based on second-order perturbation theory, for ground and excited electronic states. Unlike the complete active space family of methods, ΔSCF(2) employs a set of self-consistent Hartree-Fock determinants, also known as ΔSCF states. Each ΔSCF electronic state is modified by a first-order correction from Møller-Plesset perturbation theory and used to construct a Hamiltonian in a configuration interactions like framework. We present formulas for the resulting matrix elements between nonorthogonal states that scale as N{sub occ}{sup 2}N{sub virt}{sup 3}. Unlike most active space methods, ΔSCF(2) treats the ground and excited statemore » determinants even-handedly. We apply ΔSCF(2) to the H{sub 2}, hydrogen fluoride, and H{sub 4} systems and show that the method provides accurate descriptions of ground- and excited-state potential energy surfaces with no single active space containing more than 10 ΔSCF states.« less

Relativistic Brueckner-Hartree-Fock theory for neutron drops

NASA Astrophysics Data System (ADS)

Shen, Shihang; Liang, Haozhao; Meng, Jie; Ring, Peter; Zhang, Shuangquan

2018-05-01

Neutron drops confined in an external field are studied in the framework of relativistic Brueckner-Hartree-Fock theory using the bare nucleon-nucleon interaction. The ground-state energies and radii of neutron drops with even numbers from N =4 to N =50 are calculated and compared with results obtained from other nonrelativistic ab initio calculations and from relativistic density functional theory. Special attention has been paid to the magic numbers and to the subshell closures. The single-particle energies are investigated and the monopole effect of the tensor force on the evolutions of the spin-orbit and the pseudospin-orbit splittings is discussed. The results provide interesting insights into neutron-rich systems and can form an important guide for future density functionals.

Semiempirical evaluation of post-Hartree-Fock diagonal-Born-Oppenheimer corrections for organic molecules.

PubMed

Mohallem, José R

2008-04-14

Recent post-Hartree-Fock calculations of the diagonal-Born-Oppenheimer correction empirically show that it behaves quite similar to atomic nuclear mass corrections. An almost constant contribution per electron is identified, which converges with system size for specific series of organic molecules. This feature permits pocket-calculator evaluation of the corrections within thermochemical accuracy (10(-1) mhartree or kcal/mol).

Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Small, David W.; Sundstrom, Eric J.; Head-Gordon, Martin

2015-01-14

Restricted Hartree Fock using complex-valued orbitals (cRHF) is studied. We introduce an orbital pairing theorem, with which we obtain a concise connection between cRHF and real-valued RHF, and use it to uncover the close relationship between cRHF, unrestricted Hartree Fock, and generalized valence bond perfect pairing. This enables an intuition for cRHF, contrasting with the generally unintuitive nature of complex orbitals. We also describe an efficient computer implementation of cRHF and its corresponding stability analysis. By applying cRHF to the Be + H{sub 2} insertion reaction, a Woodward-Hoffmann violating reaction, and a symmetry-driven conical intersection, we demonstrate in genuine molecularmore » systems that cRHF is capable of removing certain potential energy surface singularities that plague real-valued RHF and related methods. This complements earlier work that showed this capability in a model system. We also describe how cRHF is the preferred RHF method for certain radicaloid systems like singlet oxygen and antiaromatic molecules. For singlet O{sub 2}, we show that standard methods fail even at the equilibrium geometry. An implication of this work is that, regardless of their individual efficacies, cRHF solutions to the HF equations are fairly commonplace.« less

Generalization of the Hartree-Fock approach to collision processes

NASA Astrophysics Data System (ADS)

Hahn, Yukap

1997-06-01

The conventional Hartree and Hartree-Fock approaches for bound states are generalized to treat atomic collision processes. All the single-particle orbitals, for both bound and scattering states, are determined simultaneously by requiring full self-consistency. This generalization is achieved by introducing two Ansäauttze: (a) the weak asymptotic boundary condition, which maintains the correct scattering energy and target orbitals with correct number of nodes, and (b) square integrable amputated scattering functions to generate self-consistent field (SCF) potentials for the target orbitals. The exact initial target and final-state asymptotic wave functions are not required and thus need not be specified a priori, as they are determined simultaneously by the SCF iterations. To check the asymptotic behavior of the solution, the theory is applied to elastic electron-hydrogen scattering at low energies. The solution is found to be stable and the weak asymptotic condition is sufficient to produce the correct scattering amplitudes. The SCF potential for the target orbital shows the strong penetration by the projectile electron during the collision, but the exchange term tends to restore the original form. Potential applicabilities of this extension are discussed, including the treatment of ionization and shake-off processes.

Near Hartree-Fock quality GTO basis sets for the second-row atoms

NASA Technical Reports Server (NTRS)

Partridge, Harry

1987-01-01

Energy optimized, near Hartree-Fock quality Gaussian basis sets ranging in size from (17s12p) to (20s15p) are presented for the ground states of the second-row atoms for Na(2P), Na(+), Na(-), Mg(3P), P(-), S(-), and Cl(-). In addition, optimized supplementary functions are given for the ground state basis sets to describe the negative ions, and the excited Na(2P) and Mg(3P) atomic states. The ratios of successive orbital exponents describing the inner part of the 1s and 2p orbitals are found to be nearly independent of both nuclear charge and basis set size. This provides a method of obtaining good starting estimates for other basis set optimizations.

Proper and improper zero energy modes in Hartree-Fock theory and their relevance for symmetry breaking and restoration.

PubMed

Cui, Yao; Bulik, Ireneusz W; Jiménez-Hoyos, Carlos A; Henderson, Thomas M; Scuseria, Gustavo E

2013-10-21

We study the spectra of the molecular orbital Hessian (stability matrix) and random-phase approximation (RPA) Hamiltonian of broken-symmetry Hartree-Fock solutions, focusing on zero eigenvalue modes. After all negative eigenvalues are removed from the Hessian by following their eigenvectors downhill, one is left with only positive and zero eigenvalues. Zero modes correspond to orbital rotations with no restoring force. These rotations determine states in the Goldstone manifold, which originates from a spontaneously broken continuous symmetry in the wave function. Zero modes can be classified as improper or proper according to their different mathematical and physical properties. Improper modes arise from symmetry breaking and their restoration always lowers the energy. Proper modes, on the other hand, correspond to degeneracies of the wave function, and their symmetry restoration does not necessarily lower the energy. We discuss how the RPA Hamiltonian distinguishes between proper and improper modes by doubling the number of zero eigenvalues associated with the latter. Proper modes in the Hessian always appear in pairs which do not double in RPA. We present several pedagogical cases exemplifying the above statements. The relevance of these results for projected Hartree-Fock methods is also addressed.

Multiconfiguration Dirac-Hartree-Fock calculations of energy levels and radiative rates of Fe VII

NASA Astrophysics Data System (ADS)

Li, Yang; Xu, Xiaokai; Li, Bowen; Jönsson, Per; Chen, Ximeng

2018-06-01

Detailed calculations are performed for 134 fine-structure levels of the 3p63d2, 3p63d4s, 3p53d3 and 3p63d4p configurations in Fe VII using the multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (RCI) methods. Important electron correlation effects are systematically accounted for through active space (AS) expansions. Our results compare well with experimental measurements, emphasizing the importance of a careful treatment of electron correlation, and provide some missing data in the NIST atomic database. The data obtained are expected to be useful in astrophysical applications, particularly for the research of the solar coronal plasma.

Exact exchange potential evaluated from occupied Kohn-Sham and Hartree-Fock solutions

NASA Astrophysics Data System (ADS)

Cinal, M.; Holas, A.

2011-06-01

The reported algorithm determines the exact exchange potential vx in an iterative way using energy shifts (ESs) and orbital shifts (OSs) obtained with finite-difference formulas from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to vx and the latter for increments of ES and OS due to subsequent changes of vx. Thus, the need for solution of the differential equations for OSs, used by Kümmel and Perdew [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.90.043004 90, 043004 (2003)], is bypassed. The iterated exchange potential, expressed in terms of ESs and OSs, is improved by modifying ESs at odd iteration steps and OSs at even steps. The modification formulas are related to the optimized-effective-potential equation (satisfied at convergence) written as the condition of vanishing density shift (DS). They are obtained, respectively, by enforcing its satisfaction through corrections to approximate OSs and by determining the optimal ESs that minimize the DS norm. The proposed method, successfully tested for several closed-(sub)shell atoms, from Be to Kr, within the density functional theory exchange-only approximation, proves highly efficient. The calculations using the pseudospectral method for representing orbitals give iterative sequences of approximate exchange potentials (starting with the Krieger-Li-Iafrate approximation) that rapidly approach the exact vx so that, for Ne, Ar, and Zn, the corresponding DS norm becomes less than 10-6 after 13, 13, and 9 iteration steps for a given electron density. In self-consistent density calculations, orbital energies of 10-4 hartree accuracy are obtained for these atoms after, respectively, 9, 12, and 12 density iteration steps, each involving just two steps of vx iteration, while the accuracy limit of 10-6 to 10-7 hartree is reached after 20 density iterations.

Self-consistent Hartree-Fock RPA calculations in 208Pb

NASA Astrophysics Data System (ADS)

Taqi, Ali H.; Ali, Mohammed S.

2018-01-01

The nuclear structure of 208Pb is studied in the framework of the self-consistent random phase approximation (SCRPA). The Hartree-Fock mean field and single particle states are used to implement a completely SCRPA with Skyrme-type interactions. The Hamiltonian is diagonalised within a model space using five Skyrme parameter sets, namely LNS, SkI3, SkO, SkP and SLy4. In view of the huge number of the existing Skyrme-force parameterizations, the question remains which of them provide the best description of data. The approach attempts to accurately describe the structure of the spherical even-even nucleus 208Pb. To illustrate our approach, we compared the binding energy, charge density distribution, excitation energy levels scheme with the available experimental data. Moreover, we calculated isoscalar and isovector monopole, dipole, and quadrupole transition densities and strength functions.

The limits of the nuclear landscape explored by the relativistic continuum Hartree-Bogoliubov theory

NASA Astrophysics Data System (ADS)

Xia, X. W.; Lim, Y.; Zhao, P. W.; Liang, H. Z.; Qu, X. Y.; Chen, Y.; Liu, H.; Zhang, L. F.; Zhang, S. Q.; Kim, Y.; Meng, J.

2018-05-01

The ground-state properties of nuclei with 8 ⩽ Z ⩽ 120 from the proton drip line to the neutron drip line have been investigated using the spherical relativistic continuum Hartree-Bogoliubov (RCHB) theory with the relativistic density functional PC-PK1. With the effects of the continuum included, there are totally 9035 nuclei predicted to be bound, which largely extends the existing nuclear landscapes predicted with other methods. The calculated binding energies, separation energies, neutron and proton Fermi surfaces, root-mean-square (rms) radii of neutron, proton, matter, and charge distributions, ground-state spins and parities are tabulated. The extension of the nuclear landscape obtained with RCHB is discussed in detail, in particular for the neutron-rich side, in comparison with the relativistic mean field calculations without pairing correlations and also other predicted landscapes. It is found that the coupling between the bound states and the continuum due to the pairing correlations plays an essential role in extending the nuclear landscape. The systematics of the separation energies, radii, densities, potentials and pairing energies of the RCHB calculations are also discussed. In addition, the α-decay energies and proton emitters based on the RCHB calculations are investigated.

Molecular wave function and effective adiabatic potentials calculated by extended multi-configuration time-dependent Hartree-Fock method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kato, Tsuyoshi; Ide, Yoshihiro; Yamanouchi, Kaoru

We first calculate the ground-state molecular wave function of 1D model H{sub 2} molecule by solving the coupled equations of motion formulated in the extended multi-configuration time-dependent Hartree-Fock (MCTDHF) method by the imaginary time propagation. From the comparisons with the results obtained by the Born-Huang (BH) expansion method as well as with the exact wave function, we observe that the memory size required in the extended MCTDHF method is about two orders of magnitude smaller than in the BH expansion method to achieve the same accuracy for the total energy. Second, in order to provide a theoretical means to understandmore » dynamical behavior of the wave function, we propose to define effective adiabatic potential functions and compare them with the conventional adiabatic electronic potentials, although the notion of the adiabatic potentials is not used in the extended MCTDHF approach. From the comparison, we conclude that by calculating the effective potentials we may be able to predict the energy differences among electronic states even for a time-dependent system, e.g., time-dependent excitation energies, which would be difficult to be estimated within the BH expansion approach.« less

Optimized norm-conserving Hartree-Fock pseudopotentials for plane-wave calculations

NASA Astrophysics Data System (ADS)

Al-Saidi, W. A.; Walter, E. J.; Rappe, A. M.

2008-02-01

We report Hartree-Fock (HF)-based pseudopotentials suitable for plane-wave calculations. Unlike typical effective core potentials, the present pseudopotentials are finite at the origin and exhibit rapid convergence in a plane-wave basis; the optimized pseudopotential method [A. M. Rappe , Phys. Rev. B 41, 1227 (1990)] improves plane-wave convergence. Norm-conserving HF pseudopotentials are found to develop long-range non-Coulombic behavior which does not decay faster than 1/r , and is nonlocal. This behavior, which stems from the nonlocality of the exchange potential, is remedied using a recently developed self-consistent procedure [J. R. Trail and R. J. Needs, J. Chem. Phys. 122, 014112 (2005)]. The resulting pseudopotentials slightly violate the norm conservation of the core charge. We calculated several atomic properties using these pseudopotentials, and the results are in good agreement with all-electron HF values. The dissociation energies, equilibrium bond lengths, and frequencies of vibration of several dimers obtained with these HF pseudopotentials and plane waves are also in good agreement with all-electron results.

Linear scaling computation of the Fock matrix. II. Rigorous bounds on exchange integrals and incremental Fock build

NASA Astrophysics Data System (ADS)

Schwegler, Eric; Challacombe, Matt; Head-Gordon, Martin

1997-06-01

A new linear scaling method for computation of the Cartesian Gaussian-based Hartree-Fock exchange matrix is described, which employs a method numerically equivalent to standard direct SCF, and which does not enforce locality of the density matrix. With a previously described method for computing the Coulomb matrix [J. Chem. Phys. 106, 5526 (1997)], linear scaling incremental Fock builds are demonstrated for the first time. Microhartree accuracy and linear scaling are achieved for restricted Hartree-Fock calculations on sequences of water clusters and polyglycine α-helices with the 3-21G and 6-31G basis sets. Eightfold speedups are found relative to our previous method. For systems with a small ionization potential, such as graphitic sheets, the method naturally reverts to the expected quadratic behavior. Also, benchmark 3-21G calculations attaining microhartree accuracy are reported for the P53 tetramerization monomer involving 698 atoms and 3836 basis functions.

The properties of nuclear matter with lattice NN potential in relativistic Brueckner-Hartree-Fock theory

PubMed Central

Hu, Jinniu; Toki, Hiroshi; Shen, Hong

2016-01-01

We study the properties of nuclear matter with lattice nucleon-nucleon (NN) potential in the relativistic Brueckner-Hartree-Fock (RBHF) theory. To use this potential in such a microscopic many-body theory, we firstly have to construct a one-boson-exchange potential (OBEP) based on the latest lattice NN potential. Three mesons, pion, σ meson, and ω meson, are considered. Their coupling constants and cut-off momenta are determined by fitting the on-shell behaviors and phase shifts of the lattice force, respectively. Therefore, we obtain two parameter sets of the OBEP potential (named as LOBEP1 and LOBEP2) with these two fitting ways. We calculate the properties of symmetric and pure neutron matter with LOBEP1 and LOBEP2. In non-relativistic Brueckner-Hartree-Fock case, the binding energies of symmetric nuclear matter are around −3 and −5 MeV at saturation density, while it becomes −8 and −12 MeV in relativistic framework with 1S0, 3S1, and 3D1 channels using our two parameter sets. For the pure neutron matter, the equations of state in non-relativistic and relativistic cases are very similar due to only consideration 1S0 channel with isospin T = 1 case. PMID:27752124

The properties of nuclear matter with lattice NN potential in relativistic Brueckner-Hartree-Fock theory.

PubMed

Hu, Jinniu; Toki, Hiroshi; Shen, Hong

2016-10-18

We study the properties of nuclear matter with lattice nucleon-nucleon (NN) potential in the relativistic Brueckner-Hartree-Fock (RBHF) theory. To use this potential in such a microscopic many-body theory, we firstly have to construct a one-boson-exchange potential (OBEP) based on the latest lattice NN potential. Three mesons, pion, σ meson, and ω meson, are considered. Their coupling constants and cut-off momenta are determined by fitting the on-shell behaviors and phase shifts of the lattice force, respectively. Therefore, we obtain two parameter sets of the OBEP potential (named as LOBEP1 and LOBEP2) with these two fitting ways. We calculate the properties of symmetric and pure neutron matter with LOBEP1 and LOBEP2. In non-relativistic Brueckner-Hartree-Fock case, the binding energies of symmetric nuclear matter are around -3 and -5 MeV at saturation density, while it becomes -8 and -12 MeV in relativistic framework with 1 S 0 , 3 S 1 , and 3 D 1 channels using our two parameter sets. For the pure neutron matter, the equations of state in non-relativistic and relativistic cases are very similar due to only consideration 1 S 0 channel with isospin T = 1 case.

Hartree-Fock calculation of the differential photoionization cross sections of small Li clusters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Galitskiy, S. A.; Artemyev, A. N.; Jänkälä, K.

2015-01-21

Cross sections and angular distribution parameters for the single-photon ionization of all electron orbitals of Li{sub 2−8} are systematically computed in a broad interval of the photoelectron kinetic energies for the energetically most stable geometry of each cluster. Calculations of the partial photoelectron continuum waves in clusters are carried out by the single center method within the Hartree-Fock approximation. We study photoionization cross sections per one electron and analyze in some details general trends in the photoionization of inner and outer shells with respect to the size and geometry of a cluster. The present differential cross sections computed for Li{submore » 2} are in a good agreement with the available theoretical data, whereas those computed for Li{sub 3−8} clusters can be considered as theoretical predictions.« less

Time-Dependent Hartree-Fock Approach to Nuclear Pasta at Finite Temperature

NASA Astrophysics Data System (ADS)

Schuetrumpf, B.; Klatt, M. A.; Iida, K.; Maruhn, J. A.; Mecke, K.; Reinhard, P.-G.

2013-03-01

We present simulations of neutron-rich matter at subnuclear densities, like supernova matter, with the time-dependent Hartree-Fock approximation at temperatures of several MeV. The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. This matter evolves into spherical, rod-like, and slab-like shapes and mixtures thereof. The simulations employ a full Skyrme interaction in a periodic three-dimensional grid. By an improved morphological analysis based on Minkowski functionals, all eight pasta shapes can be uniquely identified by the sign of only two valuations, namely the Euler characteristic and the integral mean curvature.

Exact exchange potential evaluated from occupied Kohn-Sham and Hartree-Fock solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cinal, M.; Holas, A.

2011-06-15

The reported algorithm determines the exact exchange potential v{sub x} in an iterative way using energy shifts (ESs) and orbital shifts (OSs) obtained with finite-difference formulas from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to v{sub x} and the latter for increments of ES and OS due to subsequent changes of v{sub x}. Thus, the need for solution of the differential equations for OSs, used by Kuemmel and Perdew [Phys. Rev. Lett. 90, 043004 (2003)], is bypassed. The iterated exchange potential, expressed in terms ofmore » ESs and OSs, is improved by modifying ESs at odd iteration steps and OSs at even steps. The modification formulas are related to the optimized-effective-potential equation (satisfied at convergence) written as the condition of vanishing density shift (DS). They are obtained, respectively, by enforcing its satisfaction through corrections to approximate OSs and by determining the optimal ESs that minimize the DS norm. The proposed method, successfully tested for several closed-(sub)shell atoms, from Be to Kr, within the density functional theory exchange-only approximation, proves highly efficient. The calculations using the pseudospectral method for representing orbitals give iterative sequences of approximate exchange potentials (starting with the Krieger-Li-Iafrate approximation) that rapidly approach the exact v{sub x} so that, for Ne, Ar, and Zn, the corresponding DS norm becomes less than 10{sup -6} after 13, 13, and 9 iteration steps for a given electron density. In self-consistent density calculations, orbital energies of 10{sup -4} hartree accuracy are obtained for these atoms after, respectively, 9, 12, and 12 density iteration steps, each involving just two steps of v{sub x} iteration, while the accuracy limit of 10{sup -6} to 10{sup -7} hartree is reached after 20 density iterations.« less

Automatic Differentiation in Quantum Chemistry with Applications to Fully Variational Hartree-Fock.

PubMed

Tamayo-Mendoza, Teresa; Kreisbeck, Christoph; Lindh, Roland; Aspuru-Guzik, Alán

2018-05-23

Automatic differentiation (AD) is a powerful tool that allows calculating derivatives of implemented algorithms with respect to all of their parameters up to machine precision, without the need to explicitly add any additional functions. Thus, AD has great potential in quantum chemistry, where gradients are omnipresent but also difficult to obtain, and researchers typically spend a considerable amount of time finding suitable analytical forms when implementing derivatives. Here, we demonstrate that AD can be used to compute gradients with respect to any parameter throughout a complete quantum chemistry method. We present DiffiQult , a Hartree-Fock implementation, entirely differentiated with the use of AD tools. DiffiQult is a software package written in plain Python with minimal deviation from standard code which illustrates the capability of AD to save human effort and time in implementations of exact gradients in quantum chemistry. We leverage the obtained gradients to optimize the parameters of one-particle basis sets in the context of the floating Gaussian framework.

Dispersion correction derived from first principles for density functional theory and Hartree-Fock theory.

PubMed

Guidez, Emilie B; Gordon, Mark S

2015-03-12

The modeling of dispersion interactions in density functional theory (DFT) is commonly performed using an energy correction that involves empirically fitted parameters for all atom pairs of the system investigated. In this study, the first-principles-derived dispersion energy from the effective fragment potential (EFP) method is implemented for the density functional theory (DFT-D(EFP)) and Hartree-Fock (HF-D(EFP)) energies. Overall, DFT-D(EFP) performs similarly to the semiempirical DFT-D corrections for the test cases investigated in this work. HF-D(EFP) tends to underestimate binding energies and overestimate intermolecular equilibrium distances, relative to coupled cluster theory, most likely due to incomplete accounting for electron correlation. Overall, this first-principles dispersion correction yields results that are in good agreement with coupled-cluster calculations at a low computational cost.

Parallel implementation of Hartree-Fock and density functional theory analytical second derivatives

NASA Astrophysics Data System (ADS)

Baker, Jon; Wolinski, Krzysztof; Malagoli, Massimo; Pulay, Peter

2004-01-01

We present an efficient, parallel implementation for the calculation of Hartree-Fock and density functional theory analytical Hessian (force constant, nuclear second derivative) matrices. These are important for the determination of harmonic vibrational frequencies, and to classify stationary points on potential energy surfaces. Our program is designed for modest parallelism (4-16 CPUs) as exemplified by our standard eight-processor QuantumCube™. We can routinely handle systems with up to 100+ atoms and 1000+ basis functions using under 0.5 GB of RAM memory per CPU. Timings are presented for several systems, ranging in size from aspirin (C9H8O4) to nickel octaethylporphyrin (C36H44N4Ni).

A density matrix-based method for the linear-scaling calculation of dynamic second- and third-order properties at the Hartree-Fock and Kohn-Sham density functional theory levels.

PubMed

Kussmann, Jörg; Ochsenfeld, Christian

2007-11-28

A density matrix-based time-dependent self-consistent field (D-TDSCF) method for the calculation of dynamic polarizabilities and first hyperpolarizabilities using the Hartree-Fock and Kohn-Sham density functional theory approaches is presented. The D-TDSCF method allows us to reduce the asymptotic scaling behavior of the computational effort from cubic to linear for systems with a nonvanishing band gap. The linear scaling is achieved by combining a density matrix-based reformulation of the TDSCF equations with linear-scaling schemes for the formation of Fock- or Kohn-Sham-type matrices. In our reformulation only potentially linear-scaling matrices enter the formulation and efficient sparse algebra routines can be employed. Furthermore, the corresponding formulas for the first hyperpolarizabilities are given in terms of zeroth- and first-order one-particle reduced density matrices according to Wigner's (2n+1) rule. The scaling behavior of our method is illustrated for first exemplary calculations with systems of up to 1011 atoms and 8899 basis functions.

Optimal plane-wave Hartree-Fock states for many-fermion systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

de Llano, M.; Plastino, A.; Zabolitzky, J.G.

1979-12-01

The possibility of taking plane-wave orbitals of a Hartree-Fock determinant to fill k space differently from the ''normal'' Fermi sphere is investigated for several two-body potentials including the ''homework'' v/sub 0/, v/sub 1/, and v/sub 2/ - aken from the Reid nucleon-nucleon force - as well as a sum-of-Gaussians potential chosen to fit the deuteron binding and size. A random-search and random-walk numerical algorithm shows that, provided the potential strengths are made large enough, a single-shell ''abnormal'' occupation is always found to be lower in energy than the normal one if sufficient attraction is present in the two-body interaction. Nomore » abnormal occupation is possible for, among other pair interactions, the electron or charged-boson fluid, the repulsive square barrier, and a common form of the He-He interaction.« less

The positronium and the dipositronium in a Hartree-Fock approximation of quantum electrodynamics

NASA Astrophysics Data System (ADS)

Sok, Jérémy

2016-02-01

The Bogoliubov-Dirac-Fock (BDF) model is a no-photon approximation of quantum electrodynamics. It allows to study relativistic electrons in interaction with the Dirac sea. A state is fully characterized by its one-body density matrix, an infinite rank non-negative projector. We prove the existence of the para-positronium, the bound state of an electron and a positron with antiparallel spins, in the BDF model represented by a critical point of the energy functional in the absence of an external field. We also prove the existence of the dipositronium, a molecule made of two electrons and two positrons that also appears as a critical point. More generally, for any half integer j ∈ 1/2 + Z + , we prove the existence of a critical point of the energy functional made of 2j + 1 electrons and 2j + 1 positrons.

Efficient method of evaluation for Gaussian Hartree-Fock exchange operator for Gau-PBE functional

NASA Astrophysics Data System (ADS)

Song, Jong-Won; Hirao, Kimihiko

2015-07-01

We previously developed an efficient screened hybrid functional called Gaussian-Perdew-Burke-Ernzerhof (Gau-PBE) [Song et al., J. Chem. Phys. 135, 071103 (2011)] for large molecules and extended systems, which is characterized by the usage of a Gaussian function as a modified Coulomb potential for the Hartree-Fock (HF) exchange. We found that the adoption of a Gaussian HF exchange operator considerably decreases the calculation time cost of periodic systems while improving the reproducibility of the bandgaps of semiconductors. We present a distance-based screening scheme here that is tailored for the Gaussian HF exchange integral that utilizes multipole expansion for the Gaussian two-electron integrals. We found a new multipole screening scheme helps to save the time cost for the HF exchange integration by efficiently decreasing the number of integrals of, specifically, the near field region without incurring substantial changes in total energy. In our assessment on the periodic systems of seven semiconductors, the Gau-PBE hybrid functional with a new screening scheme has 1.56 times the time cost of a pure functional while the previous Gau-PBE was 1.84 times and HSE06 was 3.34 times.

Efficient method of evaluation for Gaussian Hartree-Fock exchange operator for Gau-PBE functional

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Jong-Won; Hirao, Kimihiko, E-mail: hirao@riken.jp

2015-07-14

We previously developed an efficient screened hybrid functional called Gaussian-Perdew–Burke–Ernzerhof (Gau-PBE) [Song et al., J. Chem. Phys. 135, 071103 (2011)] for large molecules and extended systems, which is characterized by the usage of a Gaussian function as a modified Coulomb potential for the Hartree-Fock (HF) exchange. We found that the adoption of a Gaussian HF exchange operator considerably decreases the calculation time cost of periodic systems while improving the reproducibility of the bandgaps of semiconductors. We present a distance-based screening scheme here that is tailored for the Gaussian HF exchange integral that utilizes multipole expansion for the Gaussian two-electron integrals.more » We found a new multipole screening scheme helps to save the time cost for the HF exchange integration by efficiently decreasing the number of integrals of, specifically, the near field region without incurring substantial changes in total energy. In our assessment on the periodic systems of seven semiconductors, the Gau-PBE hybrid functional with a new screening scheme has 1.56 times the time cost of a pure functional while the previous Gau-PBE was 1.84 times and HSE06 was 3.34 times.« less

Direct mapping between exchange potentials of Hartree-Fock and Kohn-Sham schemes as origin of orbital proximity

NASA Astrophysics Data System (ADS)

Cinal, M.

2010-01-01

It is found that for closed-l-shell atoms, the exact local exchange potential vx(r) calculated in the exchange-only Kohn-Sham (KS) scheme of the density functional theory (DFT) is very well represented within the region of every atomic shell by each of the suitably shifted potentials obtained with the nonlocal Fock exchange operator for the individual Hartree-Fock (HF) orbitals belonging to this shell. This newly revealed property is not related to the well-known steplike shell structure in the response part of vx(r), but it results from specific relations satisfied by the HF orbital exchange potentials. These relations explain the outstanding proximity of the occupied HF and exchange-only KS orbitals as well as the high quality of the Krieger-Li-Iafrate and localized HF (or, equivalently, common-energy-denominator) approximations to the DFT exchange potential vx(r). Another highly accurate representation of vx(r) is given by the continuous piecewise function built of shell-specific exchange potentials, each defined as the weighted average of the shifted orbital exchange potentials corresponding to a given shell. The constant shifts added to the HF orbital exchange potentials, to map them onto vx(r), are nearly equal to the differences between the energies of the corresponding KS and HF orbitals. It is discussed why these differences are positive and grow when the respective orbital energies become lower for inner orbitals.

Hartree-Fock investigation of muon trapping in the chemical ferromagnet 4-(/p-chlorobenzylideneamino)-TEMPO

NASA Astrophysics Data System (ADS)

Jeong, Junho; Briere, Tina M.; Sahoo, N.; Das, T. P.; Ohira, Seiko; Nishiyama, K.; Nagamine, K.

2000-08-01

First-principles unrestricted Hartree-Fock theory is used to obtain the trapping sites for muon and muonium in ferromagnetic p-Cl-Ph-CHN-TEMPO (4-( p-chlorobenzylideneamino)- 2,2,6,6-tetramethylpiperidin-1-yloxyl) and the hyperfine interaction tensors for these sites. Using the calculated hyperfine interactions to fit the two experimentally observed muon spin rotation frequencies, it has been concluded that the two most likely candidates for explaining the experimental data are a muon trapped at the chlorine site and a singlet muonium state at the radical oxygen. The direction of the easy axis is also determined.

Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree-Fock.

PubMed

Hesselmann, Andreas; Görling, Andreas

2011-01-21

A recently introduced time-dependent exact-exchange (TDEXX) method, i.e., a response method based on time-dependent density-functional theory that treats the frequency-dependent exchange kernel exactly, is reformulated. In the reformulated version of the TDEXX method electronic excitation energies can be calculated by solving a linear generalized eigenvalue problem while in the original version of the TDEXX method a laborious frequency iteration is required in the calculation of each excitation energy. The lowest eigenvalues of the new TDEXX eigenvalue equation corresponding to the lowest excitation energies can be efficiently obtained by, e.g., a version of the Davidson algorithm appropriate for generalized eigenvalue problems. Alternatively, with the help of a series expansion of the new TDEXX eigenvalue equation, standard eigensolvers for large regular eigenvalue problems, e.g., the standard Davidson algorithm, can be used to efficiently calculate the lowest excitation energies. With the help of the series expansion as well, the relation between the TDEXX method and time-dependent Hartree-Fock is analyzed. Several ways to take into account correlation in addition to the exact treatment of exchange in the TDEXX method are discussed, e.g., a scaling of the Kohn-Sham eigenvalues, the inclusion of (semi)local approximate correlation potentials, or hybrids of the exact-exchange kernel with kernels within the adiabatic local density approximation. The lowest lying excitations of the molecules ethylene, acetaldehyde, and pyridine are considered as examples.

Multi-configuration Dirac-Hartree-Fock (MCDHF) calculations for Ni XXV

NASA Astrophysics Data System (ADS)

Singh, Narendra; Aggarwal, Sunny

2018-03-01

We present accurate 165 fine-structure energy levels related to the configurations 1s22s2, 1s22p2, 1s2nƖn‧l‧ (n = 2, n‧ = 2, 3, 4, 5, Ɩ = s,p Ɩ‧ = s, p, d, f, g) of Ni XXV which may be useful ion for astrophysical and fusion plasma. For the calculations of energy levels and radiative rates, we have used the multiconfiguration Dirac-Hartree-Fock (MCDHF) method employed in GRASP2K code. The calculations are carried out in the active space approximation with the inclusion of the Breit interaction, the finite nuclear size effect, and quantum electrodynamic corrections. The transition wavelengths, transition probabilities, line strengths, and absorption oscillator strengths are reported for electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), magnetic quadrupole (M2) transitions from the ground state. We have compared our calculated results with available theoretical and experimental data and good agreement is achieved. We predict new energy levels, oscillator strengths, line strengths and transition probabilities, where no other experimental or theoretical results are available. The present complete set of results should be of great help in line identification and the interpretation of spectra, as well as in the modelling and diagnostics of astrophysical and fusion plasmas.

Constrained Hartree-Fock Theory and Study of Deformed Structures of Closed Shell Nuclei

NASA Astrophysics Data System (ADS)

Praharaj, Choudhury

2016-03-01

We have studied some N or Z = 50 nuclei in a microscopic model with effective interaction in a reasonably large shell model space. Excitation of particles across 50 shell closure leads to well-deformed excited prolate configurations. The potential energy surfaces of nuclei are studied using Hartree-Fock theory with quadrupole constraint to explore the various deformed configurations of N = 50 nuclei 82Ge , 84Se and 86Kr . Energy spectra are calculated from various intrinsic states using Peierls-Yoccoz angular momentum projection technique. Results of spectra and electromagnetic moments and transitions will be presented for N = 50 nuclei and for Z = 50 114Sn nucleus. Supported by Grant No SB/S2/HEP-06/2013 of DST.

Accuracy of Hartree-Fock wave functions for electron-H/sub 2/ scattering calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Feldt, A.N.

1988-05-01

Recent papers on electron-N/sub 2/ scattering by Rumble, Stevens, and Truhlar (J. Phys. B 17, 3151 (1984)) and Weatherford, Brown, and Temkin (Phys. Rev. A 35, 4561 (1987)) have suggested that Hartree-Fock (HF) wave functions may not be accurate for calculating potentials for use in studying electron-molecule collisions. A comparison of results for electron-H/sub 2/ scattering using both correlated and HF wave functions is presented. It is found that for both elastic and inelastic collisions and for all energies considered (up to 10 eV) the HF wave functions yield results in excellent agreement with those obtained from the more accuratemore » wave functions.« less

Time-dependent Hartree-Fock approach to nuclear ``pasta'' at finite temperature

NASA Astrophysics Data System (ADS)

Schuetrumpf, B.; Klatt, M. A.; Iida, K.; Maruhn, J. A.; Mecke, K.; Reinhard, P.-G.

2013-05-01

We present simulations of neutron-rich matter at subnuclear densities, like supernova matter, with the time-dependent Hartree-Fock approximation at temperatures of several MeV. The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. This matter evolves into spherical, rod-like, and slab-like shapes and mixtures thereof. The simulations employ a full Skyrme interaction in a periodic three-dimensional grid. By an improved morphological analysis based on Minkowski functionals, all eight pasta shapes can be uniquely identified by the sign of only two valuations, namely the Euler characteristic and the integral mean curvature. In addition, we propose the variance in the cell density distribution as a measure to distinguish pasta matter from uniform matter.

Optimized auxiliary basis sets for density fitted post-Hartree-Fock calculations of lanthanide containing molecules

NASA Astrophysics Data System (ADS)

Chmela, Jiří; Harding, Michael E.

2018-06-01

Optimised auxiliary basis sets for lanthanide atoms (Ce to Lu) for four basis sets of the Karlsruhe error-balanced segmented contracted def2 - series (SVP, TZVP, TZVPP and QZVPP) are reported. These auxiliary basis sets enable the use of the resolution-of-the-identity (RI) approximation in post Hartree-Fock methods - as for example, second-order perturbation theory (MP2) and coupled cluster (CC) theory. The auxiliary basis sets are tested on an enlarged set of about a hundred molecules where the test criterion is the size of the RI error in MP2 calculations. Our tests also show that the same auxiliary basis sets can be used together with different effective core potentials. With these auxiliary basis set calculations of MP2 and CC quality can now be performed efficiently on medium-sized molecules containing lanthanides.

Hartree-Fock theory of the inhomogeneous electron gas at a jellium metal surface: Rigorous upper bounds to the surface energy and accurate work functions

NASA Astrophysics Data System (ADS)

Sahni, V.; Ma, C. Q.

1980-12-01

The inhomogeneous electron gas at a jellium metal surface is studied in the Hartree-Fock approximation by Kohn-Sham density functional theory. Rigorous upper bounds to the surface energy are derived by application of the Rayleigh-Ritz variational principle for the energy, the surface kinetic, electrostatic, and nonlocal exchange energy functionals being determined exactly for the accurate linear-potential model electronic wave functions. The densities obtained by the energy minimization constraint are then employed to determine work-function results via the variationally accurate "displaced-profile change-in-self-consistent-field" expression. The theoretical basis of this non-self-consistent procedure and its demonstrated accuracy for the fully correlated system (as treated within the local-density approximation for exchange and correlation) leads us to conclude these results for the surface energies and work functions to be essentially exact. Work-function values are also determined by the Koopmans'-theorem expression, both for these densities as well as for those obtained by satisfaction of the constraint set on the electrostatic potential by the Budd-Vannimenus theorem. The use of the Hartree-Fock results in the accurate estimation of correlation-effect contributions to these surface properties of the nonuniform electron gas is also indicated. In addition, the original work and approximations made by Bardeen in this attempt at a solution of the Hartree-Fock problem are briefly reviewed in order to contrast with the present work.

Holomorphic Hartree-Fock Theory: The Nature of Two-Electron Problems.

PubMed

Burton, Hugh G A; Gross, Mark; Thom, Alex J W

2018-02-13

We explore the existence and behavior of holomorphic restricted Hartree-Fock (h-RHF) solutions for two-electron problems. Through algebraic geometry, the exact number of solutions with n basis functions is rigorously identified as 1 / 2 (3 n - 1), proving that states must exist for all molecular geometries. A detailed study on the h-RHF states of HZ (STO-3G) then demonstrates both the conservation of holomorphic solutions as geometry or atomic charges are varied and the emergence of complex h-RHF solutions at coalescence points. Using catastrophe theory, the nature of these coalescence points is described, highlighting the influence of molecular symmetry. The h-RHF states of HHeH 2+ and HHeH (STO-3G) are then compared, illustrating the isomorphism between systems with two electrons and two electron holes. Finally, we explore the h-RHF states of ethene (STO-3G) by considering the π electrons as a two-electron problem and employ NOCI to identify a crossing of the lowest energy singlet and triplet states at the perpendicular geometry.

Vibrational spectroscopic investigation of p-, m- and o-nitrobenzonitrile by using Hartree-Fock and density functional theory

NASA Astrophysics Data System (ADS)

Sert, Y.; Ucun, F.

2013-08-01

In the present work, the theoretical vibrational spectra of p-, m- and o-nitrobenzonitrile molecules have been analyzed. The harmonic vibrational frequencies and geometric parameters (bond lengths and bond angles) of these molecules have been calculated using ab initio Hartree-Fock and density functional theory methods with 6-311++G(d,p) basis set by Gaussian 03 W, for the first time. Assignments of the vibrational frequencies have been performed by potential energy distribution by using VEDA 4 program. The optimized geometric parameters and harmonic vibrational frequencies have been compared with the corresponding experimental data and seen to be in a good agreement with each other. Also, the highest occupied molecular orbital and lowest unoccupied molecular orbital energies have been obtained.

Toward a muon-specific electronic structure theory: effective electronic Hartree-Fock equations for muonic molecules.

PubMed

Rayka, Milad; Goli, Mohammad; Shahbazian, Shant

2018-02-07

An effective set of Hartree-Fock (HF) equations are derived for electrons of muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator, which are completely equivalent to the usual two-component HF equations used to derive stationary states of the muonic molecules. In these effective equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and the electrons effectively and is optimized during the self-consistent field cycles. While in the two-component HF equations a muon is treated as a quantum particle, in the effective HF equations it is absorbed into the effective potential and practically transformed into an effective potential field experienced by electrons. The explicit form of the effective potential depends on the nature of muon's vibrations and is derivable from the basis set used to expand the muonic spatial orbital. The resulting effective Hartree-Fock equations are implemented computationally and used successfully, as a proof of concept, in a series of muonic molecules containing all atoms from the second and third rows of the Periodic Table. To solve the algebraic version of the equations muon-specific Gaussian basis sets are designed for both muon and surrounding electrons and it is demonstrated that the optimized exponents are quite distinct from those derived for the hydrogen isotopes. The developed effective HF theory is quite general and in principle can be used for any muonic system while it is the starting point for a general effective electronic structure theory that incorporates various types of quantum correlations into the muonic systems beyond the HF equations.

Construction of the Fock Matrix on a Grid-Based Molecular Orbital Basis Using GPGPUs.

PubMed

Losilla, Sergio A; Watson, Mark A; Aspuru-Guzik, Alán; Sundholm, Dage

2015-05-12

We present a GPGPU implementation of the construction of the Fock matrix in the molecular orbital basis using the fully numerical, grid-based bubbles representation. For a test set of molecules containing up to 90 electrons, the total Hartree-Fock energies obtained from reference GTO-based calculations are reproduced within 10(-4) Eh to 10(-8) Eh for most of the molecules studied. Despite the very large number of arithmetic operations involved, the high performance obtained made the calculations possible on a single Nvidia Tesla K40 GPGPU card.

Linear-scaling method for calculating nuclear magnetic resonance chemical shifts using gauge-including atomic orbitals within Hartree-Fock and density-functional theory.

PubMed

Kussmann, Jörg; Ochsenfeld, Christian

2007-08-07

Details of a new density matrix-based formulation for calculating nuclear magnetic resonance chemical shifts at both Hartree-Fock and density functional theory levels are presented. For systems with a nonvanishing highest occupied molecular orbital-lowest unoccupied molecular orbital gap, the method allows us to reduce the asymptotic scaling order of the computational effort from cubic to linear, so that molecular systems with 1000 and more atoms can be tackled with today's computers. The key feature is a reformulation of the coupled-perturbed self-consistent field (CPSCF) theory in terms of the one-particle density matrix (D-CPSCF), which avoids entirely the use of canonical MOs. By means of a direct solution for the required perturbed density matrices and the adaptation of linear-scaling integral contraction schemes, the overall scaling of the computational effort is reduced to linear. A particular focus of our formulation is to ensure numerical stability when sparse-algebra routines are used to obtain an overall linear-scaling behavior.

Analytic energy gradient of projected Hartree-Fock within projection after variation

NASA Astrophysics Data System (ADS)

Uejima, Motoyuki; Ten-no, Seiichiro

2017-03-01

We develop a geometrical optimization technique for the projection-after-variation (PAV) scheme of the recently refined projected Hartree-Fock (PHF) as a fast alternative to the variation-after-projection (VAP) approach for optimizing the structures of molecules/clusters in symmetry-adapted electronic states at the mean-field computational cost. PHF handles the nondynamic correlation effects by restoring the symmetry of a broken-symmetry single reference wavefunction and moreover enables a black-box treatment of orbital selections. Using HF orbitals instead of PHF orbitals, our approach saves the computational cost for the orbital optimization, avoiding the convergence problem that sometimes emerges in the VAP scheme. We show that PAV-PHF provides geometries comparable to those of the complete active space self-consistent field and VAP-PHF for the tested systems, namely, CH2, O3, and the [Cu2O2 ] 2 + core, where nondynamic correlation is abundant. The proposed approach is useful for large systems mainly dominated by nondynamic correlation to find stable structures in many symmetry-adapted states.

Spin Hartree-Fock approach to studying quantum Heisenberg antiferromagnets in low dimensions

NASA Astrophysics Data System (ADS)

Werth, A.; Kopietz, P.; Tsyplyatyev, O.

2018-05-01

We construct a new mean-field theory for a quantum (spin-1/2) Heisenberg antiferromagnet in one (1D) and two (2D) dimensions using a Hartree-Fock decoupling of the four-point correlation functions. We show that the solution to the self-consistency equations based on two-point correlation functions does not produce any unphysical finite-temperature phase transition, in accord with the Mermin-Wagner theorem, unlike the common approach based on the mean-field equation for the order parameter. The next-neighbor spin-spin correlation functions, calculated within this approach, reproduce closely the strong renormalization by quantum fluctuations obtained via a Bethe ansatz in 1D and a small renormalization of the classical antiferromagnetic state in 2D. The heat capacity approximates with reasonable accuracy the full Bethe ansatz result at all temperatures in 1D. In 2D, we obtain a reduction of the peak height in the heat capacity at a finite temperature that is accessible by high-order 1 /T expansions.

Quantum treatment of protons with the reduced explicitly correlated Hartree-Fock approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sirjoosingh, Andrew; Pak, Michael V.; Brorsen, Kurt R.

2015-06-07

The nuclear-electronic orbital (NEO) approach treats select nuclei quantum mechanically on the same level as the electrons and includes nonadiabatic effects between the electrons and the quantum nuclei. The practical implementation of this approach is challenging due to the significance of electron-nucleus dynamical correlation. Herein, we present a general extension of the previously developed reduced NEO explicitly correlated Hartree-Fock (RXCHF) approach, in which only select electronic orbitals are explicitly correlated to each quantum nuclear orbital via Gaussian-type geminal functions. Approximations of the electronic exchange between the geminal-coupled electronic orbitals and the other electronic orbitals are also explored. This general approachmore » enables computationally tractable yet accurate calculations on molecular systems with quantum protons. The RXCHF method is applied to the hydrogen cyanide (HCN) and FHF{sup −} systems, where the proton and all electrons are treated quantum mechanically. For the HCN system, only the two electronic orbitals associated with the CH covalent bond are geminal-coupled to the proton orbital. For the FHF{sup −} system, only the four electronic orbitals associated with the two FH covalent bonds are geminal-coupled to the proton orbital. For both systems, the RXCHF method produces qualitatively accurate nuclear densities, in contrast to mean field-based NEO approaches. The development and implementation of the RXCHF method provide the framework to perform calculations on systems such as proton-coupled electron transfer reactions, where electron-proton nonadiabatic effects are important.« less

An efficient implementation of semi-numerical computation of the Hartree-Fock exchange on the Intel Phi processor

NASA Astrophysics Data System (ADS)

Liu, Fenglai; Kong, Jing

2018-07-01

Unique technical challenges and their solutions for implementing semi-numerical Hartree-Fock exchange on the Phil Processor are discussed, especially concerning the single- instruction-multiple-data type of processing and small cache size. Benchmark calculations on a series of buckyball molecules with various Gaussian basis sets on a Phi processor and a six-core CPU show that the Phi processor provides as much as 12 times of speedup with large basis sets compared with the conventional four-center electron repulsion integration approach performed on the CPU. The accuracy of the semi-numerical scheme is also evaluated and found to be comparable to that of the resolution-of-identity approach.

Molecular structure and vibrational spectra of three substituted 4-thioflavones by density functional theory and ab initio Hartree-Fock calculations

NASA Astrophysics Data System (ADS)

Li, Xiao-Hong; Liu, Xiang-Ru; Zhang, Xian-Zhou

2011-01-01

The vibrational frequencies of three substituted 4-thioflavones in the ground state have been calculated using the Hartree-Fock and density functional method (B3LYP) with 6-31G* and 6-31+G** basis sets. The structural analysis shows that there exists H-bonding in the selected compounds and the hydrogen bond lengths increase with the augment of the conjugate parameters of the substituent group on the benzene ring. A complete vibrational assignment aided by the theoretical harmonic wavenumber analysis was proposed. The theoretical spectrograms for FT-IR spectra of the title compounds have been constructed. In addition, it is noted that the selected compounds show significant activity against Shigella flexniri. Several electronic properties and thermodynamic parameters were also calculated.

A Fortran 90 Hartree-Fock program for one-dimensional periodic π-conjugated systems using Pariser-Parr-Pople model

NASA Astrophysics Data System (ADS)

Kondayya, Gundra; Shukla, Alok

2012-03-01

Pariser-Parr-Pople (P-P-P) model Hamiltonian is employed frequently to study the electronic structure and optical properties of π-conjugated systems. In this paper we describe a Fortran 90 computer program which uses the P-P-P model Hamiltonian to solve the Hartree-Fock (HF) equation for infinitely long, one-dimensional, periodic, π-electron systems. The code is capable of computing the band structure, as also the linear optical absorption spectrum, by using the tight-binding and the HF methods. Furthermore, using our program the user can solve the HF equation in the presence of a finite external electric field, thereby, allowing the simulation of gated systems. We apply our code to compute various properties of polymers such as trans-polyacetylene, poly- para-phenylene, and armchair and zigzag graphene nanoribbons, in the infinite length limit. Program summaryProgram title: ppp_bulk.x Catalogue identifier: AEKW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 87 464 No. of bytes in distributed program, including test data, etc.: 2 046 933 Distribution format: tar.gz Programming language: Fortran 90 Computer: PCs and workstations Operating system: Linux, Code was developed and tested on various recent versions of 64-bit Fedora including Fedora 14 (kernel version 2.6.35.12-90). Classification: 7.3 External routines: This program needs to link with LAPACK/BLAS libraries compiled with the same compiler as the program. For the Intel Fortran Compiler we used the ACML library version 4.4.0, while for the gfortran compiler we used the libraries supplied with the Fedora distribution. Nature of problem: The electronic structure of one-dimensional periodic π-conjugated systems is an intense area of research at

Nuclear Pasta at Finite Temperature with the Time-Dependent Hartree-Fock Approach

NASA Astrophysics Data System (ADS)

Schuetrumpf, B.; Klatt, M. A.; Iida, K.; Maruhn, J. A.; Mecke, K.; Reinhard, P.-G.

2016-01-01

We present simulations of neutron-rich matter at sub-nuclear densities, like supernova matter. With the time-dependent Hartree-Fock approximation we can study the evolution of the system at temperatures of several MeV employing a full Skyrme interaction in a periodic three-dimensional grid [1]. The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. The matter evolves into spherical, rod-like, connected rod-like and slab-like shapes. Further we observe gyroid-like structures, discussed e.g. in [2], which are formed spontaneously choosing a certain value of the simulation box length. The ρ-T-map of pasta shapes is basically consistent with the phase diagrams obtained from QMD calculations [3]. By an improved topological analysis based on Minkowski functionals [4], all observed pasta shapes can be uniquely identified by only two valuations, namely the Euler characteristic and the integral mean curvature. In addition we propose the variance in the cell-density distribution as a measure to distinguish pasta matter from uniform matter.

Ab initio Bogoliubov coupled cluster theory for open-shell nuclei

DOE PAGES

Signoracci, Angelo J.; Duguet, Thomas; Hagen, Gaute; ...

2015-06-29

relatively constant for all five nuclei, in both the Hartree-Fock-Bogoliubov and BCCD approximations. Conclusions: The newly developed many-body formalism increases the potential span of ab initio calculations based on single-reference coupled cluster techniques tremendously, i.e., potentially to reach several hundred additional midmass nuclei. The new formalism offers a wealth of potential applications and further extensions dedicated to the description of ground and excited states of open-shell nuclei. Short-term goals include the implementation of three-nucleon forces at the normal-ordered two-body level. Midterm extensions include the approximate treatment of triples corrections and the development of the equation-of-motion methodology to treat both excited states and odd nuclei. Long-term extensions include exact restoration of U(1) and SU(2) symmetries.« less

A Hartree-Fock Application Using UPC++ and the New DArray Library

DOE PAGES

Ozog, David; Kamil, Amir; Zheng, Yili; ...

2016-07-21

The Hartree-Fock (HF) method is the fundamental first step for incorporating quantum mechanics into many-electron simulations of atoms and molecules, and it is an important component of computational chemistry toolkits like NWChem. The GTFock code is an HF implementation that, while it does not have all the features in NWChem, represents crucial algorithmic advances that reduce communication and improve load balance by doing an up-front static partitioning of tasks, followed by work stealing whenever necessary. To enable innovations in algorithms and exploit next generation exascale systems, it is crucial to support quantum chemistry codes using expressive and convenient programming modelsmore » and runtime systems that are also efficient and scalable. Here, this paper presents an HF implementation similar to GTFock using UPC++, a partitioned global address space model that includes flexible communication, asynchronous remote computation, and a powerful multidimensional array library. UPC++ offers runtime features that are useful for HF such as active messages, a rich calculus for array operations, hardware-supported fetch-and-add, and functions for ensuring asynchronous runtime progress. We present a new distributed array abstraction, DArray, that is convenient for the kinds of random-access array updates and linear algebra operations on block-distributed arrays with irregular data ownership. Finally, we analyze the performance of atomic fetch-and-add operations (relevant for load balancing) and runtime attentiveness, then compare various techniques and optimizations for each. Our optimized implementation of HF using UPC++ and the DArrays library shows up to 20% improvement over GTFock with Global Arrays at scales up to 24,000 cores.« less

A Hartree-Fock Application Using UPC++ and the New DArray Library

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ozog, David; Kamil, Amir; Zheng, Yili

The Hartree-Fock (HF) method is the fundamental first step for incorporating quantum mechanics into many-electron simulations of atoms and molecules, and it is an important component of computational chemistry toolkits like NWChem. The GTFock code is an HF implementation that, while it does not have all the features in NWChem, represents crucial algorithmic advances that reduce communication and improve load balance by doing an up-front static partitioning of tasks, followed by work stealing whenever necessary. To enable innovations in algorithms and exploit next generation exascale systems, it is crucial to support quantum chemistry codes using expressive and convenient programming modelsmore » and runtime systems that are also efficient and scalable. Here, this paper presents an HF implementation similar to GTFock using UPC++, a partitioned global address space model that includes flexible communication, asynchronous remote computation, and a powerful multidimensional array library. UPC++ offers runtime features that are useful for HF such as active messages, a rich calculus for array operations, hardware-supported fetch-and-add, and functions for ensuring asynchronous runtime progress. We present a new distributed array abstraction, DArray, that is convenient for the kinds of random-access array updates and linear algebra operations on block-distributed arrays with irregular data ownership. Finally, we analyze the performance of atomic fetch-and-add operations (relevant for load balancing) and runtime attentiveness, then compare various techniques and optimizations for each. Our optimized implementation of HF using UPC++ and the DArrays library shows up to 20% improvement over GTFock with Global Arrays at scales up to 24,000 cores.« less

Neutral-atom electron binding energies from relaxed-orbital relativistic Hartree-Fock-Slater calculations for Z between 2 and 106

NASA Technical Reports Server (NTRS)

Huang, K.-N.; Aoyagi, M.; Mark, H.; Chen, M. H.; Crasemann, B.

1976-01-01

Electron binding energies in neutral atoms have been calculated relativistically, with the requirement of complete relaxation. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order correction to the local approximation was thus included. Quantum-electrodynamic corrections were made. For all elements with atomic numbers ranging from 2 to 106, the following quantities are listed: total energies, electron kinetic energies, electron-nucleus potential energies, electron-electron potential energies consisting of electrostatic and Breit interaction (magnetic and retardation) terms, and vacuum polarization energies. Binding energies including relaxation are listed for all electrons in all atoms over the indicated range of atomic numbers. A self-energy correction is included for the 1s, 2s, and 2p(1/2) levels. Results for selected atoms are compared with energies calculated by other methods and with experimental values.

Many-body expansion of the Fock matrix in the fragment molecular orbital method

NASA Astrophysics Data System (ADS)

Fedorov, Dmitri G.; Kitaura, Kazuo

2017-09-01

A many-body expansion of the Fock matrix in the fragment molecular orbital method is derived up to three-body terms for restricted Hartree-Fock and density functional theory in the atomic orbital basis and compared to the expansion in the basis of fragment molecular orbitals (MOs). The physical nature of many-body corrections is revealed in terms of charge transfer terms. An improvement of the fragment MO expansion is proposed by adding exchange to the embedding. The accuracy of all developed methods is demonstrated in comparison to unfragmented results for polyalanines, a water cluster, Trp-cage (PDB: 1L2Y) and crambin (PDB: 1CRN) proteins, a zeolite cluster, a Si nano-wire, and a boron nitride ribbon. The physical nature of metallicity is discussed, and it is shown what kinds of metallic systems can be treated by fragment-based methods. The density of states is calculated for a fully closed and a partially open nano-ring of boron nitride with a diameter of 105 nm.

A single-electron picture based on the multiconfiguration time-dependent Hartree-Fock method: application to the anisotropic ionization and subsequent high-harmonic generation of the CO molecule

NASA Astrophysics Data System (ADS)

Ohmura, S.; Kato, T.; Oyamada, T.; Koseki, S.; Ohmura, H.; Kono, H.

2018-02-01

The mechanisms of anisotropic near-IR tunnel ionization and high-order harmonic generation (HHG) in a CO molecule are theoretically investigated by using the multiconfiguration time-dependent Hartree-Fock (MCTDHF) method developed for the simulation of multielectron dynamics of molecules. The multielectron dynamics obtained by numerically solving the equations of motion (EOMs) in the MCTDHF method is converted to a single orbital picture in the natural orbital representation where the first-order reduced density matrix is diagonalized. The ionization through each natural orbital is examined and the process of HHG is classified into different optical paths designated by a combinations of initial, intermediate and final natural orbitals. The EOMs for natural spin-orbitals are also derived within the framework of the MCTDHF, which maintains the first-order reduced density matrix to be a diagonal one throughout the time propagation of a many-electron wave function. The orbital dependent, time-dependent effective potentials that govern the dynamics of respective time-dependent natural orbitals are deduced from the derived EOMs, of which the temporal variation can be used to interpret the motion of the electron density associated with each natural spin-orbital. The roles of the orbital shape, multiorbital ionization, linear Stark effect and multielectron interaction in the ionization and HHG of a CO molecule are revealed by the effective potentials obtained. When the laser electric field points to the nucleus O from C, tunnel ionization from the C atom side is enhanced; a hump structure originating from multielectron interaction is then formed on the top of the field-induced distorted barrier of the HOMO effective potential. This hump formation, responsible for the directional anisotropy of tunnel ionization, restrains the influence of the linear Stark effect on the energy shifts of bound states.

Hartree-Fock treatment of Fermi polarons using the Lee-Low-Pine transformation

NASA Astrophysics Data System (ADS)

Kain, Ben; Ling, Hong Y.

2017-09-01

We consider the Fermi polaron problem at zero temperature, where a single impurity interacts with noninteracting host fermions. We approach the problem starting with a Fröhlich-like Hamiltonian where the impurity is described with canonical position and momentum operators. We apply the Lee-Low-Pine (LLP) transformation to change the fermionic Fröhlich Hamiltonian into the fermionic LLP Hamiltonian, which describes a many-body system containing host fermions only. We adapt the self-consistent Hartree-Fock (HF) approach, first proposed by Edwards, to the fermionic LLP Hamiltonian in which a pair of host fermions with momenta k and k' interact with a potential proportional to k .k' . We apply the HF theory, which has the advantage of not restricting the number of particle-hole pairs, to repulsive Fermi polarons in one dimension. When the impurity and host fermion masses are equal our variational ansatz, where HF orbitals are expanded in terms of free-particle states, produces results in excellent agreement with McGuire's exact analytical results based on the Bethe ansatz. This work raises the prospect of using the HF ansatz and its time-dependent generalization as building blocks for developing all-coupling theories for both equilibrium and nonequilibrium Fermi polarons in higher dimensions.

Dispersion corrected hartree-fock and density functional theory for organic crystal structure prediction.

PubMed

Brandenburg, Jan Gerit; Grimme, Stefan

2014-01-01

We present and evaluate dispersion corrected Hartree-Fock (HF) and Density Functional Theory (DFT) based quantum chemical methods for organic crystal structure prediction. The necessity of correcting for missing long-range electron correlation, also known as van der Waals (vdW) interaction, is pointed out and some methodological issues such as inclusion of three-body dispersion terms are discussed. One of the most efficient and widely used methods is the semi-classical dispersion correction D3. Its applicability for the calculation of sublimation energies is investigated for the benchmark set X23 consisting of 23 small organic crystals. For PBE-D3 the mean absolute deviation (MAD) is below the estimated experimental uncertainty of 1.3 kcal/mol. For two larger π-systems, the equilibrium crystal geometry is investigated and very good agreement with experimental data is found. Since these calculations are carried out with huge plane-wave basis sets they are rather time consuming and routinely applicable only to systems with less than about 200 atoms in the unit cell. Aiming at crystal structure prediction, which involves screening of many structures, a pre-sorting with faster methods is mandatory. Small, atom-centered basis sets can speed up the computation significantly but they suffer greatly from basis set errors. We present the recently developed geometrical counterpoise correction gCP. It is a fast semi-empirical method which corrects for most of the inter- and intramolecular basis set superposition error. For HF calculations with nearly minimal basis sets, we additionally correct for short-range basis incompleteness. We combine all three terms in the HF-3c denoted scheme which performs very well for the X23 sublimation energies with an MAD of only 1.5 kcal/mol, which is close to the huge basis set DFT-D3 result.

Spiral magnetism in the single-band Hubbard model: the Hartree-Fock and slave-boson approaches.

PubMed

Igoshev, P A; Timirgazin, M A; Gilmutdinov, V F; Arzhnikov, A K; Irkhin, V Yu

2015-11-11

The ground-state magnetic phase diagram is investigated within the single-band Hubbard model for square and different cubic lattices. The results of employing the generalized non-correlated mean-field (Hartree-Fock) approximation and generalized slave-boson approach by Kotliar and Ruckenstein with correlation effects included are compared. We take into account commensurate ferromagnetic, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often lacking in previous investigations. It is found that the spiral states and especially ferromagnetism are generally strongly suppressed up to non-realistically large Hubbard U by the correlation effects if nesting is absent and van Hove singularities are well away from the paramagnetic phase Fermi level. The magnetic phase separation plays an important role in the formation of magnetic states, the corresponding phase regions being especially wide in the vicinity of half-filling. The details of non-collinear and collinear magnetic ordering for different cubic lattices are discussed.

Ab initio study of MF2 (M=Mn, Fe, Co, Ni) rutile-type compounds using the periodic unrestricted Hartree-Fock approach

NASA Astrophysics Data System (ADS)

de P. R. Moreira, Ibério; Dovesi, Roberto; Roetti, Carla; Saunders, Victor R.; Orlando, Roberto

2000-09-01

The ab initio periodic unrestricted Hartree-Fock method has been applied in the investigation of the ground-state structural, electronic, and magnetic properties of the rutile-type compounds MF2 (M=Mn, Fe, Co, and Ni). All electron Gaussian basis sets have been used. The systems turn out to be large band-gap antiferromagnetic insulators; the optimized geometrical parameters are in good agreement with experiment. The calculated most stable electronic state shows an antiferromagnetic order in agreement with that resulting from neutron scattering experiments. The magnetic coupling constants between nearest-neighbor magnetic ions along the [001], [111], and [100] (or [010]) directions have been calculated using several supercells. The resulting ab initio magnetic coupling constants are reasonably satisfactory when compared with available experimental data. The importance of the Jahn-Teller effect in FeF2 and CoF2 is also discussed.

Bubble nuclei within the self-consistent Hartree-Fock mean field plus pairing approach

NASA Astrophysics Data System (ADS)

Phuc, L. Tan; Hung, N. Quang; Dang, N. Dinh

2018-02-01

The depletion of the nuclear density at its center, called the nuclear bubble, is studied within the Skyrme Hartree-Fock mean field consistently incorporating the superfluid pairing. The latter is obtained within the finite-temperature Bardeen-Cooper-Schrieffer theory and within the approach using the exact pairing. The numerical calculations are carried out for 22O and 34Si nuclei, whose bubble structures, caused by a very low occupancy of the 2 s1 /2 level, were previously predicted at T =0 . Among 24 Skyrme interactions under consideration, the MSk3 is the only one which reproduces the experimentally measured occupancy of the 2 s1 /2 proton level as well as the binding energy, and consequently produces the most pronounced bubble structure in 34Si. As compared to the approaches employing the same BSk14 interaction, our approach with exact pairing predicts a pairing effect which is stronger in 22O and weaker in 34Si. The increase in temperature depletes the bubble structure and completely washes it out when the temperature reaches a critical value, at which the factor measuring the depletion of the nucleon density vanishes.

Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.. (VI) HFODD (v2.40h): A new version of the program

NASA Astrophysics Data System (ADS)

Dobaczewski, J.; Satuła, W.; Carlsson, B. G.; Engel, J.; Olbratowski, P.; Powałowski, P.; Sadziak, M.; Sarich, J.; Schunck, N.; Staszczak, A.; Stoitsov, M.; Zalewski, M.; Zduńczuk, H.

2009-11-01

We describe the new version (v2.40h) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented: (i) projection on good angular momentum (for the Hartree-Fock states), (ii) calculation of the GCM kernels, (iii) calculation of matrix elements of the Yukawa interaction, (iv) the BCS solutions for state-dependent pairing gaps, (v) the HFB solutions for broken simplex symmetry, (vi) calculation of Bohr deformation parameters, (vii) constraints on the Schiff moments and scalar multipole moments, (viii) the DT2h transformations and rotations of wave functions, (ix) quasiparticle blocking for the HFB solutions in odd and odd-odd nuclei, (x) the Broyden method to accelerate the convergence, (xi) the Lipkin-Nogami method to treat pairing correlations, (xii) the exact Coulomb exchange term, (xiii) several utility options, and we have corrected three insignificant errors. New version program summaryProgram title: HFODD (v2.40h) Catalogue identifier: ADFL_v2_2 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v2_2.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 79 618 No. of bytes in distributed program, including test data, etc.: 372 548 Distribution format: tar.gz Programming language: FORTRAN-77 and Fortran-90 Computer: Pentium-III, AMD-Athlon, AMD-Opteron Operating system: UNIX, LINUX, Windows XP Has the code been

Two-parameter partially correlated ground-state electron density of some light spherical atoms from Hartree-Fock theory with nonintegral nuclear charge

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cordero, Nicolas A.; March, Norman H.; Alonso, Julio A.

2007-05-15

Partially correlated ground-state electron densities for some spherical light atoms are calculated, into which nonrelativistic ionization potentials represent essential input data. The nuclear cusp condition of Kato is satisfied precisely. The basic theoretical starting point, however, is Hartree-Fock (HF) theory for the N electrons under consideration but with nonintegral nuclear charge Z{sup '} slightly different from the atomic number Z (=N). This HF density is scaled with a parameter {lambda}, near to unity, to preserve normalization. Finally, some tests are performed on the densities for the atoms Ne and Ar, as well as for Be and Mg.

Roothaan-Hartree-Fock ground-state atomic wave functions: Slater-type orbital expansions and expectation values for Z = 2-54

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bunge, C.F.; Barrientos, J.A.; Bunge, A.V.

1993-01-01

Roothaan-Hartree-Fock orbitals expressed in a Slater-type basis are reported for the ground states of He through Xe. Energy accuracy ranges between 8 and 10 significant figures, reducing by between 21 and 2,770 times the energy errors of the previous such compilation (E. Clementi and C. Roetti, Atomic Data and Nuclear Data Tables 14, 177, 1974). For each atom, the total energy, kinetic energy, potential energy, virial ratio, electron density at the nucleus, and the Kato cusp are given together with radial expectation values [l angle]r[sup n][r angle] with n from [minus]3 to 2 for each orbital, orbital energies, and orbitalmore » expansion coefficients. 29 refs., 1 tab.« less

Application of the top-on-top model to 135Pr

NASA Astrophysics Data System (ADS)

Sugawara-Tanabe, Kazuko; Tanabe, Kosai

2017-09-01

It is proved that the Holstein-Primakoff (HP) boson expansion method is very effective for a case where both total and single-particle angular momenta have the diagonal representation along the same direction. The algebraic solution is described by two kinds of quantum numbers classifying the rotational band’s characteristic of the particle-rotor model. One is related with the wobbling motion of the rotor, and the other to the precession of the single-particle angular momentum. Employing angular-momentum dependent rigid (rig) moments of inertia (MoI), which simulate Coriolis anti-pairing effect based on the constrained self-consistent Hartree-Fock-Bogoliubov (HFB) equation, we obtain good fitting not only to the energy-level scheme, but also to the electromagnetic transition rates and the mixing ratio for 135Pr.

Hartree-Fock implementation using a Laguerre-based wave function for the ground state and correlation energies of two-electron atoms.

PubMed

King, Andrew W; Baskerville, Adam L; Cox, Hazel

2018-03-13

An implementation of the Hartree-Fock (HF) method using a Laguerre-based wave function is described and used to accurately study the ground state of two-electron atoms in the fixed nucleus approximation, and by comparison with fully correlated (FC) energies, used to determine accurate electron correlation energies. A variational parameter A is included in the wave function and is shown to rapidly increase the convergence of the energy. The one-electron integrals are solved by series solution and an analytical form is found for the two-electron integrals. This methodology is used to produce accurate wave functions, energies and expectation values for the helium isoelectronic sequence, including at low nuclear charge just prior to electron detachment. Additionally, the critical nuclear charge for binding two electrons within the HF approach is calculated and determined to be Z HF C =1.031 177 528.This article is part of the theme issue 'Modern theoretical chemistry'. © 2018 The Author(s).

Development of the Nuclear-Electronic Orbital Approach and Applications to Ionic Liquids and Tunneling Processes

DTIC Science & Technology

2010-02-24

electronic Schrodinger equation . In previous grant cycles, we implemented the NEO approach at the Hartree-Fock (NEO-HF),13 configuration interaction...electronic and nuclear molecular orbitals. The resulting electronic and nuclear Hartree-Fock-Roothaan equations are solved iteratively until self...directly into the standard Hartree- Fock-Roothaan equations , which are solved iteratively to self-consistency. The density matrix representation

A Fock space representation for the quantum Lorentz gas

NASA Astrophysics Data System (ADS)

Maassen, H.; Tip, A.

1995-02-01

A Fock space representation is given for the quantum Lorentz gas, i.e., for random Schrödinger operators of the form H(ω)=p2+Vω=p2+∑ φ(x-xj(ω)), acting in H=L2(Rd), with Poisson distributed xjs. An operator H is defined in K=H⊗P=H⊗L2(Ω,P(dω))=L2(Ω,P(dω);H) by the action of H(ω) on its fibers in a direct integral decomposition. The stationarity of the Poisson process allows a unitarily equivalent description in terms of a new family {H(k)||k∈Rd}, where each H(k) acts in P [A. Tip, J. Math. Phys. 35, 113 (1994)]. The space P is then unitarily mapped upon the symmetric Fock space over L2(Rd,ρdx), with ρ the intensity of the Poisson process (the average number of points xj per unit volume; the scatterer density), and the equivalent of H(k) is determined. Averages now become vacuum expectation values and a further unitary transformation (removing ρ in ρdx) is made which leaves the former invariant. The resulting operator HF(k) has an interesting structure: On the nth Fock layer we encounter a single particle moving in the field of n scatterers and the randomness now appears in the coefficient √ρ in a coupling term connecting neighboring Fock layers. We also give a simple direct self-adjointness proof for HF(k), based upon Nelson's commutator theorem. Restriction to a finite number of layers (a kind of low scatterer density approximation) still gives nontrivial results, as is demonstrated by considering an example.

The molecular structure and vibrational spectra of N-(2,2-diphenylacetyl)- N'-(naphthalen-1yl)-thiourea by Hartree-Fock and density functional methods

NASA Astrophysics Data System (ADS)

Arslan, Hakan; Mansuroglu, Demet Sezgin; VanDerveer, Don; Binzet, Gun

2009-04-01

N-(2,2-Diphenylacetyl)- N'-(naphthalen-1yl)-thiourea (PANT) has been synthesized and characterized by elemental analysis, IR spectroscopy and 1H NMR spectroscopy. The crystal and molecular structure of the title compound has been determined from single crystal X-ray diffraction data. It crystallizes in the triclinic space group P-1, Z = 2 with a = 10.284(2) Å, b = 10.790(2) Å, c = 11.305(2) Å, α = 64.92(3)°, β = 89.88(3)°, γ = 62.99(3)°, V = 983.7(3) Å 3 and Dcalc = 1.339 Mg/m 3. The molecular structure, vibrational frequencies and infrared intensities of PANT were calculated by the Hartree-Fock and density functional theory methods (BLYP and B3LYP) using the 6-31G* basis set. The calculated geometric parameters were compared to the corresponding X-ray structure of the title compound. We obtained 22 stable conformers for the title compound; however Conformer 1 is approximately 9.53 kcal/mol more stable than Conformer 22. The comparison of the theoretical and experimental geometry of the title compound shows that the X-ray parameters fairly well reproduce the geometry of Conformer 17. The harmonic vibrations computed for this compound by the B3LYP/6-31G* method are in good agreement with the observed IR spectral data. Theoretical vibrational spectra of the title compound were interpreted by means of PEDs using the VEDA 4 program. A general better performance of the investigated methods was calculated by PAVF 1.0 program.

Orbital dependent functionals: An atom projector augmented wave method implementation

NASA Astrophysics Data System (ADS)

Xu, Xiao

This thesis explores the formulation and numerical implementation of orbital dependent exchange-correlation functionals within electronic structure calculations. These orbital-dependent exchange-correlation functionals have recently received renewed attention as a means to improve the physical representation of electron interactions within electronic structure calculations. In particular, electron self-interaction terms can be avoided. In this thesis, an orbital-dependent functional is considered in the context of Hartree-Fock (HF) theory as well as the Optimized Effective Potential (OEP) method and the approximate OEP method developed by Krieger, Li, and Iafrate, known as the KLI approximation. In this thesis, the Fock exchange term is used as a simple well-defined example of an orbital-dependent functional. The Projected Augmented Wave (PAW) method developed by P. E. Blochl has proven to be accurate and efficient for electronic structure calculations for local and semi-local functions because of its accurate evaluation of interaction integrals by controlling multiple moments. We have extended the PAW method to treat orbital-dependent functionals in Hartree-Fock theory and the Optimized Effective Potential method, particularly in the KLI approximation. In the course of study we develop a frozen-core orbital approximation that accurately treats the core electron contributions for above three methods. The main part of the thesis focuses on the treatment of spherical atoms. We have investigated the behavior of PAW-Hartree Fock and PAW-KLI basis, projector, and pseudopotential functions for several elements throughout the periodic table. We have also extended the formalism to the treatment of solids in a plane wave basis and implemented PWPAW-KLI code, which will appear in future publications.

All-electron molecular Dirac-Hartree-Fock calculations - Properties of the group IV monoxides GeO, SnO, and PbO

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.

1993-01-01

Dirac-Hartree-Fock calculations have been carried out on the ground states of the group IV monoxides GeO, SnO and PbO. Geometries, dipole moments and infrared data are presented. For comparison, nonrelativistic, first-order perturbation and relativistic effective core potential calculations have also been carried out. Where appropriate the results are compared with the experimental data and previous calculations. Spin-orbit effects are of great importance for PbO, where first-order perturbation theory including only the mass-velocity and Darwin terms is inadequate to predict the relativistic corrections to the properties. The relativistic effective core potential results show a larger deviation from the all-electron values than for the hydrides, and confirm the conclusions drawn on the basis of the hydride calculations.

All-electron molecular Dirac-Hartree-Fock calculations: Properties of the group IV monoxides GeO, SnO and PbO

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.

1991-01-01

Dirac-Hartree-Fock calculations have been carried out on the ground states of the group IV monoxides GeO, SnO and PbO. Geometries, dipole moments and infrared data are presented. For comparison, nonrelativistic, first-order perturbation and relativistic effective core potential calculations have also been carried out. Where appropriate the results are compared with the experimental data and previous calculations. Spin-orbit effects are of great importance for PbO, where first-order perturbation theory including only the mass-velocity and Darwin terms is inadequate to predict the relativistic corrections to the properties. The relativistic effective core potential results show a larger deviation from the all-electron values than for the hydrides, and confirm the conclusions drawn on the basis of the hydride calculations.

Microscopic optical model potential based on a Dirac Brueckner Hartree Fock approach and the relevant uncertainty analysis

NASA Astrophysics Data System (ADS)

Xu, Ruirui; Ma, Zhongyu; Muether, Herbert; van Dalen, E. N. E.; Liu, Tinjin; Zhang, Yue; Zhang, Zhi; Tian, Yuan

2017-09-01

A relativistic microscopic optical model potential, named CTOM, for nucleon-nucleus scattering is investigated in the framework of Dirac-Brueckner-Hartree-Fock approach. The microscopic feature of CTOM is guaranteed through rigorously adopting the isospin dependent DBHF calculation within the subtracted T matrix scheme. In order to verify its prediction power, a global study n, p+ A scattering are carried out. The predicted scattering observables coincide with experimental data within a good accuracy over a broad range of targets and a large region of energies only with two free items, namely the free-range factor t in the applied improved local density approximation and minor adjustments of the scalar and vector potentials in the low-density region. In addition, to estimate the uncertainty of the theoretical results, the deterministic simple least square approach is preliminarily employed to derive the covariance of predicted angular distributions, which is also briefly contained in this paper.

Stopping power and range calculations in human tissues by using the Hartree-Fock-Roothaan wave functions

NASA Astrophysics Data System (ADS)

Usta, Metin; Tufan, Mustafa Çağatay

2017-11-01

The object of this work is to present the consequences for the stopping power and range values of some human tissues at energies ranging from 1 MeV to 1 GeV and 1-500 MeV, respectively. The considered human tissues are lung, intestine, skin, larynx, breast, bladder, prostate and ovary. In this work, the stopping power is calculated by considering the number of velocity-dependent effective charge and effective mean excitation energies of the target material. We used the Hartree-Fock-Roothaan (HFR) atomic wave function to determine the charge density and the continuous slowing down approximation (CSDA) method for the calculation of the proton range. Electronic stopping power values of tissues results have been compared with the ICRU 44, 46 reports, SRIM, Janni and CasP data over the percent error rate. Range values relate to tissues have compared the range results with the SRIM, FLUKA and Geant4 data. For electronic stopping power results, ICRU, SRIM and Janni's data indicated the best fit with our values at 1-50, 50-250 MeV and 250 MeV-1 GeV, respectively. For range results, the best accordance with the calculated values have been found the SRIM data and the error level is less than 10% in proton therapy. However, greater 30% errors were observed in the 250 MeV and over energies.

Norm overlap between many-body states: Uncorrelated overlap between arbitrary Bogoliubov product states

NASA Astrophysics Data System (ADS)

Bally, B.; Duguet, T.

2018-02-01

-form expression allowing its computation without any phase ambiguity. The formula is physically intuitive, accurate, and versatile. It equally applies to norm overlaps between Bogoliubov states of even or odd number parity. Numerical applications illustrate these features and provide a transparent representation of the content of the norm overlaps. Conclusions: The complex norm overlap between arbitrary Bogoliubov states is computed, without any phase ambiguity, via elementary linear algebra operations. The method can be used in any configuration mixing of orthogonal and non-orthogonal product states. Furthermore, the closed-form expression extends naturally to correlated overlaps at play in PNR-BCC and PNR-BMBPT. As such, the straight overlap between Bogoliubov states is the zero-order reduction of more involved norm kernels to be studied in a forthcoming paper.

Assessing the role of Hartree-Fock exchange, correlation energy and long range corrections in evaluating ionization potential, and electron affinity in density functional theory.

PubMed

Vikramaditya, Talapunur; Lin, Shiang-Tai

2017-06-05

Accurate determination of ionization potentials (IPs), electron affinities (EAs), fundamental gaps (FGs), and HOMO, LUMO energy levels of organic molecules play an important role in modeling and predicting the efficiencies of organic photovoltaics, OLEDs etc. In this work, we investigate the effects of Hartree Fock (HF) Exchange, correlation energy, and long range corrections in predicting IP and EA in Hybrid Functionals. We observe increase in percentage of HF exchange results in increase of IPs and decrease in EAs. Contrary to the general expectations inclusion of both HF exchange and correlation energy (from the second order perturbation theory MP2) leads to poor prediction. Range separated Hybrid Functionals are found to be more reliable among various DFT Functionals investigated. DFT Functionals predict accurate IPs whereas post HF methods predict accurate EAs. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Effect of Hartree-Fock exact exchange on intramolecular magnetic coupling constants of organic diradicals

NASA Astrophysics Data System (ADS)

Cho, Daeheum; Ko, Kyoung Chul; Ikabata, Yasuhiro; Wakayama, Kazufumi; Yoshikawa, Takeshi; Nakai, Hiromi; Lee, Jin Yong

2015-01-01

The intramolecular magnetic coupling constant (J) of diradical systems linked with five- or six-membered aromatic rings was calculated to obtain the scaling factor (experimental J/calculated J ratio) for various density functional theory (DFT) functionals. Scaling factors of group A (PBE, TPSSh, B3LYP, B97-1, X3LYP, PBE0, and BH&HLYP) and B (M06-L, M06, M06-2X, and M06-HF) were shown to decrease as the amount of Hartree-Fock exact exchange (HFx) increases, in other words, overestimation of calculated J becomes more severe as the HFx increases. We further investigated the effect of HFx fraction of DFT functional on J value, spin contamination, and spin density distributions by comparing the B3LYP analogues containing different amount of HFx. It was revealed that spin contamination and spin densities at each atom increases as the HFx increases. Above all, newly developed BLYP-5 functional, which has 5% of HFx, was found to have the scaling factor of 1.029, indicating that calculated J values are very close to that of experimental values without scaling. BLYP-5 has potential to be utilized for accurate evaluation of intramolecular magnetic coupling constant (J) of diradicals linked by five- or six-membered aromatic ring couplers.

Effect of Hartree-Fock exact exchange on intramolecular magnetic coupling constants of organic diradicals.

PubMed

Cho, Daeheum; Ko, Kyoung Chul; Ikabata, Yasuhiro; Wakayama, Kazufumi; Yoshikawa, Takeshi; Nakai, Hiromi; Lee, Jin Yong

2015-01-14

The intramolecular magnetic coupling constant (J) of diradical systems linked with five- or six-membered aromatic rings was calculated to obtain the scaling factor (experimental J/calculated J ratio) for various density functional theory (DFT) functionals. Scaling factors of group A (PBE, TPSSh, B3LYP, B97-1, X3LYP, PBE0, and BH&HLYP) and B (M06-L, M06, M06-2X, and M06-HF) were shown to decrease as the amount of Hartree-Fock exact exchange (HFx) increases, in other words, overestimation of calculated J becomes more severe as the HFx increases. We further investigated the effect of HFx fraction of DFT functional on J value, spin contamination, and spin density distributions by comparing the B3LYP analogues containing different amount of HFx. It was revealed that spin contamination and spin densities at each atom increases as the HFx increases. Above all, newly developed BLYP-5 functional, which has 5% of HFx, was found to have the scaling factor of 1.029, indicating that calculated J values are very close to that of experimental values without scaling. BLYP-5 has potential to be utilized for accurate evaluation of intramolecular magnetic coupling constant (J) of diradicals linked by five- or six-membered aromatic ring couplers.

Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (III) HFBTHO (v3.00): A new version of the program

NASA Astrophysics Data System (ADS)

Perez, R. Navarro; Schunck, N.; Lasseri, R.-D.; Zhang, C.; Sarich, J.

2017-11-01

We describe the new version 3.00 of the code HFBTHO that solves the nuclear Hartree-Fock (HF) or Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle-hole and particle-particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck, (iv) the regularization of zero-range pairing forces, (v) the calculation of localization functions, (vi) a MPI interface for large-scale mass table calculations. Program Files doi:http://dx.doi.org/10.17632/c5g2f92by3.1 Licensing provisions: GPL v3 Programming language: FORTRAN-95 Journal reference of previous version: M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013). Does the new version supersede the previous one: Yes Summary of revisions: 1. the Gogny force in both particle-hole and particle-particle channels was implemented; 2. the nuclear collective inertia at the perturbative cranking approximation was implemented; 3. fission fragment charge, mass and deformations were implemented based on the determination of the position of the neck between nascent fragments; 4. the regularization method of zero-range pairing forces was implemented; 5. the localization functions of the HFB solution were implemented; 6. a MPI interface for large-scale mass table calculations was implemented. Nature of problem:HFBTHO is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the energy density functional (EDF) approach to atomic nuclei, where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton

Solution of the Skyrme Hartree Fock Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (V) HFODD(v2.08k)

NASA Astrophysics Data System (ADS)

Dobaczewski, J.; Olbratowski, P.

2005-05-01

-range interaction, allows for a simple implementation of pairing effects within the Hartree-Fock-Bogolyubov method. Solution method: The program uses the Cartesian harmonic-oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constrains are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in [J. Dobaczewski, J. Dudek, Comput. Phys. Comm. 102 (1997) 166]. Summary of revisions: 1. Incorrect value of the " t" force parameter for SLY5 has been corrected. 2. Opening of an empty file "FILREC" for IWRIRE=-1 has been removed. 3. Call to subroutine "OLSTOR" has been moved before that to "SPZERO". In this way, correct data transferred to "FLISIG", "FLISIM", "FLISIQ" or "FLISIZ" allow for a correct determination of the candidate states for diabatic blocking. These corrections pertain to the user interface of the code and do not affect results performed for forces other than SLY5. Restrictions on the complexity of the problem: The main restriction is the CPU time required for calculations of heavy deformed nuclei and for a given precision required. Pairing correlations are only included for even-even nuclei and conserved simplex symmetry. Unusual features: The user must have access to the NAGLIB subroutine F02AXE or to the LAPACK subroutines ZHPEV or ZHPEVX, which diagonalize complex Hermitian matrices, or provide another subroutine which can perform such a task. The LAPACK subroutines ZHPEV and ZHPEVX can be obtained from the Netlib Repository at University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/cgi-bin/netlibfiles.pl?filename=/lapack/complex16/zhpev.f and

The Dielectric Permittivity of Crystals in the Reduced Hartree-Fock Approximation

NASA Astrophysics Data System (ADS)

Cancès, Éric; Lewin, Mathieu

2010-07-01

In a recent article (Cancès et al. in Commun Math Phys 281:129-177, 2008), we have rigorously derived, by means of bulk limit arguments, a new variational model to describe the electronic ground state of insulating or semiconducting crystals in the presence of local defects. In this so-called reduced Hartree-Fock model, the ground state electronic density matrix is decomposed as {γ = γ^0_per + Q_{ν,\\varepsilon_F}}, where {γ^0_per} is the ground state density matrix of the host crystal and {Q_{ν,\\varepsilon_F}} the modification of the electronic density matrix generated by a modification ν of the nuclear charge of the host crystal, the Fermi level ɛ F being kept fixed. The purpose of the present article is twofold. First, we study in more detail the mathematical properties of the density matrix {Q_{ν,\\varepsilon_F}} (which is known to be a self-adjoint Hilbert-Schmidt operator on {L^2(mathbb{R}^3)}). We show in particular that if {int_{mathbb{R}^3} ν neq 0, Q_{ν,\\varepsilon_F}} is not trace-class. Moreover, the associated density of charge is not in {L^1(mathbb{R}^3)} if the crystal exhibits anisotropic dielectric properties. These results are obtained by analyzing, for a small defect ν, the linear and nonlinear terms of the resolvent expansion of {Q_{ν,\\varepsilon_F}}. Second, we show that, after an appropriate rescaling, the potential generated by the microscopic total charge (nuclear plus electronic contributions) of the crystal in the presence of the defect converges to a homogenized electrostatic potential solution to a Poisson equation involving the macroscopic dielectric permittivity of the crystal. This provides an alternative (and rigorous) derivation of the Adler-Wiser formula.

Interplay of quasiparticle-vibration coupling and pairing correlations on β-decay half-lives

NASA Astrophysics Data System (ADS)

Niu, Y. F.; Niu, Z. M.; Colò, G.; Vigezzi, E.

2018-05-01

The nuclear β-decay half-lives of Ni and Sn isotopes, around the closed shell nuclei 78Ni and 132Sn, are investigated by computing the distribution of the Gamow-Teller strength using the Quasiparticle Random Phase Approximation (QRPA) with quasiparticle-vibration coupling (QPVC), based on ground-state properties obtained by Hartree-Fock-Bogoliubov (HFB) calculations. We employ the effective interaction SkM* and a zero-range effective pairing force. The half-lives are strongly reduced by including the QPVC. We study in detail the effects of isovector (IV) and isoscalar (IS) pairing. Increasing the IV strength tends to increase the lifetime for nuclei in the proximity of, but lighter than, the closed-shell ones in QRPA calculations, while the effect is significantly reduced by taking into account the QPVC. On the contrary, the IS pairing mainly plays a role for nuclei after the shell closure. Increasing its strength decreases the half-lives, and the effect at QRPA and QRPA+QPVC level is comparable. The effect of IS pairing is particularly pronounced in the case of the Sn isotopes, where it turns out to be instrumental to obtain good agreement with experimental data.

The unrestricted Hartree-Fock self consistent field calculation for spin density wave state in metallic carbon nanotube

NASA Astrophysics Data System (ADS)

Kobayashi, Katsushi

1997-06-01

The possibility of a spin density wave (SDW) state in a metallic carbon nanotube (CN) and its electronic properties are investigated within the Hartree-Fock self consistent field (SCF) energy-band calculation. Two kinds of spatial SDW states are assumed in this study. Each assumed SDW on the wave function is constructed with the degenerate π orbital in the metallic CN system. The results calculated for the one SDW model of CN always have a relative stability (˜ 0.1 eV/cell) in SCF total energy compared with the original model in which no SDW is assumed. All the results calculated for another SDW model are completely equal to the original one. Moreover, in the energy dispersion of the former stable SDW model, the degenerate π level found in the original model disappears and the band gap (3-5 eV) occurs around at the Fermi level. The energetic stability and the band gap are also found in the π-electron band calculation within the Hubbard Hamiltonian.

Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (IV) HFODD (v2.08i): a new version of the program

NASA Astrophysics Data System (ADS)

Dobaczewski, J.; Olbratowski, P.

2004-04-01

an effective and fast solution of the self-consistent Hartree-Fock equations, even for heavy nuclei, and for various nucleonic (n-particle n-hole) configurations, deformations, excitation energies, or angular momenta. Similar Local Density Approximation in the particle-particle channel, which is equivalent to using a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree-Fock-Bogolyubov method. Method of solution: The program uses the Cartesian harmonic oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean field Hamiltonians or Routhians which depend non-linearly on the local neutron and proton densities. Suitable constraints are used to obtain states corresponding to a given configuration, deformation or angular momentum. The method of solution has been presented in: J. Dobaczewski, J. Dudek, Comput. Phys. Commun. 102 (1997) 166. Summary of revisions:Two insignificant errors have been corrected. Breaking of all the three plane-reflection symmetries has been implemented. Breaking of all the three time-reversal×plane-reflection symmetries has been implemented. Conservation of parity with simultaneously broken simplex has been implemented. Tilted-axis cranking has been implemented. Cranking with isovector angular frequency has been implemented. Quadratic constraint on tilted angular momentum has been added. Constraint on the vector product of angular frequency and angular momentum has been added. Calculation of surface multipole moments has been added. Constraints on surface multipole moments have been added. Calculation of magnetic moments has been added. Calculation of multipole and surface multipole moments in the center-of-mass reference frame has been added. Calculation of multipole, surface

Spinors in Hilbert Space

NASA Astrophysics Data System (ADS)

Plymen, Roger; Robinson, Paul

1995-01-01

Infinite-dimensional Clifford algebras and their Fock representations originated in the quantum mechanical study of electrons. In this book, the authors give a definitive account of the various Clifford algebras over a real Hilbert space and of their Fock representations. A careful consideration of the latter's transformation properties under Bogoliubov automorphisms leads to the restricted orthogonal group. From there, a study of inner Bogoliubov automorphisms enables the authors to construct infinite-dimensional spin groups. Apart from assuming a basic background in functional analysis and operator algebras, the presentation is self-contained with complete proofs, many of which offer a fresh perspective on the subject.

Combining density functional and incremental post-Hartree-Fock approaches for van der Waals dominated adsorbate-surface interactions: Ag{sub 2}/graphene

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lara-Castells, María Pilar de, E-mail: Pilar.deLara.Castells@csic.es; Mitrushchenkov, Alexander O.; Stoll, Hermann

2015-09-14

A combined density functional (DFT) and incremental post-Hartree-Fock (post-HF) approach, proven earlier to calculate He-surface potential energy surfaces [de Lara-Castells et al., J. Chem. Phys. 141, 151102 (2014)], is applied to describe the van der Waals dominated Ag{sub 2}/graphene interaction. It extends the dispersionless density functional theory developed by Pernal et al. [Phys. Rev. Lett. 103, 263201 (2009)] by including periodic boundary conditions while the dispersion is parametrized via the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)]. Starting with the elementary cluster unit of the target surface (benzene), continuing through the realistic cluster model (coronene), andmore » ending with the periodic model of the extended system, modern ab initio methodologies for intermolecular interactions as well as state-of-the-art van der Waals-corrected density functional-based approaches are put together both to assess the accuracy of the composite scheme and to better characterize the Ag{sub 2}/graphene interaction. The present work illustrates how the combination of DFT and post-HF perspectives may be efficient to design simple and reliable ab initio-based schemes in extended systems for surface science applications.« less

All-electron molecular Dirac-Hartree-Fock calculations - The group IV tetrahydrides CH4, SiH4, GeH4, SnH4, and PbH4

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.; Taylor, Peter R.; Faegri, Knut, Jr.; Partridge, Harry

1991-01-01

A basis-set-expansion Dirac-Hartree-Fock program for molecules is described. Bond lengths and harmonic frequencies are presented for the ground states of the group 4 tetrahydrides, CH4, SiH4, GeH4, SnH4, and PbH4. The results are compared with relativistic effective core potential (RECP) calculations, first-order perturbation theory (PT) calculations and with experimental data. The bond lengths are well predicted by first-order perturbation theory for all molecules, but none of the RECP's considered provides a consistent prediction. Perturbation theory overestimates the relativistic correction to the harmonic frequencies; the RECP calculations underestimate the correction.

All-electron molecular Dirac-Hartree-Fock calculations: The group 4 tetrahydrides CH4, SiH4, GeH4, SnH4 and PbH4

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.; Taylor, Peter R.; Faegri, Knut, Jr.; Partridge, Harry

1990-01-01

A basis-set-expansion Dirac-Hartree-Fock program for molecules is described. Bond lengths and harmonic frequencies are presented for the ground states of the group 4 tetrahydrides, CH4, SiH4, GeH4, SnH4, and PbH4. The results are compared with relativistic effective core potential (RECP) calculations, first-order perturbation theory (PT) calculations and with experimental data. The bond lengths are well predicted by first-order perturbation theory for all molecules, but non of the RECP's considered provides a consistent prediction. Perturbation theory overestimates the relativistic correction to the harmonic frequencies; the RECP calculations underestimate the correction.

Tensor force effect on the evolution of single-particle energies in some isotopic chains in the relativistic Hartree-Fock approximation

NASA Astrophysics Data System (ADS)

López-Quelle, M.; Marcos, S.; Niembro, R.; Savushkin, L. N.

2018-03-01

Within a nonlinear relativistic Hartree-Fock approximation combined with the BCS method, we study the effect of the nucleon-nucleon tensor force of the π-exchange potential on the spin- and pseudospin-orbit doublets along the Ca and Sn isotopic chains. We show how the self-consistent tensor force effect modifies the splitting of both kinds of doublets in an interdependent form, leading, quite generally, to opposite effects in the accomplishment of the spin and pseudospin symmetries (the one is restored, the other one deteriorates and vice versa). The ordering of the single-particle energy levels is crucial to this respect. Also, we observe a mutual dependence on the evolution of the shell closure gap Z = 50 and the energy band outside the core, along the Sn chain, as due to the tensor force. In fact, when the shell gap is quenched the outside energy band is enlarged, and vice versa. A reduction of the strength of the pion tensor force with respect to its experimental value from the nucleon-nucleon scattering is needed to get results closer to the experiment. Pairing correlations act to some extent in the opposite direction of the tensor term of the one-pion-exchange force.

Studies of the electron density in the highest occupied molecular orbitals of PH 3, PF 3 and P(CH 3) 3 by electron momentum spectroscopy and Hartree-Fock, MRSD-CI and DFT calculations

NASA Astrophysics Data System (ADS)

Rolke, J.; Brion, C. E.

1996-06-01

The spherically averaged momentum profiles for the highest occupied molecular orbitals of PF 3 and P(CH 3) 3 have been obtained by electron momentum spectroscopy. The measurements provide a stringent test of basis set effects and the quality of ab-initio methods in the description of these larger molecular systems. As in previous work on the methyl-substituted amines, intuitive arguments fail to predict the correct amount of s- and p-type contributions to the momentum profile while delocalized molecular orbital concepts provide a more adequate description of the HOMOs. The experimental momentum profiles have been compared with theoretical momentum profiles calculated at the level of the target Hartree-Fock approximation with a range of basis sets. New Hartree-Fock calculations are also presented for the HOMO of PH 3 and compared to previously published experimental and theoretical momentum profiles. The experimental momentum profiles have further been compared to calculations at the level of the target Kohn-Sham approximation using density functional theory with the local density approximation and also with gradient corrected (non-local) exchange correlation potentials. In addition, total energies and dipole moments have been calculated for all three molecules by the various theoretical methods and compared to experimental values. Calculated 'density difference maps' show the regions where the HOMO momentum and position electron densities of PF 3 and P(CH 3) 3 change relative to the corresponding HOMO density of PH 3. The results suggest that methyl groups have an electron-attracting effect (relative to H) on the HOMO charge density in trimethyl phosphines. These conclusions are supported by a consideration of dipole moments and the 31P NMR chemical shifts for PH 3, PF 3 and P(CH 3) 3.

Calculation of longitudinal polarizability and second hyperpolarizability of polyacetylene with the coupled perturbed Hartree-Fock/Kohn-Sham scheme: Where it is shown how finite oligomer chains tend to the infinite periodic polymer

NASA Astrophysics Data System (ADS)

Lacivita, Valentina; Rèrat, Michel; Orlando, Roberto; Ferrero, Mauro; Dovesi, Roberto

2012-03-01

The longitudinal polarizability, αxx, and second hyperpolarizability, γxxxx, of polyacetylene are evaluated by using the coupled perturbed Hartree-Fock/Kohn-Sham (HF/KS) scheme as implemented in the periodic CRYSTAL code and a split valence type basis set. Four different density functionals, namely local density approximation (LDA) (pure local), Perdew-Becke-Ernzerhof (PBE) (gradient corrected), PBE0, and B3LYP (hybrid), and the Hartree-Fock Hamiltonian are compared. It is shown that very tight computational conditions must be used to obtain well converged results, especially for γxxxx, that is, very sensitive to the number of k points in reciprocal space when the band gap is small (as for LDA and PBE), and to the extension of summations of the exact exchange series (HF and hybrids). The band gap in LDA is only 0.01 eV: at least 300 k points are required to obtain well converged total energy and equilibrium geometry, and 1200 for well converged optical properties. Also, the exchange series convergence is related to the band gap. The PBE0 band gap is as small as 1.4 eV and the exchange summation must extend to about 130 Å from the origin cell. Total energy, band gap, equilibrium geometry, polarizability, and second hyperpolarizability of oligomers -(C2H2)m-, with m up to 50 (202 atoms), and of the polymer have been compared. It turns out that oligomers of that length provide an extremely poor representation of the infinite chain polarizability and hyperpolarizability when the gap is smaller than 0.2 eV (that is, for LDA and PBE). Huge differences are observed on αxx and γxxxx of the polymer when different functionals are used, that is in connection to the well-known density functional theory (DFT) overshoot, reported in the literature about short oligomers: for the infinite model the ratio between LDA (or PBE) and HF becomes even more dramatic (about 500 for αxx and 1010 for γxxxx). On the basis of previous systematic comparisons of results obtained with

Long-range corrected density functional theory with accelerated Hartree-Fock exchange integration using a two-Gaussian operator [LC-ωPBE(2Gau)].

PubMed

Song, Jong-Won; Hirao, Kimihiko

2015-10-14

Since the advent of hybrid functional in 1993, it has become a main quantum chemical tool for the calculation of energies and properties of molecular systems. Following the introduction of long-range corrected hybrid scheme for density functional theory a decade later, the applicability of the hybrid functional has been further amplified due to the resulting increased performance on orbital energy, excitation energy, non-linear optical property, barrier height, and so on. Nevertheless, the high cost associated with the evaluation of Hartree-Fock (HF) exchange integrals remains a bottleneck for the broader and more active applications of hybrid functionals to large molecular and periodic systems. Here, we propose a very simple yet efficient method for the computation of long-range corrected hybrid scheme. It uses a modified two-Gaussian attenuating operator instead of the error function for the long-range HF exchange integral. As a result, the two-Gaussian HF operator, which mimics the shape of the error function operator, reduces computational time dramatically (e.g., about 14 times acceleration in C diamond calculation using periodic boundary condition) and enables lower scaling with system size, while maintaining the improved features of the long-range corrected density functional theory.

A poly-epoxy surface explored by Hartree-Fock ΔSCF simulations of C1s XPS spectra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gavrielides, A.; Duguet, T., E-mail: thomas.duguet@ensiacet.fr, E-mail: Paul.Bagus@unt.edu; Esvan, J.

Whereas poly-epoxy polymers represent a class of materials with a wide range of applications, the structural disorder makes them difficult to model. In the present work, we use good experimental model samples in the sense that they are pure, fully polymerized, flat and smooth, defect-free, and suitable for ultrahigh vacuum x-ray photoelectron spectroscopy, XPS, experiments. In parallel, we perform Hartree-Fock, HF, calculations of the binding energies, BEs, of the C1s electrons in a model molecule composed of the two constituents of the poly-epoxy sample. These C1s BEs were determined using the HF ΔSCF method, which is known to yield accuratemore » values, especially for the shifts of the BEs, ΔBEs. We demonstrate the benefits of combining rigorous theory with careful XPS measurements in order to obtain correct assignments of the C1s XPS spectra of the polymer sample. Both the relative binding energies—by the ΔSCF method—and relative intensities—in the sudden approximation, SA, are calculated. It results in an excellent match with the experimental spectra. We are able to identify 9 different chemical environments under the C1s peak, where an exclusively experimental work would have found only 3 contributions. In addition, we observe that some contributions are localized at discrete binding energies, whereas others allow a much wider range because of the variation of their second neighbor bound polarization. Therefore, HF-ΔSCF simulations significantly increase the spectral resolution of XPS and thus offer a new avenue for the exploration of the surface of polymers.« less

Hartree-Fock study of the Anderson metal-insulator transition in the presence of Coulomb interaction: Two types of mobility edges and their multifractal scaling exponents

NASA Astrophysics Data System (ADS)

Lee, Hyun-Jung; Kim, Ki-Seok

2018-04-01

We investigate the role of Coulomb interaction in the multifractality of Anderson metal-insulator transition, where the Coulomb interaction is treated within the Hartree-Fock approximation, but disorder effects are taken into account exactly. An innovative technical aspect in our simulation is to utilize the Ewald-sum technique, which allows us to introduce the long-range nature of the Coulomb interaction into Hartree-Fock self-consistent equations of order parameters more accurately. This numerical simulation reproduces the Altshuler-Aronov correction in a metallic state and the Efros-Shklovskii pseudogap in an insulating phase, where the density of states ρ (ω ) is evaluated in three dimensions. Approaching the quantum critical point of a metal-insulator transition from either the metallic or insulting phase, we find that the density of states is given by ρ (ω ) ˜|ω| 1 /2 , which determines one critical exponent of the McMillan-Shklovskii scaling theory. Our main result is to evaluate the eigenfunction multifractal scaling exponent αq, given by the Legendre transformation of the fractal dimension τq, which characterizes the scaling behavior of the inverse participation ratio with respect to the system size L . Our multifractal analysis leads us to identify two kinds of mobility edges, one of which occurs near the Fermi energy and the other of which appears at a high energy, where the density of states at the Fermi energy shows the Coulomb-gap feature. We observe that the multifractal exponent at the high-energy mobility edge remains to be almost identical to that of the Anderson localization transition in the absence of Coulomb interactions. On the other hand, we find that the multifractal exponent near the Fermi energy is more enhanced than that at the high-energy mobility edge, suspected to result from interaction effects. However, both the multifractal exponents do not change even if the strength of the Coulomb interaction varies. We also show that the

High spin states of 72-74Kr

NASA Astrophysics Data System (ADS)

Kaushik, M.; Kumawat, M.; Singh, U. K.; Saxena, G.

2018-05-01

A theoretical investigation has made on the structure of high spin states of 72-74Kr within the framework of cranked Hartree-Fock-Bogoliubov (CHFB) theory employing a pairing + quadrupole + hexadecapole model interaction. Dependence of shape with the spin, excitation energy, alignment of proton as well as neutron 0g9/2 orbital along with backbending phenomenon are discussed upto a high spin J = 26. We found reasonable agreement with the experimental values and other theoretical calculations.

Calculation of longitudinal polarizability and second hyperpolarizability of polyacetylene with the coupled perturbed Hartree-Fock/Kohn-Sham scheme: where it is shown how finite oligomer chains tend to the infinite periodic polymer.

PubMed

Lacivita, Valentina; Rèrat, Michel; Orlando, Roberto; Ferrero, Mauro; Dovesi, Roberto

2012-03-21

The longitudinal polarizability, α(xx), and second hyperpolarizability, γ(xxxx), of polyacetylene are evaluated by using the coupled perturbed Hartree-Fock/Kohn-Sham (HF/KS) scheme as implemented in the periodic CRYSTAL code and a split valence type basis set. Four different density functionals, namely local density approximation (LDA) (pure local), Perdew-Becke-Ernzerhof (PBE) (gradient corrected), PBE0, and B3LYP (hybrid), and the Hartree-Fock Hamiltonian are compared. It is shown that very tight computational conditions must be used to obtain well converged results, especially for γ(xxxx), that is, very sensitive to the number of k(->) points in reciprocal space when the band gap is small (as for LDA and PBE), and to the extension of summations of the exact exchange series (HF and hybrids). The band gap in LDA is only 0.01 eV: at least 300 k(->) points are required to obtain well converged total energy and equilibrium geometry, and 1200 for well converged optical properties. Also, the exchange series convergence is related to the band gap. The PBE0 band gap is as small as 1.4 eV and the exchange summation must extend to about 130 Å from the origin cell. Total energy, band gap, equilibrium geometry, polarizability, and second hyperpolarizability of oligomers -(C(2)H(2))(m)-, with m up to 50 (202 atoms), and of the polymer have been compared. It turns out that oligomers of that length provide an extremely poor representation of the infinite chain polarizability and hyperpolarizability when the gap is smaller than 0.2 eV (that is, for LDA and PBE). Huge differences are observed on α(xx) and γ(xxxx) of the polymer when different functionals are used, that is in connection to the well-known density functional theory (DFT) overshoot, reported in the literature about short oligomers: for the infinite model the ratio between LDA (or PBE) and HF becomes even more dramatic (about 500 for α(xx) and 10(10) for γ(xxxx)). On the basis of previous systematic

Structure of Be9Λ and 10Be Λ Λ using the beyond-mean-field Skyrme-Hartree-Fock approach

NASA Astrophysics Data System (ADS)

Li, Wen-Ying; Cui, Ji-Wei; Zhou, Xian-Rong

2018-03-01

Based on the beyond-mean-field Skyrme-Hartree-Fock model, the up-to-date Skyrme-type N Λ interaction, SLL4, is used to investigate the properties of Be9Λ comprehensively. Energies of different configurations, such as 8Be⊗Λ [000 ] 1 /2+ , 8Be⊗Λ [110 ] 1 /2- , 8Be⊗Λ [101 ] 3 /2- , and 8Be⊗Λ [101 ] 1 /2- are given and used to study the effects of Λ occupying different orbitals. The calculated energy spectra, including both positive- and negative-parity levels, are given and compared to the experimental data. The observed positive-parity spin doublets (3 /2+,5 /2+ ) are successfully reproduced, but the energy difference needs further investigation. The two well-known band structures corresponding to the genuine hypernuclear states and the 9Be-analog states are also obtained and compared with the observed ones. The shrinkage effect of Λ occupying Λ [000 ] 1 /2+ is investigated through the density distributions of nuclear core. And finally, the E 2 transition rates are given and compared with the observed data and with the results of the hypernuclear particle-rotor model. Properties of 10Be Λ Λ are also studied to show the completeness of this current model.

Molecular structure, vibrational spectra, AIM, HOMO-LUMO, NBO, UV, first order hyperpolarizability, analysis of 3-thiophenecarboxylic acid monomer and dimer by Hartree-Fock and density functional theory

NASA Astrophysics Data System (ADS)

Issaoui, Noureddine; Ghalla, Houcine; Muthu, S.; Flakus, H. T.; Oujia, Brahim

2015-02-01

In this work, the molecular structure, harmonic vibrational frequencies, UV, NBO and AIM of 3-thiophenecarboxilic acid (abbreviated as 3-TCA) monomer and dimer has been investigated. The FT-IR and FT-Raman spectra were recorded. The ground-state molecular geometry and vibrational frequencies have been calculated by using the Hartree-Fock (HF) and density functional theory (DFT)/B3LYP methods and 6-311++G(d,p) as a basis set. The fundamental vibrations were assigned on the basis of the total energy distribution (TED) of the vibrational modes, calculated with VEDA program. Comparison of the observed fundamental vibrational frequencies of 3-TCA with calculated results by HF and DFT methods indicates that B3LYP is better to HF method for molecular vibrational problems. The difference between the observed and scaled wavenumber values is very small. The theoretically predicted FT-IR and FT-Raman spectra of the title compound have been constructed. A study on the Mulliken atomic charges, the electronic properties were performed by time-dependent DFT (TD-DFT) approach, frontier molecular orbitals (HOMO-LUMO), molecular electrostatic potential (MEP) and thermodynamic properties have been performed. The electric dipole moment (μ) and the first hyperpolarizability (β) values of the investigated molecule have been also computed.

A highly optimized code for calculating atomic data at neutron star magnetic field strengths using a doubly self-consistent Hartree-Fock-Roothaan method

NASA Astrophysics Data System (ADS)

Schimeczek, C.; Engel, D.; Wunner, G.

2012-07-01

account the shielding of the core potential for outer electrons by inner electrons, and an optimal finite-element decomposition of each individual longitudinal wave function. These measures largely enhance the convergence properties compared to the previous code, and lead to speed-ups by factors up to two orders of magnitude compared with the implementation of the Hartree-Fock-Roothaan method used by Engel and Wunner in [D. Engel, G. Wunner, Phys. Rev. A 78 (2008) 032515]. New version program summaryProgram title: HFFER II Catalogue identifier: AECC_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECC_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: v 55 130 No. of bytes in distributed program, including test data, etc.: 293 700 Distribution format: tar.gz Programming language: Fortran 95 Computer: Cluster of 1-13 HP Compaq dc5750 Operating system: Linux Has the code been vectorized or parallelized?: Yes, parallelized using MPI directives. RAM: 1 GByte per node Classification: 2.1 External routines: MPI/GFortran, LAPACK, BLAS, FMlib (included in the package) Catalogue identifier of previous version: AECC_v1_0 Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 302 Does the new version supersede the previous version?: Yes Nature of problem: Quantitative modellings of features observed in the X-ray spectra of isolated magnetic neutron stars are hampered by the lack of sufficiently large and accurate databases for atoms and ions up to the last fusion product, iron, at strong magnetic field strengths. Our code is intended to provide a powerful tool for calculating energies and oscillator strengths of medium-Z atoms and ions at neutron star magnetic field strengths with sufficient accuracy in a routine way to create such databases. Solution method: The

Investigation of Gamow Teller transition properties in 56-64Ni isotopes using QRPA methods

NASA Astrophysics Data System (ADS)

Cakmak, Sadiye; Nabi, Jameel-Un; Babacan, Tahsin

2018-02-01

Weak rates in nickel isotopes play an integral role in the dynamics of supernovae. Electron capture and β-decay of nickel isotopes, dictated by Gamow-Teller transitions, significantly alter the lepton fraction of the stellar matter. In this paper we calculate Gamow-Teller (GT) transitions for isotopes of nickel, Ni6456-, using QRPA methods. The GT strength distributions were calculated using four different QRPA models. Our results are also compared with previous theoretical calculations and measured strength distributions wherever available. Our investigation concluded that amongst all RPA models, the pn-QRPA(C) model best described the measured GT distributions (including total GT strength and centroid placement). It is hoped that the current investigation of GT properties would prove handy and may lead to a better understanding of the presupernova evolution of massive stars.

Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.. (VII) HFODD (v2.49t): A new version of the program

NASA Astrophysics Data System (ADS)

Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.

2012-01-01

We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite-temperature formalism for the HFB and HF + BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex-breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected. New version program summaryProgram title:HFODD (v2.49t) Catalogue identifier: ADFL_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence v3 No. of lines in distributed program, including test data, etc.: 190 614 No. of bytes in distributed program, including test data, etc.: 985 898 Distribution

Non-Born-Oppenheimer self-consistent field calculations with cubic scaling

NASA Astrophysics Data System (ADS)

Moncada, Félix; Posada, Edwin; Flores-Moreno, Roberto; Reyes, Andrés

2012-05-01

An efficient nuclear molecular orbital methodology is presented. This approach combines an auxiliary density functional theory for electrons (ADFT) and a localized Hartree product (LHP) representation for the nuclear wave function. A series of test calculations conducted on small molecules exposed that energy and geometry errors introduced by the use of ADFT and LHP approximations are small and comparable to those obtained by the use of electronic ADFT. In addition, sample calculations performed on (HF)n chains disclosed that the combined ADFT/LHP approach scales cubically with system size (n) as opposed to the quartic scaling of Hartree-Fock/LHP or DFT/LHP methods. Even for medium size molecules the improved scaling of the ADFT/LHP approach resulted in speedups of at least 5x with respect to Hartree-Fock/LHP calculations. The ADFT/LHP method opens up the possibility of studying nuclear quantum effects on large size systems that otherwise would be impractical.

Molecular structure, vibrational spectra, AIM, HOMO-LUMO, NBO, UV, first order hyperpolarizability, analysis of 3-thiophenecarboxylic acid monomer and dimer by Hartree-Fock and density functional theory.

PubMed

Issaoui, Noureddine; Ghalla, Houcine; Muthu, S; Flakus, H T; Oujia, Brahim

2015-02-05

In this work, the molecular structure, harmonic vibrational frequencies, UV, NBO and AIM of 3-thiophenecarboxilic acid (abbreviated as 3-TCA) monomer and dimer has been investigated. The FT-IR and FT-Raman spectra were recorded. The ground-state molecular geometry and vibrational frequencies have been calculated by using the Hartree-Fock (HF) and density functional theory (DFT)/B3LYP methods and 6-311++G(d,p) as a basis set. The fundamental vibrations were assigned on the basis of the total energy distribution (TED) of the vibrational modes, calculated with VEDA program. Comparison of the observed fundamental vibrational frequencies of 3-TCA with calculated results by HF and DFT methods indicates that B3LYP is better to HF method for molecular vibrational problems. The difference between the observed and scaled wavenumber values is very small. The theoretically predicted FT-IR and FT-Raman spectra of the title compound have been constructed. A study on the Mulliken atomic charges, the electronic properties were performed by time-dependent DFT (TD-DFT) approach, frontier molecular orbitals (HOMO-LUMO), molecular electrostatic potential (MEP) and thermodynamic properties have been performed. The electric dipole moment (μ) and the first hyperpolarizability (β) values of the investigated molecule have been also computed. Copyright © 2014 Elsevier B.V. All rights reserved.

On Fock-space representations of quantized enveloping algebras related to noncommutative differential geometry

NASA Astrophysics Data System (ADS)

Jurčo, B.; Schlieker, M.

1995-07-01

In this paper explicitly natural (from the geometrical point of view) Fock-space representations (contragradient Verma modules) of the quantized enveloping algebras are constructed. In order to do so, one starts from the Gauss decomposition of the quantum group and introduces the differential operators on the corresponding q-deformed flag manifold (assumed as a left comodule for the quantum group) by a projection to it of the right action of the quantized enveloping algebra on the quantum group. Finally, the representatives of the elements of the quantized enveloping algebra corresponding to the left-invariant vector fields on the quantum group are expressed as first-order differential operators on the q-deformed flag manifold.

Description of plasmon-like band in silver clusters: the importance of the long-range Hartree-Fock exchange in time-dependent density-functional theory simulations.

PubMed

Rabilloud, Franck

2014-10-14

Absorption spectra of Ag20 and Ag55(q) (q = +1, -3) nanoclusters are investigated in the framework of the time-dependent density functional theory in order to analyse the role of the d electrons in plasmon-like band of silver clusters. The description of the plasmon-like band from calculations using density functionals containing an amount of Hartree-Fock exchange at long range, namely, hybrid and range-separated hybrid (RSH) density functionals, is in good agreement with the classical interpretation of the plasmon-like structure as a collective excitation of valence s-electrons. In contrast, using local or semi-local exchange functionals (generalized gradient approximations (GGAs) or meta-GGAs) leads to a strong overestimation of the role of d electrons in the plasmon-like band. The semi-local asymptotically corrected model potentials also describe the plasmon as mainly associated to d electrons, though calculated spectra are in fairly good agreement with those calculated using the RSH scheme. Our analysis shows that a portion of non-local exchange modifies the description of the plasmon-like band.

Majorana neutrino and the vacuum of Bogoliubov quasiparticle

NASA Astrophysics Data System (ADS)

Fujikawa, Kazuo

2018-06-01

The Lagrangian of the seesaw mechanism is C violating but the same Lagrangian when re-written in terms of Majorana neutrinos is manifestly C invariant. To resolve this puzzling feature, a relativistic analogue of Bogoliubov transformation, which preserves CP but explicitly breaks C and P separately, was introduced together with the notions of a Bogoliubov quasiparticle and an analogue of the energy gap in BCS theory. The idea of Majorana neutrino as Bogoliubov quasiparticle was then suggested. In this paper, we study the vacuum structure of the Bogoliubov quasiparticle which becomes heavy by absorbing the C-breaking. By treating an infinitesimally small C violating term as an analogue of the chiral symmetry breaking nucleon mass in the model of Nambu and Jona-Lasinio, we construct an explicit form of the vacuum of the Bogoliubov quasiparticle which defines Majorana neutrinos in seesaw mechanism. The vacuum of the Bogoliubov quasiparticle thus constructed has an analogous condensate structure as the vacuum of the quasiparticle (nucleon) in the Nambu-Jona-Lasinio model.

Fock expansion of multimode pure Gaussian states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cariolaro, Gianfranco; Pierobon, Gianfranco, E-mail: gianfranco.pierobon@unipd.it

2015-12-15

The Fock expansion of multimode pure Gaussian states is derived starting from their representation as displaced and squeezed multimode vacuum states. The approach is new and appears to be simpler and more general than previous ones starting from the phase-space representation given by the characteristic or Wigner function. Fock expansion is performed in terms of easily evaluable two-variable Hermite–Kampé de Fériet polynomials. A relatively simple and compact expression for the joint statistical distribution of the photon numbers in the different modes is obtained. In particular, this result enables one to give a simple characterization of separable and entangled states, asmore » shown for two-mode and three-mode Gaussian states.« less

Low-lying electric-dipole strengths of Ca, Ni, and Sn isotopes imprinted on total reaction cross sections

NASA Astrophysics Data System (ADS)

Horiuchi, W.; Hatakeyama, S.; Ebata, S.; Suzuki, Y.

2017-08-01

Low-lying electric-dipole (E 1 ) strength of a neutron-rich nucleus contains information on neutron-skin thickness, deformation, and shell evolution. We discuss the possibility of making use of total reaction cross sections on 40Ca, 120Sn, and 208Pb targets to probe the E 1 strength of neutron-rich Ca, Ni, and Sn isotopes. They exhibit large enhancement of the E 1 strength at neutron number N >28 , 50, and 82, respectively, due to a change of the single-particle orbits near the Fermi surface participating in the transitions. The density distributions and the electric-multipole strength functions of those isotopes are calculated by the Hartree-Fock+BCS and the canonical-basis-time-dependent-Hartree-Fock-Bogoliubov methods, respectively, using three kinds of Skyrme-type effective interaction. The nuclear and Coulomb breakup processes are respectively described with the Glauber model and the equivalent photon method in which the effect of finite-charge distribution is taken into account. The three Skyrme interactions give different results for the total reaction cross sections because of different Coulomb breakup contributions. The contribution of the low-lying E 1 strength is amplified when the low-incident energy is chosen. With an appropriate choice of the incident energy and target nucleus, the total reaction cross section can be complementary to the Coulomb excitation for analyzing the low-lying E 1 strength of unstable nuclei.

Toroidal high-spin isomers in the nucleus 304120

NASA Astrophysics Data System (ADS)

Staszczak, A.; Wong, Cheuk-Yin; Kosior, A.

2017-05-01

Background: Strongly deformed oblate superheavy nuclei form an intriguing region where the toroidal nuclear structures may bifurcate from the oblate spheroidal shape. The bifurcation may be facilitated when the nucleus is endowed with a large angular moment about the symmetry axis with I =Iz . The toroidal high-K isomeric states at their local energy minima can be theoretically predicted using the cranked self-consistent Skyrme-Hartree-Fock method. Purpose: We use the cranked Skyrme-Hartree-Fock method to predict the properties of the toroidal high-spin isomers in the superheavy nucleus 120304184. Method: Our method consists of three steps: First, we use the deformation-constrained Skyrme-Hartree-Fock-Bogoliubov approach to search for the nuclear density distributions with toroidal shapes. Next, using these toroidal distributions as starting configurations, we apply an additional cranking constraint of a large angular momentum I =Iz about the symmetry z axis and search for the energy minima of the system as a function of the deformation. In the last step, if a local energy minimum with I =Iz is found, we perform at this point the cranked symmetry- and deformation-unconstrained Skyrme-Hartree-Fock calculations to locate a stable toroidal high-spin isomeric state in free convergence. Results: We have theoretically located two toroidal high-spin isomeric states of 120304184 with an angular momentum I =Iz=81 ℏ (proton 2p-2h, neutron 4p-4h excitation) and I =Iz=208 ℏ (proton 5p-5h, neutron 8p-8h) at the quadrupole moment deformations Q20=-297.7 b and Q20=-300.8 b with energies 79.2 and 101.6 MeV above the spherical ground state, respectively. The nuclear density distributions of the toroidal high-spin isomers 120304184(Iz=81 ℏ and 208 ℏ ) have the maximum density close to the nuclear matter density, 0.16 fm-3, and a torus major to minor radius aspect ratio R /d =3.25 . Conclusions: We demonstrate that aligned angular momenta of Iz=81 ℏ and 208 ℏ arising from

Roothaan's approach to solve the Hartree-Fock equations for atoms confined by soft walls: Basis set with correct asymptotic behavior.

PubMed

Rodriguez-Bautista, Mariano; Díaz-García, Cecilia; Navarrete-López, Alejandra M; Vargas, Rubicelia; Garza, Jorge

2015-07-21

In this report, we use a new basis set for Hartree-Fock calculations related to many-electron atoms confined by soft walls. One- and two-electron integrals were programmed in a code based in parallel programming techniques. The results obtained with this proposal for hydrogen and helium atoms were contrasted with other proposals to study just one and two electron confined atoms, where we have reproduced or improved the results previously reported. Usually, an atom enclosed by hard walls has been used as a model to study confinement effects on orbital energies, the main conclusion reached by this model is that orbital energies always go up when the confinement radius is reduced. However, such an observation is not necessarily valid for atoms confined by penetrable walls. The main reason behind this result is that for atoms with large polarizability, like beryllium or potassium, external orbitals are delocalized when the confinement is imposed and consequently, the internal orbitals behave as if they were in an ionized atom. Naturally, the shell structure of these atoms is modified drastically when they are confined. The delocalization was an argument proposed for atoms confined by hard walls, but it was never verified. In this work, the confinement imposed by soft walls allows to analyze the delocalization concept in many-electron atoms.

Comparative study of the requantization of the time-dependent mean field for the dynamics of nuclear pairing

NASA Astrophysics Data System (ADS)

Ni, Fang; Nakatsukasa, Takashi

2018-04-01

To describe quantal collective phenomena, it is useful to requantize the time-dependent mean-field dynamics. We study the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory for the two-level pairing Hamiltonian, and compare results of different quantization methods. The one constructing microscopic wave functions, using the TDHFB trajectories fulfilling the Einstein-Brillouin-Keller quantization condition, turns out to be the most accurate. The method is based on the stationary-phase approximation to the path integral. We also examine the performance of the collective model which assumes that the pairing gap parameter is the collective coordinate. The applicability of the collective model is limited for the nuclear pairing with a small number of single-particle levels, because the pairing gap parameter represents only a half of the pairing collective space.

The relation between the Gross Pitaevskii and Bogoliubov descriptions of a dilute Bose gas

NASA Astrophysics Data System (ADS)

Leggett, A. J.

2003-07-01

I formulate a 'pseudo-paradox' in the theory of a dilute Bose gas with repulsive interactions: the standard expression for the ground state energy within the Gross-Pitaevskii (GP) approximation is lower than that in the Bogoliubov approximation, and hence, by the standard variational argument, the former should prima facie be a better approximation than the latter to the true ground state—a conclusion which is of course opposite to the established wisdom concerning this problem. It is shown that the pseudo-paradox is (unsurprisingly) resolved by a correct transcription of the two-body scattering theory to the many-body case; however, contrary to what appears to be a widespread belief, the resolution has nothing to do with any spurious ultraviolet divergences which result from the replacement of the true interatomic potential by a delta-function pseudopotential. Rather, it relates to an infrared divergence which has the consequence that (a) the most obvious form of the GP 'approximation' actually does not correspond to any well-defined ansatz for the many-body wavefunction, and (b) that the 'best shot' at such a wavefunction always produces an energy which exceeds, or at best equals, that calculated in the Bogoliubov approximation. In fact, the necessity of the latter may be seen as a consequence of the need to reduce the Fock term in the energy, which is absent in the two-particle problem but dominant in the many-body case; it does this by increasing the density correlations, at distances less than or approximately equal to the correlation length \\xi , above the value extrapolated from the two-body case. As a by-product I devise an alternative formulation of the Bogoliubov approximation which does not require the explicit replacement of the true interatomic potential by a delta-function pseudopotential.

Structure and decays of nuclear three-body systems: The Gamow coupled-channel method in Jacobi coordinates

NASA Astrophysics Data System (ADS)

Wang, S. M.; Michel, N.; Nazarewicz, W.; Xu, F. R.

2017-10-01

Background: Weakly bound and unbound nuclear states appearing around particle thresholds are prototypical open quantum systems. Theories of such states must take into account configuration mixing effects in the presence of strong coupling to the particle continuum space. Purpose: To describe structure and decays of three-body systems, we developed a Gamow coupled-channel (GCC) approach in Jacobi coordinates by employing the complex-momentum formalism. We benchmarked the complex-energy Gamow shell model (GSM) against the new framework. Methods: The GCC formalism is expressed in Jacobi coordinates, so that the center-of-mass motion is automatically eliminated. To solve the coupled-channel equations, we use hyperspherical harmonics to describe the angular wave functions while the radial wave functions are expanded in the Berggren ensemble, which includes bound, scattering, and Gamow states. Results: We show that the GCC method is both accurate and robust. Its results for energies, decay widths, and nucleon-nucleon angular correlations are in good agreement with the GSM results. Conclusions: We have demonstrated that a three-body GSM formalism explicitly constructed in the cluster-orbital shell model coordinates provides results similar to those with a GCC framework expressed in Jacobi coordinates, provided that a large configuration space is employed. Our calculations for A =6 systems and 26O show that nucleon-nucleon angular correlations are sensitive to the valence-neutron interaction. The new GCC technique has many attractive features when applied to bound and unbound states of three-body systems: it is precise, is efficient, and can be extended by introducing a microscopic model of the core.

Roothaan’s approach to solve the Hartree-Fock equations for atoms confined by soft walls: Basis set with correct asymptotic behavior

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rodriguez-Bautista, Mariano; Díaz-García, Cecilia; Navarrete-López, Alejandra M.

2015-07-21

In this report, we use a new basis set for Hartree-Fock calculations related to many-electron atoms confined by soft walls. One- and two-electron integrals were programmed in a code based in parallel programming techniques. The results obtained with this proposal for hydrogen and helium atoms were contrasted with other proposals to study just one and two electron confined atoms, where we have reproduced or improved the results previously reported. Usually, an atom enclosed by hard walls has been used as a model to study confinement effects on orbital energies, the main conclusion reached by this model is that orbital energiesmore » always go up when the confinement radius is reduced. However, such an observation is not necessarily valid for atoms confined by penetrable walls. The main reason behind this result is that for atoms with large polarizability, like beryllium or potassium, external orbitals are delocalized when the confinement is imposed and consequently, the internal orbitals behave as if they were in an ionized atom. Naturally, the shell structure of these atoms is modified drastically when they are confined. The delocalization was an argument proposed for atoms confined by hard walls, but it was never verified. In this work, the confinement imposed by soft walls allows to analyze the delocalization concept in many-electron atoms.« less

Accurate Gaussian basis sets for atomic and molecular calculations obtained from the generator coordinate method with polynomial discretization.

PubMed

Celeste, Ricardo; Maringolo, Milena P; Comar, Moacyr; Viana, Rommel B; Guimarães, Amanda R; Haiduke, Roberto L A; da Silva, Albérico B F

2015-10-01

Accurate Gaussian basis sets for atoms from H to Ba were obtained by means of the generator coordinate Hartree-Fock (GCHF) method based on a polynomial expansion to discretize the Griffin-Wheeler-Hartree-Fock equations (GWHF). The discretization of the GWHF equations in this procedure is based on a mesh of points not equally distributed in contrast with the original GCHF method. The results of atomic Hartree-Fock energies demonstrate the capability of these polynomial expansions in designing compact and accurate basis sets to be used in molecular calculations and the maximum error found when compared to numerical values is only 0.788 mHartree for indium. Some test calculations with the B3LYP exchange-correlation functional for N2, F2, CO, NO, HF, and HCN show that total energies within 1.0 to 2.4 mHartree compared to the cc-pV5Z basis sets are attained with our contracted bases with a much smaller number of polarization functions (2p1d and 2d1f for hydrogen and heavier atoms, respectively). Other molecular calculations performed here are also in very good accordance with experimental and cc-pV5Z results. The most important point to be mentioned here is that our generator coordinate basis sets required only a tiny fraction of the computational time when compared to B3LYP/cc-pV5Z calculations.

A q-deformation of the Bogoliubov transformations

NASA Astrophysics Data System (ADS)

Arraut, Ivan; Segovia, Carlos

2018-02-01

An approach for q-deformed Bogoliubov transformations is presented. Assuming a left-right module action together with an *-operation and deformed commutation relations, we construct a q-deformation of the nonlinear Bogoliubov transformation. Finally, we introduce a Hopf structure when q is a root of unity.

On the Time-Dependent Analysis of Gamow Decay

ERIC Educational Resources Information Center

Durr, Detlef; Grummt, Robert; Kolb, Martin

2011-01-01

Gamow's explanation of the exponential decay law uses complex "eigenvalues" and exponentially growing "eigenfunctions". This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based on real eigenvalues and square integrable wavefunctions. Observing that the time evolution of any…

Gamow on Newton: Another Look at Centripetal Acceleration

ERIC Educational Resources Information Center

Corrao, Christian

2012-01-01

Presented here is an adaptation of George Gamow's derivation of the centripetal acceleration formula as it applies to Earth's orbiting Moon. The derivation appears in Gamows short but engaging book "Gravity", first published in 1962, and is essentially a distillation of Newton's work. While "TPT" contributors have offered several insightful…

Symbolic computation of the Hartree-Fock energy from a chiral EFT three-nucleon interaction at N 2LO

NASA Astrophysics Data System (ADS)

Gebremariam, B.; Bogner, S. K.; Duguet, T.

2010-06-01

We present the first of a two-part Mathematica notebook collection that implements a symbolic approach for the application of the density matrix expansion (DME) to the Hartree-Fock (HF) energy from a chiral effective field theory (EFT) three-nucleon interaction at N 2LO. The final output from the notebooks is a Skyrme-like energy density functional that provides a quasi-local approximation to the non-local HF energy. In this paper, we discuss the derivation of the HF energy and its simplification in terms of the scalar/vector-isoscalar/isovector parts of the one-body density matrix. Furthermore, a set of steps is described and illustrated on how to extend the approach to other three-nucleon interactions. Program summaryProgram title: SymbHFNNN Catalogue identifier: AEGC_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGC_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 96 666 No. of bytes in distributed program, including test data, etc.: 378 083 Distribution format: tar.gz Programming language: Mathematica 7.1 Computer: Any computer running Mathematica 6.0 and later versions Operating system: Windows Xp, Linux/Unix RAM: 256 Mb Classification: 5, 17.16, 17.22 Nature of problem: The calculation of the HF energy from the chiral EFT three-nucleon interaction at N 2LO involves tremendous spin-isospin algebra. The problem is compounded by the need to eventually obtain a quasi-local approximation to the HF energy, which requires the HF energy to be expressed in terms of scalar/vector-isoscalar/isovector parts of the one-body density matrix. The Mathematica notebooks discussed in this paper solve the latter issue. Solution method: The HF energy from the chiral EFT three-nucleon interaction at N 2LO is cast into a form suitable for an automatic simplification of

Nuclear level densities of 64 , 66 Zn from neutron evaporation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ramirez, A. P. D.; Voinov, A. V.; Grimes, S. M.

Double differential cross sections of neutrons from d+ 63,65Cu reactions have been measured at deuteron energies of 6 and 7.5 MeV. The cross sections measured at backward angles have been compared to theoretical calculations in the framework of the statistical Hauser-Feshbach model. Three different level density models were tested: the Fermi-gas model, the Gilbert-Cameron model, and the microscopic approach through the Hartree-Fock-Bogoliubov method (HFBM). The calculations using the Gilbert-Cameron model are in best agreement with our experimental data. Level densities of the residual nuclei 64Zn and 66Zn have been obtained from statistical neutron evaporation spectra. In conclusion, the angle-integrated crossmore » sections have been analyzed with the exciton model of nuclear reaction.« less

Nuclear level densities of 64 , 66 Zn from neutron evaporation

DOE PAGES

Ramirez, A. P. D.; Voinov, A. V.; Grimes, S. M.; ...

2013-12-26

Double differential cross sections of neutrons from d+ 63,65Cu reactions have been measured at deuteron energies of 6 and 7.5 MeV. The cross sections measured at backward angles have been compared to theoretical calculations in the framework of the statistical Hauser-Feshbach model. Three different level density models were tested: the Fermi-gas model, the Gilbert-Cameron model, and the microscopic approach through the Hartree-Fock-Bogoliubov method (HFBM). The calculations using the Gilbert-Cameron model are in best agreement with our experimental data. Level densities of the residual nuclei 64Zn and 66Zn have been obtained from statistical neutron evaporation spectra. In conclusion, the angle-integrated crossmore » sections have been analyzed with the exciton model of nuclear reaction.« less

High-field instability of a field-induced triplon Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Rakhimov, Abdulla; Sherman, E. Ya.; Kim, Chul Koo

2010-01-01

We study properties of magnetic field-induced Bose-Einstein condensate of triplons as a function of temperature and the field within the Hartree-Fock-Bogoliubov approach including the anomalous density. We show that the magnetization is continuous across the transition, in agreement with the experiment. In sufficiently strong fields the condensate becomes unstable due to triplon-triplon repulsion. As a result, the system is characterized by two critical magnetic fields: one producing the condensate and the other destroying it. We show that nonparabolic triplon dispersion arising due to the gapped bare spectrum and the crystal structure has a strong influence on the phase diagram.

Realistic Gamow shell model for resonance and continuum in atomic nuclei

NASA Astrophysics Data System (ADS)

Xu, F. R.; Sun, Z. H.; Wu, Q.; Hu, B. S.; Dai, S. J.

2018-02-01

The Gamow shell model can describe resonance and continuum for atomic nuclei. The model is established in the complex-moment (complex-k) plane of the Berggren coordinates in which bound, resonant and continuum states are treated on equal footing self-consistently. In the present work, the realistic nuclear force, CD Bonn, has been used. We have developed the full \\hat{Q}-box folded-diagram method to derive the realistic effective interaction in the model space which is nondegenerate and contains resonance and continuum channels. The CD-Bonn potential is renormalized using the V low-k method. With choosing 16O as the inert core, we have applied the Gamow shell model to oxygen isotopes.

Photoluminescence and gain/absorption spectra of a driven-dissipative electron-hole-photon condensate

NASA Astrophysics Data System (ADS)

Hanai, Ryo; Littlewood, Peter B.; Ohashi, Yoji

2018-06-01

We investigate theoretically nonequilibrium effects on photoluminescence and gain/absorption spectra of a driven-dissipative exciton-polariton condensate, by employing the combined Hartree-Fock-Bogoliubov theory with the generalized random phase approximation extended to the Keldysh formalism. Our calculated photoluminescence spectra is in semiquantitative agreement with experiments, where features such as a blue shift of the emission from the condensate, the appearance of the dispersionless feature of a diffusive Goldstone mode, and the suppression of the dispersive profile of the mode are obtained. We show that the nonequilibrium nature of the exciton-polariton condensate strongly suppresses the visibility of the Bogoliubov dispersion in the negative energy branch (ghost branch) in photoluminescence spectra. We also show that the trace of this branch can be captured as a hole burning effect in gain/absorption spectra. Our results indicate that the nonequilibrium nature of the exciton-polariton condensate strongly reduces quantum depletion, while a scattering channel to the ghost branch is still present.

Toroidal high-spin isomers in the nucleus 120 304

DOE PAGES

Staszczak, A.; Wong, Cheuk-Yin; Kosior, A.

2017-05-22

Strongly deformed oblate superheavy nuclei form an intriguing region where the toroidal nuclear structures may bifurcate from the oblate spheroidal shape. The bifurcation may be facilitated when the nucleus is endowed with a large angular moment about the symmetry axis withmore » $$I=I_{z}$$. The toroidal high-$K$ isomeric states at their local energy minima can be theoretically predicted using the cranked self-consistent Skyrme-Hartree-Fock method. We use the cranked Skyrme-Hartree-Fock method to predict the properties of the toroidal high-spin isomers in the superheavy nucleus $$^{304}{120}_{184}$$. This method consists of three steps: first, we use the deformation-constrained Skyrme-Hartree-Fock-Bogoliubov approach to search for the nuclear density distributions with toroidal shapes. Next, using these toroidal distributions as starting configurations we apply an additional cranking constraint of a large angular momentum $$I=I_{z}$$ about the symmetry $z$-axis and search for the energy minima of the system as a function of the deformation. In the last step, if a local energy minimum with $$I=I_{z}$$ is found, we perform at this point the cranked symmetry- and deformation-unconstrained Skyrme-Hartree-Fock calculations to locate a stable toroidal high-spin isomeric state in free convergence. Furthemore, we have theoretically located two toroidal high-spin isomeric states of $$^{304}{120}_{184}$$ with an angular momentum $I$=$$I_z$$=81$$\\hbar$$ (proton 2p-2h, neutron 4p-4h excitation) and $I$=$$I_z$$=208$$\\hbar$$ (proton 5p-5h, neutron 8p-8h) at the quadrupole moment deformations $$Q_{20}=-297.7$$~b and $$Q_{20}=-300.8$$~b with energies 79.2 MeV and 101.6 MeV above the spherical ground state, respectively. The nuclear density distributions of the toroidal high-spin isomers $$^{304}{120}_{184}(I_z$$=81$$\\hbar$$ and 208$$\\hbar$$) have the maximum density close to the nuclear matter density, 0.16 fm$$^{-3}$$, and a torus major to minor radius aspect ratio $R/d=3

Photoionization of Atoms and Molecules using a Configuration-Average Distorted-Wave Method

NASA Astrophysics Data System (ADS)

Pindzola, M. S.; Balance, C. P.; Loch, S. D.; Ludlow, J. A.

2011-05-01

A configuration-average distorted-wave method is applied to calculate the photoionization cross section for the outer subshells of the C atom and the C2 diatomic molecule. Comparisions are made with previous R-matrix and Hartree- Fock distorted-wave calculations.

An ab initio time-dependent Hartree Fock study of solvent effects on the polarizability and second hyperpolarizability of polyacetylene chains within the polarizable continuum model

NASA Astrophysics Data System (ADS)

Champagne, Benoı̂t; Mennucci, Benedetta; Cossi, Maurizio; Cammi, Roberto; Tomasi, Jacopo

1998-11-01

The solvent effects upon the longitudinal polarizability ( αL) and second hyperpolarizability ( γL) of small all-trans polyacetylene (PA) chains ranging from C 2H 4 to C 10H 12 have been evaluated at the time-dependent Hartree-Fock (TDHF) level within the framework of the polarizable continuum model. The solvent effects, which correspond to the solvent-induced modifications of the solute properties, result in large increases of the linear and nonlinear responses even for solvents with low dielectric constants. When the dielectric constant is increased, the αL values tend to saturate at values 30%-40% larger than in vacuo, whereas for γL it ranges from 100% to 400% depending upon the nonlinear optical process and the length of the PA chain. These solvent-induced αL and γL enhancements can partially be accounted for by the corresponding decrease of the energy of the lowest optically-allowed electronic excitation. The geometrical parameters of the ground state of the PA chains are almost unaffected by the solvent. This shows that the solvent effects are mainly of electronic nature. In addition, the local field factors, which relate the macroscopic or Maxwell field to the field experienced by the solute, tend towards unity with increasing chain length for the longitudinal PA axis.

The limits of the nuclear landscape explored by the relativistic continuum Hartree–Bogoliubov theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xia, X. W.; Lim, Y.; Zhao, P. W.

The ground-state properties of nuclei with 8more » $$\\leqslant$$ Z $$\\leqslant$$ 120 from the proton drip line to the neutron drip line have been investigated using the relativistic continuum Hartree-Bogoliubov (RCHB) theory with the relativistic density functional PC-PK1. With the effects of the continuum included, there are totally 9035 nuclei predicted to be bound, which largely extends the existing nuclear landscapes predicted with other methods. The calculated binding energies, separation energies, neutron and proton Fermi surfaces, root-mean-square (rms) radii of neutron, proton, matter, and charge distributions, ground-state spins and parities are tabulated. The extension of the nuclear landscape obtained with RCHB is discussed in detail, in particular for the neutron-rich side, in comparison with the relativistic mean field calculations without pairing correlations and also other predicted landscapes. Here, it is found that the coupling between the bound states and the continuum due to the pairing correlations plays an essential role in extending the nuclear landscape. The systematics of the separation energies, radii, densities, potentials and pairing energies of the RCHB calculations are also discussed. In addition, the α-decay energies and proton emitters based on the RCHB calculations are investigated.« less

The limits of the nuclear landscape explored by the relativistic continuum Hartree–Bogoliubov theory

DOE PAGES

Xia, X. W.; Lim, Y.; Zhao, P. W.; ...

2017-11-01

The ground-state properties of nuclei with 8more » $$\\leqslant$$ Z $$\\leqslant$$ 120 from the proton drip line to the neutron drip line have been investigated using the relativistic continuum Hartree-Bogoliubov (RCHB) theory with the relativistic density functional PC-PK1. With the effects of the continuum included, there are totally 9035 nuclei predicted to be bound, which largely extends the existing nuclear landscapes predicted with other methods. The calculated binding energies, separation energies, neutron and proton Fermi surfaces, root-mean-square (rms) radii of neutron, proton, matter, and charge distributions, ground-state spins and parities are tabulated. The extension of the nuclear landscape obtained with RCHB is discussed in detail, in particular for the neutron-rich side, in comparison with the relativistic mean field calculations without pairing correlations and also other predicted landscapes. Here, it is found that the coupling between the bound states and the continuum due to the pairing correlations plays an essential role in extending the nuclear landscape. The systematics of the separation energies, radii, densities, potentials and pairing energies of the RCHB calculations are also discussed. In addition, the α-decay energies and proton emitters based on the RCHB calculations are investigated.« less

Projected quasiparticle theory for molecular electronic structure

NASA Astrophysics Data System (ADS)

Scuseria, Gustavo E.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Samanta, Kousik; Ellis, Jason K.

2011-09-01

We derive and implement symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations and apply them to the molecular electronic structure problem. All symmetries (particle number, spin, spatial, and complex conjugation) are deliberately broken and restored in a self-consistent variation-after-projection approach. We show that the resulting method yields a comprehensive black-box treatment of static correlations with effective one-electron (mean-field) computational cost. The ensuing wave function is of multireference character and permeates the entire Hilbert space of the problem. The energy expression is different from regular HFB theory but remains a functional of an independent quasiparticle density matrix. All reduced density matrices are expressible as an integration of transition density matrices over a gauge grid. We present several proof-of-principle examples demonstrating the compelling power of projected quasiparticle theory for quantum chemistry.

On a Class of Hairy Square Barriers and Gamow Vectors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fernandez-Garcia, N.

The second order Darboux-Gamow transformation is applied to deform square one dimensional barriers in non-relativistic quantum mechanics. The initial and the new 'hairy' potentials have the same transmission probabilities (for the appropriate parameters). In general, new Gamow vectors are constructed as Darboux deformations of the initial ones.

Ab initio Hartree-Fock and density functional theory investigations on the conformational stability, molecular structure and vibrational spectra of 5-chloro-3-(2-(4-methylpiperazin-1-yl)-2-oxoethyl)benzo[d]thiazol-2(3H)-one drug molecule.

PubMed

Taşal, Erol; Kumalar, Mustafa

2012-09-01

In this work, the experimental and theoretical spectra of 5-chloro-3-(2-(4-methylpiperazin-1-yl)-2-oxoethyl)benzo[d]thiazol-2(3H)-one molecule (abbreviated as 5CMOT) are studied. The molecular geometry and vibrational frequencies are calculated in the ground state of molecule using ab initio Hartree-Fock (HF) and Density Function Theory (DFT) methods with 6-311++G(d,p), 6-31G++(d,p), 6-31G(d,p), 6-31G(d) and 6-31G basis sets. Three staggered stable conformers were observed on the torsional potential energy surfaces. The complete assignments were performed on the basis of the total energy distribution (TED) of the vibrational modes calculated. The comparison of the theoretical and experimental geometries of the title compound indicated that the X-ray parameters fairly well agree with the theoretically obtained values for the most stable conformer. The theoretical results showed an excellent agreement with the experimental values. The calculated HOMO and LUMO energies show that the charge transfer occurs within the molecule. Copyright © 2012 Elsevier B.V. All rights reserved.

Wavepacket dynamics and the multi-configurational time-dependent Hartree approach

NASA Astrophysics Data System (ADS)

Manthe, Uwe

2017-06-01

Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient, accurate, and versatile methods for high-dimensional quantum dynamics simulations. Applications range from detailed investigations of polyatomic reaction processes in the gas phase to high-dimensional simulations studying the dynamics of condensed phase systems described by typical solid state physics model Hamiltonians. The present article presents an overview of the different areas of application and provides a comprehensive review of the underlying theory. The concepts and guiding ideas underlying the MCTDH approach and its multi-mode and multi-layer extensions are discussed in detail. The general structure of the equations of motion is highlighted. The representation of the Hamiltonian and the correlated discrete variable representation (CDVR), which provides an efficient multi-dimensional quadrature in MCTDH calculations, are discussed. Methods which facilitate the calculation of eigenstates, the evaluation of correlation functions, and the efficient representation of thermal ensembles in MCTDH calculations are described. Different schemes for the treatment of indistinguishable particles in MCTDH calculations and recent developments towards a unified multi-layer MCTDH theory for systems including bosons and fermions are discussed.

George Gamow: Scientific Amateur and Polymath

NASA Astrophysics Data System (ADS)

Harper, Eamon

George Gamow (1904-1968) was among the first of the many brilliant scientists who forsook Europe for the United States in the early 1930s. Although most were fleeing the fascist imperium of Hitler and Mussolini, Gamow was one of a few who managed to escape the burgeoning despotism of Stalin in the Soviet Union. His early application of quantum mechanics to the atomic nucleus and his subsequent insight into the role played by the physics of the atom and its nucleus in stars, galaxies, and the universe identifies him as a scientist of unusual genius. Gamow displayed a boisterous, infectious - almost Rutherfordian - interest in all aspects of pure science. His interests were broad and his industry prodigious. His scientific output covered areas as diverse as nuclear physics, astrophysics, cosmology, biological genetics, and the fascinating question of the relationship of the large-scale structure and development of the universe to the properties of elementary particles and fields. He also was an immensely imaginative and prolific author of popular expositions on scientific subjects. One who is as well-known for his authorship of the Mr. Tompkins series of science popularizations as for his contributions to the development of the physical consequences of the big-bang theory of the expanding universe and the prediction of the cosmic background radiation must be unique in the scientific pantheon.

Probe-type of superconductivity by impurity in materials with short coherence length: the s-wave and η-wave phases study

NASA Astrophysics Data System (ADS)

Ptok, Andrzej; Jerzy Kapcia, Konrad

2015-04-01

The effects of a single non-magnetic impurity on superconducting states in the Penson-Kolb-Hubbard model have been analyzed. The investigations have been performed within the Hartree-Fock mean field approximation in two steps: (i) the homogeneous system is analysed using the Bogoliubov transformation, whereas (ii) the inhomogeneous system is investigated by self-consistent Bogoliubov-de Gennes equations (with the exact diagonalization and the kernel polynomial method). We analysed both signs of the pair hopping, which correspond to s-wave and η-wave superconductivity. Our results show that an enhancement of the local superconducting gap at the impurity-site occurs for both cases. We obtained that Cooper pairs are scattered (at the impurity site) into the states which are from the neighborhoods of the states, which are commensurate ones with the crystal lattice. Additionally, in the η-phase there are peaks in the local-energy gap (in momentum space), which are connected with long-range oscillations in the spatial distribution of the energy gap, superconducting order parameter (SOP), as well as effective pairing potential. Our results can be contrasted with the experiment and predicts how to experimentally differentiate these two different symmetries of SOP by the scanning tunneling microscopy technique.

Calculation of the vibrational excited states of malonaldehyde and their tunneling splittings with the multi-configuration time-dependent Hartree method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schröder, Markus, E-mail: Markus.Schroeder@pci.uni-heidelberg.de; Meyer, Hans-Dieter, E-mail: Hans-Dieter.Meyer@pci.uni-heidelberg.de

2014-07-21

We report energies and tunneling splittings of vibrational excited states of malonaldehyde which have been obtained using full dimensional quantum mechanical calculations. To this end we employed the multi configuration time-dependent Hartree method. The results have been obtained using a recently published potential energy surface [Y. Wang, B. J. Braams, J. M. Bowman, S. Carter, and D. P. Tew, J. Chem. Phys. 128, 224314 (2008)] which has been brought into a suitable form by a modified version of the n-mode representation which was used with two different arrangements of coordinates. The relevant terms of the expansion have been identified withmore » a Metropolis algorithm and a diffusion Monte-Carlo technique, respectively.« less

Self-consistent description of the SHFB equations for 112Sn

NASA Astrophysics Data System (ADS)

Ghafouri, M.; Sadeghi, H.; Torkiha, M.

2018-03-01

The Hartree-Fock (HF) method is an excellent approximation of the closed shell magic nuclei. Pair correlation is essential for the description of open shell nuclei and has been derived for even-even, odd-odd and even-odd nuclei. These effects are reported by Hartree-Fock with BCS (HFBCS) or Hartree-Fock-Bogolyubov (HFB). These issues have been investigated, especially in the nuclear charts, and such studies have been compared with the observed information. We compute observations such as total binding energy, charge radius, densities, separation energies, pairing gaps and potential energy surfaces for neutrons and protons, and compare them with experimental data and the result of the spherical codes. In spherical even-even neutron-rich nuclei are considered in the Skyrme-Hartree-Fock-Bogolyubov (SHFB) method with density-dependent pairing interaction. Zero-range density-dependent interactions is used in the pairing channel. We solve SHF or SHFB equations in the spatial coordinates with spherical symmetry for tin isotopes such as 112Sn. The numerical accuracy of solving equations in the coordinate space is much greater than the fundamental extensions, which yields almost precise results.

Tables Of Gaussian-Type Orbital Basis Functions

NASA Technical Reports Server (NTRS)

Partridge, Harry

1992-01-01

NASA technical memorandum contains tables of estimated Hartree-Fock wave functions for atoms lithium through neon and potassium through krypton. Sets contain optimized Gaussian-type orbital exponents and coefficients, and near Hartree-Fock quality. Orbital exponents optimized by minimizing restricted Hartree-Fock energy via scaled Newton-Raphson scheme in which Hessian evaluated numerically by use of analytically determined gradients.

Calculation of yrast spectra in the doubly even cadmium isotopes

NASA Astrophysics Data System (ADS)

Khosa, S. K.; Mattu, P. K.

1991-02-01

The observed systematics of the low-lying states in 98-110Cd nuclei and the high-spin yrast spectra with Jπmax<=14+ are examined by carrying out Hartree-Fock-Bogoliubov calculations employing a pairing-plus-quadrupole-quadrupole effective interaction operating in a reasonably large valence space outside an inert 80Zr core. Our calculations reveal that the systematics of the low-lying yrast states in 98-110Cd are intricately linked with the deformation producing tendency of the n-p interaction when operating between spin-orbit-partner (SOP) orbits. Our results indicate that such systematics depend crucially on the simultaneous increase of relative occupation probabilities of the (d5/2)-proton and (d3/2)-neutron orbits in the 98-100Cd isotopes.

Unconventional minimal subtraction and Bogoliubov-Parasyuk-Hepp-Zimmermann method: Massive scalar theory and critical exponents

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carvalho, Paulo R. S.; Leite, Marcelo M.

2013-09-15

We introduce a simpler although unconventional minimal subtraction renormalization procedure in the case of a massive scalar λφ{sup 4} theory in Euclidean space using dimensional regularization. We show that this method is very similar to its counterpart in massless field theory. In particular, the choice of using the bare mass at higher perturbative order instead of employing its tree-level counterpart eliminates all tadpole insertions at that order. As an application, we compute diagrammatically the critical exponents η and ν at least up to two loops. We perform an explicit comparison with the Bogoliubov-Parasyuk-Hepp-Zimmermann (BPHZ) method at the same loop order,more » show that the proposed method requires fewer diagrams and establish a connection between the two approaches.« less

The trust-region self-consistent field method in Kohn-Sham density-functional theory.

PubMed

Thøgersen, Lea; Olsen, Jeppe; Köhn, Andreas; Jørgensen, Poul; Sałek, Paweł; Helgaker, Trygve

2005-08-15

The trust-region self-consistent field (TRSCF) method is extended to the optimization of the Kohn-Sham energy. In the TRSCF method, both the Roothaan-Hall step and the density-subspace minimization step are replaced by trust-region optimizations of local approximations to the Kohn-Sham energy, leading to a controlled, monotonic convergence towards the optimized energy. Previously the TRSCF method has been developed for optimization of the Hartree-Fock energy, which is a simple quadratic function in the density matrix. However, since the Kohn-Sham energy is a nonquadratic function of the density matrix, the local energy functions must be generalized for use with the Kohn-Sham model. Such a generalization, which contains the Hartree-Fock model as a special case, is presented here. For comparison, a rederivation of the popular direct inversion in the iterative subspace (DIIS) algorithm is performed, demonstrating that the DIIS method may be viewed as a quasi-Newton method, explaining its fast local convergence. In the global region the convergence behavior of DIIS is less predictable. The related energy DIIS technique is also discussed and shown to be inappropriate for the optimization of the Kohn-Sham energy.

Majorana neutrinos in the seesaw mechanism and Bogoliubov quasiparticles

NASA Astrophysics Data System (ADS)

Fujikawa, Kazuo; Tureanu, Anca

2018-03-01

The idea that the Majorana neutrino should be identified as a Bogoliubov quasiparticle is applied to the seesaw mechanism for the three generations of neutrinos in the Standard Model. A relativistic analog of the Bogoliubov transformation in the present context is a C P -preserving canonical transformation but modifies charge conjugation properties in such a way that the C-noninvariant fermion number-violating term (condensate) is converted to a Dirac mass term. Puzzling aspects associated with the charge conjugation of chiral Weyl fermions are clarified.

Role of deformation in odd-even staggering in reaction cross sections for 30,31,32Ne and 36,37,38Mg isotopes

NASA Astrophysics Data System (ADS)

Urata, Y.; Hagino, K.; Sagawa, H.

2017-12-01

We discuss the role of pairing antihalo effect in the observed odd-even staggering in reaction cross sections for 30,31,32Ne and 36,37,38Mg isotopes by taking into account the ground-state deformation of these nuclei. To this end, we construct the ground-state density for the Ne,3130 and Mg,3736 nuclei based on a deformed Woods-Saxon potential, while for the 32Ne and 38Mg nuclei we also take into account the pairing correlation using the Hartree-Fock-Bogoliubov method. We demonstrate that, when the one-neutron separation energy is small for the odd-mass nuclei, a significant odd-even staggering still appears even with finite deformation, although the degree of staggering is somewhat reduced compared to the spherical case. This implies that the pairing antihalo effect in general plays an important role in generating the odd-even staggering in reaction cross sections for weakly bound nuclei.

Fast and accurate 3D tensor calculation of the Fock operator in a general basis

NASA Astrophysics Data System (ADS)

Khoromskaia, V.; Andrae, D.; Khoromskij, B. N.

2012-11-01

The present paper contributes to the construction of a “black-box” 3D solver for the Hartree-Fock equation by the grid-based tensor-structured methods. It focuses on the calculation of the Galerkin matrices for the Laplace and the nuclear potential operators by tensor operations using the generic set of basis functions with low separation rank, discretized on a fine N×N×N Cartesian grid. We prove the Ch2 error estimate in terms of mesh parameter, h=O(1/N), that allows to gain a guaranteed accuracy of the core Hamiltonian part in the Fock operator as h→0. However, the commonly used problem adapted basis functions have low regularity yielding a considerable increase of the constant C, hence, demanding a rather large grid-size N of about several tens of thousands to ensure the high resolution. Modern tensor-formatted arithmetics of complexity O(N), or even O(logN), practically relaxes the limitations on the grid-size. Our tensor-based approach allows to improve significantly the standard basis sets in quantum chemistry by including simple combinations of Slater-type, local finite element and other basis functions. Numerical experiments for moderate size organic molecules show efficiency and accuracy of grid-based calculations to the core Hamiltonian in the range of grid parameter N3˜1015.

Self-consistent collective coordinate for reaction path and inertial mass

NASA Astrophysics Data System (ADS)

Wen, Kai; Nakatsukasa, Takashi

2016-11-01

We propose a numerical method to determine the optimal collective reaction path for a nucleus-nucleus collision, based on the adiabatic self-consistent collective coordinate (ASCC) method. We use an iterative method, combining the imaginary-time evolution and the finite amplitude method, for the solution of the ASCC coupled equations. It is applied to the simplest case, α -α scattering. We determine the collective path, the potential, and the inertial mass. The results are compared with other methods, such as the constrained Hartree-Fock method, Inglis's cranking formula, and the adiabatic time-dependent Hartree-Fock (ATDHF) method.

Electric dipole transitions for four-times ionized cerium (Ce V)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Usta, Betül Karaçoban, E-mail: bkaracoban@sakarya.edu.tr; Akgün, Elif, E-mail: elif.akgun@ogr.sakarya.edu.tr; Alparslan, Büşra, E-mail: busra.alparslan1@ogr.sakarya.edu.tr

2016-03-25

We have calculated the transition parameters, such as wavelengths, oscillator strengths, and transition probabilities (or rates), for the electric dipole (E1) transitions in four-times ionized cerium (Ce V, Z = 58) by using the multiconfiguration Hartree-Fock method within the framework of Breit-Pauli (MCHF+BP) relativistic corrections and the relativistic Hartree-Fock (HFR) method. The obtained results have been compared with other works available in literature. A discussion of these calculations for Ce V in this study has also been in view of the MCHF+BP and HFR methods.

Shell-model method for Gamow-Teller transitions in heavy deformed odd-mass nuclei

NASA Astrophysics Data System (ADS)

Wang, Long-Jun; Sun, Yang; Ghorui, Surja K.

2018-04-01

A shell-model method for calculating Gamow-Teller (GT) transition rates in heavy deformed odd-mass nuclei is presented. The method is developed within the framework of the projected shell model. To implement the computation requirement when many multi-quasiparticle configurations are included in the basis, a numerical advancement based on the Pfaffian formula is introduced. With this new many-body technique, it becomes feasible to perform state-by-state calculations for the GT nuclear matrix elements of β -decay and electron-capture processes, including those at high excitation energies in heavy nuclei which are usually deformed. The first results, β- decays of the well-deformed A =153 neutron-rich nuclei, are shown as the example. The known log(f t ) data corresponding to the B (GT- ) decay rates of the ground state of 153Nd to the low-lying states of 153Pm are well described. It is further shown that the B (GT) distributions can have a strong dependence on the detailed microscopic structure of relevant states of both the parent and daughter nuclei.

Nuclear Mass Predictions within the Skyrme HFB Theory

NASA Astrophysics Data System (ADS)

Samyn, M.; Goriely, S.; Pearson, J. M.

2005-05-01

To increase the reliability of predictions of highly neutron-rich nuclear masses we systematically analyze the sensitivity of Hartree-Fock-Bogoliubov (HFB) mass formulae to various physical inputs, such as a density dependence of the pairing interaction, a low effective mass, the particle-number projection, the symmetry energy, … We typically use a 10-parameter Skyrme force and a 4-parameter δ-function pairing force. The 14 degrees of freedom are adjusted to the masses of all measured nuclei with N,Z ⩾ 8 given in the 2001 and 2003 Audi et al. compilations. The masses of light and proton-rich nuclei are corrected by a 4-parameter phenomenological Wigner term. With more than ten such parameter sets complete mass tables are constructed, going from one drip line to the other, up to Z = 120.

Charge renormalization at the large-D limit for N-electron atoms and weakly bound systems

NASA Astrophysics Data System (ADS)

Kais, S.; Bleil, R.

1995-05-01

We develop a systematic way to determine an effective nuclear charge ZRD such that the Hartree-Fock results will be significantly closer to the exact energies by utilizing the analytically known large-D limit energies. This method yields an expansion for the effective nuclear charge in powers of (1/D), which we have evaluated to the first order. This first order approximation to the desired effective nuclear charge has been applied to two-electron atoms with Z=2-20, and weakly bound systems such as H-. The errors for the two-electron atoms when compared with exact results were reduced from ˜0.2% for Z=2 to ˜0.002% for large Z. Although usual Hartree-Fock calculations for H- show this to be unstable, our results reduce the percent error of the Hartree-Fock energy from 7.6% to 1.86% and predicts the anion to be stable. For N-electron atoms (N=3-18, Z=3-28), using only the zeroth order approximation for the effective charge significantly reduces the error of Hartree-Fock calculations and recovers more than 80% of the correlation energy.

Multiconfiguration Dirac-Hartree-Fock energy levels, oscillator strengths, transition probabilities, hyperfine constants and Landé g-factor of intermediate Rydberg series in neutral argon atom

NASA Astrophysics Data System (ADS)

Salah, Wa'el; Hassouneh, Ola

2017-04-01

We computed the energy levels, oscillator strengths f_{ij}, the radiative transition rates A_{ij}, the Landé g -factor, the magnetic dipole moment and the electric quadrupole hyperfine constants of the intermediate Rydberg series ns [k]J ( 4 ≤ n ≤ 6), nd [k]J (3 ≤ n ≤ 4), np [k]J (4 ≤ n ≤ 5) relative to the ground state 3p6 1S0 for neutral argon atom spectra. The values are obtained in the framework of the multiconfiguration Dirac-Hartree-Fock (MCDHF) approach. In this approach, Breit interaction, leading quantum electrodynamics (QED) effects and self-energy correction are taken into account. Moreover, these spectroscopic parameters have been calculated for many levels belonging to the configuration 3p54s, 3p55s, 3p56s, 3p53d, 3p54d, 3p54p, 3p55p as well as for transitions between levels 3p54s-3p54p, 3p54p-3p53d, 3p54p-3p55s, 3p55s-3p55p and 3p55p-3p56s. The large majority of the lines from the 4p-5s and 4p-3d, 5s-5p and 5p-6s transition arrays have been observed and the calculations are consistent with the J -file-sum rule. The obtained theoretical values are compared with previous experimental and theoretical data available in the literature. An overall satisfactory agreement is noticed allowing assessing the reliability of our data.

Relativistic extended Thomas-Fermi calculations with exchange term contributions

NASA Astrophysics Data System (ADS)

Haddad, S.; Weigel, M. K.

1994-10-01

In this investigation we present self-consistent relativistic extended Thomas-Fermi (ETF) and extended Thomas-Fermi-Fock (ETFF) approaches, derived from the semiclassical treatment of the relativistic nuclear Hartree-Fock problem. The approximations are used to describe the ground-state properties of finite nuclei. The resulting equations are solved numerically for several one-boson-exchange (OBE) lagrangians. The results are discussed and compared with the outcome of full quantal Hartree and Hartree-Fock calculations, other semiclassical treatments and experimental data.

Roothaan approach in the thermodynamic limit

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gutierrez, G.; Plastino, A.

1982-02-01

A systematic method for the solution of the Hartree-Fock equations in the thermodynamic limit is presented. The approach is seen to be a natural extension of the one usually employed in the finite-fermion case, i.e., that developed by Roothaan. The new techniques developed here are applied, as an example, to neutron matter, employing the so-called V/sub 1/ Bethe homework potential. The results obtained are, by far, superior to those that the ordinary plane-wave Hartree-Fock theory yields.

Quantum shielding effects on the Gamow penetration factor for nuclear fusion reaction in quantum plasmas

NASA Astrophysics Data System (ADS)

Lee, Myoung-Jae; Jung, Young-Dae

2017-01-01

The quantum shielding effects on the nuclear fusion reaction process are investigated in quantum plasmas. The closed expression of the classical turning point for the Gamow penetration factor in quantum plasmas is obtained by the Lambert W-function. The closed expressions of the Gamow penetration factor and the cross section for the nuclear fusion reaction in quantum plasmas are obtained as functions of the plasmon energy and the relative kinetic energy by using the effective interaction potential with the WKB analysis. It is shown that the influence of quantum screening suppresses the Sommerfeld reaction factor. It is also shown that the Gamow penetration factor increases with an increase of the plasmon energy. It is also shown that the quantum shielding effect enhances the deuterium formation by the proton-proton reaction in quantum plasmas. In addition, it is found that the energy dependences on the reaction cross section and the Gamow penetration factor are more significant in high plasmon-energy domains.

A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations for large systems

NASA Astrophysics Data System (ADS)

Kruse, Holger; Grimme, Stefan

2012-04-01

A semi-empirical counterpoise-type correction for basis set superposition error (BSSE) in molecular systems is presented. An atom pair-wise potential corrects for the inter- and intra-molecular BSSE in supermolecular Hartree-Fock (HF) or density functional theory (DFT) calculations. This geometrical counterpoise (gCP) denoted scheme depends only on the molecular geometry, i.e., no input from the electronic wave-function is required and hence is applicable to molecules with ten thousands of atoms. The four necessary parameters have been determined by a fit to standard Boys and Bernadi counterpoise corrections for Hobza's S66×8 set of non-covalently bound complexes (528 data points). The method's target are small basis sets (e.g., minimal, split-valence, 6-31G*), but reliable results are also obtained for larger triple-ζ sets. The intermolecular BSSE is calculated by gCP within a typical error of 10%-30% that proves sufficient in many practical applications. The approach is suggested as a quantitative correction in production work and can also be routinely applied to estimate the magnitude of the BSSE beforehand. The applicability for biomolecules as the primary target is tested for the crambin protein, where gCP removes intramolecular BSSE effectively and yields conformational energies comparable to def2-TZVP basis results. Good mutual agreement is also found with Jensen's ACP(4) scheme, estimating the intramolecular BSSE in the phenylalanine-glycine-phenylalanine tripeptide, for which also a relaxed rotational energy profile is presented. A variety of minimal and double-ζ basis sets combined with gCP and the dispersion corrections DFT-D3 and DFT-NL are successfully benchmarked on the S22 and S66 sets of non-covalent interactions. Outstanding performance with a mean absolute deviation (MAD) of 0.51 kcal/mol (0.38 kcal/mol after D3-refit) is obtained at the gCP-corrected HF-D3/(minimal basis) level for the S66 benchmark. The gCP-corrected B3LYP-D3/6-31G* model

Bose-Einstein condensation in atomic alkali gases

NASA Astrophysics Data System (ADS)

Dodd, Robert J.

1998-05-01

I present a review of the time-independent Gross-Pitaevskii (GP), Bogoliubov, and finite-temperature Hartree-Fock-Bogoliubov (HFB) mean-field theories used to study trapped, Bose-Einstein condensed alkali gases. Numerical solutions of the (zero-temperature) GP equation are presented for attractive (negative scattering length) and repulsive (positive scattering length) interactions. Comparison is made with the Thomas-Fermi and (variational) trial wavefunction appr oximations that are used in the literature to study condensed gases. Numerical calculations of the (zero-temperature) Bogoliubov quasi-particle excitation frequencies are found to be in excellent agreement with the experimental results. The finite-temperature properties of condensed gases are examined using the Popov approximation (of the HFB theory) and a simple two-gas model. Specific, quantitative comparisons are made with experimental results for finite-temperature excitation frequencies. Qualitative comparisons are made between the results of the Popov approximation, two-gas model, and other published models for condensate fraction and thermal density distribution. The time-independent mean-field theories are found to be in excellent agreement with experimental results at relatively low temperatures (high condensate fractions). However, at higher temperatures (and condensate fractions of less than 50%) there are significant discrepancies between experimental data and theoretical calculations. This work was undertaken at the University of Maryland at College Park and was supported in part by the National Science Foundation (PHY-9601261) and the U.S. Office of Naval Research.

Nuclear Mass Predictions within the Skyrme HFB Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Samyn, M.; Goriely, S.; Pearson, J.M.

To increase the reliability of predictions of highly neutron-rich nuclear masses we systematically analyze the sensitivity of Hartree-Fock-Bogoliubov (HFB) mass formulae to various physical inputs, such as a density dependence of the pairing interaction, a low effective mass, the particle-number projection, the symmetry energy, ... We typically use a 10-parameter Skyrme force and a 4-parameter {delta}-function pairing force. The 14 degrees of freedom are adjusted to the masses of all measured nuclei with N,Z {>=} 8 given in the 2001 and 2003 Audi et al. compilations. The masses of light and proton-rich nuclei are corrected by a 4-parameter phenomenological Wignermore » term. With more than ten such parameter sets complete mass tables are constructed, going from one drip line to the other, up to Z = 120.« less

Revised and extended level scheme of the doubly-odd nucleus {sup 188}Ir

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jungclaus, A.; Modamio, V.; Egido, J. L.

2008-02-15

High-spin states in the doubly odd Z=77 nucleus {sup 188}Ir were studied using the reaction {sup 186}W({sup 7}Li, 5n) at 59 MeV and the GASP spectrometer for {gamma}-ray detection. The level structures recently suggested to be built on the known 4.1(3) ms isomeric state of this nucleus have been considerably revised and extended and an isomer with a lifetime of 17.7(2) ns has been identified within the main decay sequence. In addition two rotational bands built on low spin states below the ms isomer have been observed for the first time. The basic features of the excitation scheme of {supmore » 188}Ir are discussed within the Hartree-Fock-Bogoliubov theory within the Lipkin-Nogami approach with the finite-range density-dependent Gogny force.« less

Pairing in exotic neutron-rich nuclei near the drip line and in the crust of neutron stars

NASA Astrophysics Data System (ADS)

Pastore, A.; Margueron, J.; Schuck, P.; Viñas, X.

2013-09-01

Exotic and drip-line nuclei as well as nuclei immersed in a low-density gas of neutrons in the inner crust of neutron stars are systematically investigated with respect to their neutron pairing properties. This is done using Skyrme density-functional and different pairing forces such as a density-dependent contact interaction and a separable form of a finite-range Gogny interaction. Hartree-Fock-Bogoliubov (HFB) and Bardeen-Cooper-Schrieffer (BCS) theories are compared. It is found that neutron pairing is reduced towards the drip line while overcast by strong shell effects. Furthermore, resonances in the continuum can have an important effect counterbalancing the tendency of reduction and leading to a persistence of pairing at the drip line. It is also shown that in these systems the difference between HFB and BCS approaches can be quantitatively large.

Distribution of nuclei in equilibrium stellar matter from the free-energy density in a Wigner-Seitz cell

NASA Astrophysics Data System (ADS)

Grams, G.; Giraud, S.; Fantina, A. F.; Gulminelli, F.

2018-03-01

The aim of the present study is to calculate the nuclear distribution associated at finite temperature to any given equation of state of stellar matter based on the Wigner-Seitz approximation, for direct applications in core-collapse simulations. The Gibbs free energy of the different configurations is explicitly calculated, with special care devoted to the calculation of rearrangement terms, ensuring thermodynamic consistency. The formalism is illustrated with two different applications. First, we work out the nuclear statistical equilibrium cluster distribution for the Lattimer and Swesty equation of state, widely employed in supernova simulations. Secondly, we explore the effect of including shell structure, and consider realistic nuclear mass tables from the Brussels-Montreal Hartree-Fock-Bogoliubov model (specifically, HFB-24). We show that the whole collapse trajectory is dominated by magic nuclei, with extremely spread and even bimodal distributions of the cluster probability around magic numbers, demonstrating the importance of cluster distributions with realistic mass models in core-collapse simulations. Simple analytical expressions are given, allowing further applications of the method to any relativistic or nonrelativistic subsaturation equation of state.

Why does the sign problem occur in evaluating the overlap of HFB wave functions?

NASA Astrophysics Data System (ADS)

Mizusaki, Takahiro; Oi, Makito; Shimizu, Noritaka

2018-04-01

For the overlap matrix element between Hartree-Fock-Bogoliubov states, there are two analytically different formulae: one with the square root of the determinant (the Onishi formula) and the other with the Pfaffian (Robledo's Pfaffian formula). The former formula is two-valued as a complex function, hence it leaves the sign of the norm overlap undetermined (i.e., the so-called sign problem of the Onishi formula). On the other hand, the latter formula does not suffer from the sign problem. The derivations for these two formulae are so different that the reasons are obscured why the resultant formulae possess different analytical properties. In this paper, we discuss the reason why the difference occurs by means of the consistent framework, which is based on the linked cluster theorem and the product-sum identity for the Pfaffian. Through this discussion, we elucidate the source of the sign problem in the Onishi formula. We also point out that different summation methods of series expansions may result in analytically different formulae.

Towards a formal definition of static and dynamic electronic correlations.

PubMed

Benavides-Riveros, Carlos L; Lathiotakis, Nektarios N; Marques, Miguel A L

2017-05-24

Some of the most spectacular failures of density-functional and Hartree-Fock theories are related to an incorrect description of the so-called static electron correlation. Motivated by recent progress in the N-representability problem of the one-body density matrix for pure states, we propose a method to quantify the static contribution to the electronic correlation. By studying several molecular systems we show that our proposal correlates well with our intuition of static and dynamic electron correlation. Our results bring out the paramount importance of the occupancy of the highest occupied natural spin-orbital in such quantification.

DOE Office of Scientific and Technical Information (OSTI.GOV)

San Fabián, J.; Omar, S.; García de la Vega, J. M., E-mail: garcia.delavega@uam.es

The effect of a fraction of Hartree-Fock exchange on the calculated spin-spin coupling constants involving fluorine through a hydrogen bond is analyzed in detail. Coupling constants calculated using wavefunction methods are revisited in order to get high-level calculations using the same basis set. Accurate MCSCF results are obtained using an additive approach. These constants and their contributions are used as a reference for density functional calculations. Within the density functional theory, the Hartree-Fock exchange functional is split in short- and long-range using a modified version of the Coulomb-attenuating method with the SLYP functional as well as with the original B3LYP.more » Results support the difficulties for calculating hydrogen bond coupling constants using density functional methods when fluorine nuclei are involved. Coupling constants are very sensitive to the Hartree-Fock exchange and it seems that, contrary to other properties, it is important to include this exchange for short-range interactions. Best functionals are tested in two different groups of complexes: those related with anionic clusters of type [F(HF){sub n}]{sup −} and those formed by difluoroacetylene and either one or two hydrogen fluoride molecules.« less

Unique Fock quantization of scalar cosmological perturbations

NASA Astrophysics Data System (ADS)

Fernández-Méndez, Mikel; Mena Marugán, Guillermo A.; Olmedo, Javier; Velhinho, José M.

2012-05-01

We investigate the ambiguities in the Fock quantization of the scalar perturbations of a Friedmann-Lemaître-Robertson-Walker model with a massive scalar field as matter content. We consider the case of compact spatial sections (thus avoiding infrared divergences), with the topology of a three-sphere. After expanding the perturbations in series of eigenfunctions of the Laplace-Beltrami operator, the Hamiltonian of the system is written up to quadratic order in them. We fix the gauge of the local degrees of freedom in two different ways, reaching in both cases the same qualitative results. A canonical transformation, which includes the scaling of the matter-field perturbations by the scale factor of the geometry, is performed in order to arrive at a convenient formulation of the system. We then study the quantization of these perturbations in the classical background determined by the homogeneous variables. Based on previous work, we introduce a Fock representation for the perturbations in which: (a) the complex structure is invariant under the isometries of the spatial sections and (b) the field dynamics is implemented as a unitary operator. These two properties select not only a unique unitary equivalence class of representations, but also a preferred field description, picking up a canonical pair of field variables among all those that can be obtained by means of a time-dependent scaling of the matter field (completed into a linear canonical transformation). Finally, we present an equivalent quantization constructed in terms of gauge-invariant quantities. We prove that this quantization can be attained by a mode-by-mode time-dependent linear canonical transformation which admits a unitary implementation, so that it is also uniquely determined.

Unique Fock quantization of a massive fermion field in a cosmological scenario

NASA Astrophysics Data System (ADS)

Cortez, Jerónimo; Elizaga Navascués, Beatriz; Martín-Benito, Mercedes; Mena Marugán, Guillermo A.; Velhinho, José M.

2016-04-01

It is well known that the Fock quantization of field theories in general spacetimes suffers from an infinite ambiguity, owing to the inequivalent possibilities in the selection of a representation of the canonical commutation or anticommutation relations, but also owing to the freedom in the choice of variables to describe the field among all those related by linear time-dependent transformations, including the dependence through functions of the background. In this work we remove this ambiguity (up to unitary equivalence) in the case of a massive Dirac free field propagating in a spacetime with homogeneous and isotropic spatial sections of spherical topology. Two physically reasonable conditions are imposed in order to arrive at this result: (a) The invariance of the vacuum under the spatial isometries of the background, and (b) the unitary implementability of the dynamical evolution that dictates the Dirac equation. We characterize the Fock quantizations with a nontrivial fermion dynamics that satisfy these two conditions. Then, we provide a complete proof of the unitary equivalence of the representations in this class under very mild requirements on the time variation of the background, once a criterion to discern between particles and antiparticles has been set.

Dirac-Fock-Breit-Gaunt calculations for tungsten hexacarbonyl W(CO)6.

PubMed

Malli, Gulzari L

2016-05-21

The first all-electron fully relativistic Dirac-Fock-Breit-Gaunt (DFBG), Dirac-Fock (DF), and nonrelativistic (NR) Hartree-Fock (HF) calculations are reported for octahedral (Oh) tungsten hexacarbonyl W(CO)6. Our DF and NR HF calculations predict atomization energy of 73.76 and 70.33 eV, respectively. The relativistic contribution of ∼3.4 eV to the atomization energy of W(CO)6 is fairly significant. The DF and NR energy for the reaction W + 6CO → W(CO)6 is calculated as -7.90 and -8.86 eV, respectively. The mean bond energy predicted by our NR and DF calculations is 142.5 kJ/mol and 177.5 kJ/mol, respectively, and our predicted DF mean bond energy is in excellent agreement with the experimental value of 179 kJ/mol quoted in the literature. The relativistic effects contribute ∼35 kJ/mol to the mean bond energy and the calculated BSSE is 1.6 kcal/mol, which indicates that the triple zeta basis set used here is fairly good. The mean bond energy and the atomization energy calculated in our DFBG SCF calculations, which include variationally both the relativistic and magnetic Breit effects, is 157.4 kJ/mol and 68.84 eV, respectively. The magnetic Breit effects lead to a decrease of ∼20 kJ/mol and ∼4.9 eV for the mean bond energy and atomization energy, respectively, for W(CO)6. Our calculated magnetic Breit interaction energy of -9.79 eV for the energy of reaction (ΔE) for W + 6CO → W(CO)6 is lower by ∼1.90 eV as compared to the corresponding DF value (ΔE) and contributes significantly to the ΔE. A detailed discussion is presented of electronic structure, bonding, and molecular energy levels at various levels of theory for W(CO)6.

An Extension of the Krieger-Li-Iafrate Approximation to the Optimized-Effective-Potential Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wilson, B.G.

1999-11-11

The Krieger-Li-Iafrate approximation can be expressed as the zeroth order result of an unstable iterative method for solving the integral equation form of the optimized-effective-potential method. By pre-conditioning the iterate a first order correction can be obtained which recovers the bulk of quantal oscillations missing in the zeroth order approximation. A comparison of calculated total energies are given with Krieger-Li-Iafrate, Local Density Functional, and Hyper-Hartree-Fock results for non-relativistic atoms and ions.

Spectroscopic criteria for identification of nuclear tetrahedral and octahedral symmetries: Illustration on a rare earth nucleus

NASA Astrophysics Data System (ADS)

Dudek, J.; Curien, D.; Dedes, I.; Mazurek, K.; Tagami, S.; Shimizu, Y. R.; Bhattacharjee, T.

2018-02-01

We formulate criteria for identification of the nuclear tetrahedral and octahedral symmetries and illustrate for the first time their possible realization in a rare earth nucleus 152Sm. We use realistic nuclear mean-field theory calculations with the phenomenological macroscopic-microscopic method, the Gogny-Hartree-Fock-Bogoliubov approach, and general point-group theory considerations to guide the experimental identification method as illustrated on published experimental data. Following group theory the examined symmetries imply the existence of exotic rotational bands on whose properties the spectroscopic identification criteria are based. These bands may contain simultaneously states of even and odd spins, of both parities and parity doublets at well-defined spins. In the exact-symmetry limit those bands involve no E 2 transitions. We show that coexistence of tetrahedral and octahedral deformations is essential when calculating the corresponding energy minima and surrounding barriers, and that it has a characteristic impact on the rotational bands. The symmetries in question imply the existence of long-lived shape isomers and, possibly, new waiting point nuclei—impacting the nucleosynthesis processes in astrophysics—and an existence of 16-fold degenerate particle-hole excitations. Specifically designed experiments which aim at strengthening the identification arguments are briefly discussed.

Optimized Hypernetted-Chain Solutions for Helium -4 Surfaces and Metal Surfaces

NASA Astrophysics Data System (ADS)

Qian, Guo-Xin

This thesis is a study of inhomogeneous Bose systems such as liquid ('4)He slabs and inhomogeneous Fermi systems such as the electron gas in metal films, at zero temperature. Using a Jastrow-type many-body wavefunction, the ground state energy is expressed by means of Bogoliubov-Born-Green-Kirkwood -Yvon and Hypernetted-Chain techniques. For Bose systems, Euler-Lagrange equations are derived for the one- and two -body functions and systematic approximation methods are physically motivated. It is shown that the optimized variational method includes a self-consistent summation of ladder- and ring-diagrams of conventional many-body theory. For Fermi systems, a linear potential model is adopted to generate the optimized Hartree-Fock basis. Euler-Lagrange equations are derived for the two-body correlations which serve to screen the strong bare Coulomb interaction. The optimization of the pair correlation leads to an expression of correlation energy in which the state averaged RPA part is separated. Numerical applications are presented for the density profile and pair distribution function for both ('4)He surfaces and metal surfaces. Both the bulk and surface energies are calculated in good agreement with experiments.

Global Futures: a multithreaded execution model for Global Arrays-based applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chavarría-Miranda, Daniel; Krishnamoorthy, Sriram; Vishnu, Abhinav

2012-05-31

We present Global Futures (GF), an execution model extension to Global Arrays, which is based on a PGAS-compatible Active Message-based paradigm. We describe the design and implementation of Global Futures and illustrate its use in a computational chemistry application benchmark (Hartree-Fock matrix construction using the Self-Consistent Field method). Our results show how we used GF to increase the scalability of the Hartree-Fock matrix build to up to 6,144 cores of an Infiniband cluster. We also show how GF's multithreaded execution has comparable performance to the traditional process-based SPMD model.

Examining empirical evidence of the effect of superfluidity on the fusion barrier

NASA Astrophysics Data System (ADS)

Scamps, Guillaume

2018-04-01

Background: Recent time-dependent Hartree-Fock-Bogoliubov (TDHFB) calculations predict that superfluidity enhances fluctuations of the fusion barrier. This effect is not fully understood and not yet experimentally revealed. Purpose: The goal of this study is to empirically investigate the effect of superfluidity on the distribution width of the fusion barrier. Method: Two new methods are proposed in the present study. First, the local regression method is introduced and used to determine the barrier distribution. The second method, which requires only the calculation of an integral of the cross section, is developed to determine accurately the fluctuations of the barrier. This integral method, showing the best performance, is systematically applied to 115 fusion reactions. Results: Fluctuations of the barrier for open-shell systems are, on average, larger than those for magic or semimagic nuclei. This is due to the deformation and the superfluidity. To disentangle these two effects, a comparison is made between the experimental width and the width estimated from a model that takes into account the tunneling, the deformation, and the vibration effect. This study reveals that superfluidity enhances the fusion barrier width. Conclusions: This analysis shows that the predicted effect of superfluidity on the width of the barrier is real and is of the order of 1 MeV.

Straightening the Hierarchical Staircase for Basis Set Extrapolations: A Low-Cost Approach to High-Accuracy Computational Chemistry

NASA Astrophysics Data System (ADS)

Varandas, António J. C.

2018-04-01

Because the one-electron basis set limit is difficult to reach in correlated post-Hartree-Fock ab initio calculations, the low-cost route of using methods that extrapolate to the estimated basis set limit attracts immediate interest. The situation is somewhat more satisfactory at the Hartree-Fock level because numerical calculation of the energy is often affordable at nearly converged basis set levels. Still, extrapolation schemes for the Hartree-Fock energy are addressed here, although the focus is on the more slowly convergent and computationally demanding correlation energy. Because they are frequently based on the gold-standard coupled-cluster theory with single, double, and perturbative triple excitations [CCSD(T)], correlated calculations are often affordable only with the smallest basis sets, and hence single-level extrapolations from one raw energy could attain maximum usefulness. This possibility is examined. Whenever possible, this review uses raw data from second-order Møller-Plesset perturbation theory, as well as CCSD, CCSD(T), and multireference configuration interaction methods. Inescapably, the emphasis is on work done by the author's research group. Certain issues in need of further research or review are pinpointed.

Spectral properties from Matsubara Green's function approach: Application to molecules

NASA Astrophysics Data System (ADS)

Schüler, M.; Pavlyukh, Y.

2018-03-01

We present results for many-body perturbation theory for the one-body Green's function at finite temperatures using the Matsubara formalism. Our method relies on the accurate representation of the single-particle states in standard Gaussian basis sets, allowing to efficiently compute, among other observables, quasiparticle energies and Dyson orbitals of atoms and molecules. In particular, we challenge the second-order treatment of the Coulomb interaction by benchmarking its accuracy for a well-established test set of small molecules, which includes also systems where the usual Hartree-Fock treatment encounters difficulties. We discuss different schemes how to extract quasiparticle properties and assess their range of applicability. With an accurate solution and compact representation, our method is an ideal starting point to study electron dynamics in time-resolved experiments by the propagation of the Kadanoff-Baym equations.

The Gamow-state description of the decay energy spectrum of neutron-unbound 25O

NASA Astrophysics Data System (ADS)

Id Betan, R. M.; de la Madrid, R.

2018-02-01

We show the feasibility of calculating the decay energy spectrum of neutron emitting nuclei within the Gamow-state description of resonances by obtaining the decay energy spectrum of 25O. We model this nucleus as a valence neutron interacting with an 24O inert core, and we obtain the resulting resonant energies, widths and decay energy spectra for the ground and first excited states. We also discuss the similarities and differences between the decay energy spectrum of a Gamow state and the Breit-Wigner distribution with energy-dependent width.

Integral processing in beyond-Hartree-Fock calculations

NASA Technical Reports Server (NTRS)

Taylor, P. R.

1986-01-01

The increasing rate at which improvements in processing capacity outstrip improvements in input/output performance of large computers has led to recent attempts to bypass generation of a disk-based integral file. The direct self-consistent field (SCF) method of Almlof and co-workers represents a very successful implementation of this approach. This paper is concerned with the extension of this general approach to configuration interaction (CI) and multiconfiguration-self-consistent field (MCSCF) calculations. After a discussion of the particular types of molecular orbital (MO) integrals for which -- at least for most current generation machines -- disk-based storage seems unavoidable, it is shown how all the necessary integrals can be obtained as matrix elements of Coulomb and exchange operators that can be calculated using a direct approach. Computational implementations of such a scheme are discussed.

Molecular modeling studies of interactions between sodium polyacrylate polymer and calcite surface

NASA Astrophysics Data System (ADS)

Ylikantola, A.; Linnanto, J.; Knuutinen, J.; Oravilahti, A.; Toivakka, M.

2013-07-01

The interactions between calcite pigment and sodium polyacrylate dispersing agent, widely used in papermaking as paper coating components, were investigated using classical force field and quantum chemical approaches. The objective was to understand interactions between the calcite surface and sodium polyacrylate polymer at 300 K using molecular dynamics simulations. A quantum mechanical ab initio Hartree-Fock method was also used to obtain detailed information about the sodium polyacrylate polymer structure. The effect of water molecules (moisture) on the interactions was also examined. Calculations showed that molecular weight, branching and the orientation of sodium polyacrylate polymers influence the interactions between the calcite surface and the polymer. The force field applied, and also water molecules, were found to have an impact on all systems studied. Ab initio Hartree-Fock calculations indicated that there are two types of coordination between sodium atoms and carboxylate groups of the sodium polyacrylate polymer, inter- and intra-carboxylate group coordination. In addition, ab initio Hartree-Fock calculations of the structure of the sodium polyacrylate polymer produced important information regarding interactions between the polymers and carboxylated styrene-butadiene latex particles.

Bogoliubov excitations in a Kronig-Penney potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Danshita, Ippei; Kurihara, Susumu; Tsuchiya, Shunji

2005-11-15

With use of the Kronig-Penney model, we study the excitation spectrum of a Bose-Einstein condensate in a one-dimensional periodic potential. We solve the Bogoliubov equations analytically and obtain the band structure of the excitation spectrum for arbitrary values of the lattice depth. We find that the excitation spectrum is gapless and linear at low energies, and that it is due to the anomalous tunneling of low-energy excitations, predicted by Kagan et al.

Contour-time approach to the Bose-Hubbard model in the strong coupling regime: Studying two-point spatio-temporal correlations at the Hartree-Fock-Bogoliubov level

NASA Astrophysics Data System (ADS)

Fitzpatrick, Matthew R. C.; Kennett, Malcolm P.

2018-05-01

We develop a formalism that allows the study of correlations in space and time in both the superfluid and Mott insulating phases of the Bose-Hubbard Model. Specifically, we obtain a two particle irreducible effective action within the contour-time formalism that allows for both equilibrium and out of equilibrium phenomena. We derive equations of motion for both the superfluid order parameter and two-point correlation functions. To assess the accuracy of this formalism, we study the equilibrium solution of the equations of motion and compare our results to existing strong coupling methods as well as exact methods where possible. We discuss applications of this formalism to out of equilibrium situations.

Inequivalent coherent state representations in group field theory

NASA Astrophysics Data System (ADS)

Kegeles, Alexander; Oriti, Daniele; Tomlin, Casey

2018-06-01

In this paper we propose an algebraic formulation of group field theory and consider non-Fock representations based on coherent states. We show that we can construct representations with an infinite number of degrees of freedom on compact manifolds. We also show that these representations break translation symmetry. Since such representations can be regarded as quantum gravitational systems with an infinite number of fundamental pre-geometric building blocks, they may be more suitable for the description of effective geometrical phases of the theory.

Predicted NMR properties of noble gas hydride cations RgH +

NASA Astrophysics Data System (ADS)

Cukras, Janusz; Sadlej, Joanna

2008-12-01

The NMR shielding constants and, for the first time, the spin-spin coupling constants of Rg and H in RgH + compounds for Rg = Ne, Ar, Kr, Xe have been investigated by non-relativistic Hartree-Fock (HF) and relativistic Dirac-Hartree-Fock (DHF) methods. Electron-correlation effects have been furthermore calculated using SOPPA and CCSD at the non-relativistic level. The correlation effects are large on both parameters and opposite to the relativistic effects. The results indicate that both the relativistic and correlation effects need to be taken into account in a quantitative computations, especially in the case of the spin-spin coupling constants.

Asymptotic behavior and interpretation of virtual states: The effects of confinement and of basis sets

NASA Astrophysics Data System (ADS)

Boffi, Nicholas M.; Jain, Manish; Natan, Amir

2016-02-01

A real-space high order finite difference method is used to analyze the effect of spherical domain size on the Hartree-Fock (and density functional theory) virtual eigenstates. We show the domain size dependence of both positive and negative virtual eigenvalues of the Hartree-Fock equations for small molecules. We demonstrate that positive states behave like a particle in spherical well and show how they approach zero. For the negative eigenstates, we show that large domains are needed to get the correct eigenvalues. We compare our results to those of Gaussian basis sets and draw some conclusions for real-space, basis-sets, and plane-waves calculations.

Elongation cutoff technique armed with quantum fast multipole method for linear scaling.

PubMed

Korchowiec, Jacek; Lewandowski, Jakub; Makowski, Marcin; Gu, Feng Long; Aoki, Yuriko

2009-11-30

A linear-scaling implementation of the elongation cutoff technique (ELG/C) that speeds up Hartree-Fock (HF) self-consistent field calculations is presented. The cutoff method avoids the known bottleneck of the conventional HF scheme, that is, diagonalization, because it operates within the low dimension subspace of the whole atomic orbital space. The efficiency of ELG/C is illustrated for two model systems. The obtained results indicate that the ELG/C is a very efficient sparse matrix algebra scheme. Copyright 2009 Wiley Periodicals, Inc.

Computational studies of molecular charge transfer complexes of heterocyclic 4-methylepyridine-2-azomethine-p-benzene derivatives with picric acid and m-dinitrobenzene.

PubMed

Al-Harbi, L M; El-Mossalamy, E H; Obaid, A Y; Al-Jedaani, A H

2014-01-01

Charge transfer complexes of substituted aryl Schiff bases as donors with picric acid and m-dinitrobenzene as acceptors were investigated by using computational analysis calculated by Configuration Interaction Singles Hartree-Fock (CIS-HF) at standard 6-31G∗ basis set and Time-Dependent Density-Functional Theory (TD-DFT) levels of theory at standard 6-31G∗∗ basis set, infrared spectra, visible and nuclear magnetic resonance spectra are investigated. The optimized geometries and vibrational frequencies were evaluated. The energy and oscillator strength were calculated by Configuration Interaction Singles Hartree-Fock method (CIS-HF) and the Time-Dependent Density-Functional Theory (TD-DFT) results. Electronic properties, such as HOMO and LUMO energies and band gaps of CTCs set, were studied by the Time-Dependent density functional theory with Becke-Lee-Young-Parr (B3LYP) composite exchange correlation functional and by Configuration Interaction Singles Hartree-Fock method (CIS-HF). The ionization potential Ip and electron affinity EA were calculated by PM3, HF and DFT methods. The columbic force was calculated theoretically by using (CIS-HF and TD-DFT) methods. This study confirms that the theoretical calculation of vibrational frequencies for (aryl Schiff bases--(m-dinitrobenzene and picric acid)) complexes are quite useful for the vibrational assignment and for predicting new vibrational frequencies. Copyright © 2013 Elsevier B.V. All rights reserved.

Analytic gradient for second order Møller-Plesset perturbation theory with the polarizable continuum model based on the fragment molecular orbital method.

PubMed

Nagata, Takeshi; Fedorov, Dmitri G; Li, Hui; Kitaura, Kazuo

2012-05-28

A new energy expression is proposed for the fragment molecular orbital method interfaced with the polarizable continuum model (FMO/PCM). The solvation free energy is shown to be more accurate on a set of representative polypeptides with neutral and charged residues, in comparison to the original formulation at the same level of the many-body expansion of the electrostatic potential determining the apparent surface charges. The analytic first derivative of the energy with respect to nuclear coordinates is formulated at the second-order Møller-Plesset (MP2) perturbation theory level combined with PCM, for which we derived coupled perturbed Hartree-Fock equations. The accuracy of the analytic gradient is demonstrated on test calculations in comparison to numeric gradient. Geometry optimization of the small Trp-cage protein (PDB: 1L2Y) is performed with FMO/PCM/6-31(+)G(d) at the MP2 and restricted Hartree-Fock with empirical dispersion (RHF/D). The root mean square deviations between the FMO optimized and NMR experimental structure are found to be 0.414 and 0.426 Å for RHF/D and MP2, respectively. The details of the hydrogen bond network in the Trp-cage protein are revealed.

Analytic gradient for second order Møller-Plesset perturbation theory with the polarizable continuum model based on the fragment molecular orbital method

NASA Astrophysics Data System (ADS)

Nagata, Takeshi; Fedorov, Dmitri G.; Li, Hui; Kitaura, Kazuo

2012-05-01

A new energy expression is proposed for the fragment molecular orbital method interfaced with the polarizable continuum model (FMO/PCM). The solvation free energy is shown to be more accurate on a set of representative polypeptides with neutral and charged residues, in comparison to the original formulation at the same level of the many-body expansion of the electrostatic potential determining the apparent surface charges. The analytic first derivative of the energy with respect to nuclear coordinates is formulated at the second-order Møller-Plesset (MP2) perturbation theory level combined with PCM, for which we derived coupled perturbed Hartree-Fock equations. The accuracy of the analytic gradient is demonstrated on test calculations in comparison to numeric gradient. Geometry optimization of the small Trp-cage protein (PDB: 1L2Y) is performed with FMO/PCM/6-31(+)G(d) at the MP2 and restricted Hartree-Fock with empirical dispersion (RHF/D). The root mean square deviations between the FMO optimized and NMR experimental structure are found to be 0.414 and 0.426 Å for RHF/D and MP2, respectively. The details of the hydrogen bond network in the Trp-cage protein are revealed.

Derivation of general analytic gradient expressions for density-fitted post-Hartree-Fock methods: An efficient implementation for the density-fitted second-order Møller–Plesset perturbation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bozkaya, Uğur, E-mail: ugur.bozkaya@atauni.edu.tr

General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller–Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele,more » Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.« less

Particle Number Conserving Approach to the Collective States in a Small Fermi-System

NASA Astrophysics Data System (ADS)

Glick, Jennifer; Zelevinsky, Vladimir

2014-03-01

The standard Bardeen-Cooper-Schrieffer (BCS) description of pairing theory, random phase approximation (RPA) and Hartree-Fock-Bogoliubov (HFB) methods, routinely used in macroscopic many-body physics when the dimension of the Hamiltonian matrix is prohibitively large, include features which are not well suited to describe mesoscopic systems such as nuclei or cold atoms in traps. Two important disadvantages are the non-conservation of exact particle number through the introduction of quasiparticles, and the absence of a non-trivial paired solution in the discrete spectrum with weak pairing. We develop the pairing theory based on the exact particle number conservation, whose first applications to the ground state physics presented in [A. Volya and V. Zelevinsky, in 50 Years of Nuclear BCS, World Scientific, 2012] demonstrated that such an approach avoids well known deficiencies of the standard treatment, especially in the region of weak pairing. Now, we use the method for low-lying collective excitations which in many cases are even more sensitive to conservation laws. We show that the RPA version based on solving the operator equations of motion is reduced to the set of recurrence relations for neighboring systems which precisely conserve the exact particle number. Supported by the NSF grant PHY-1068217.

Efficient two-component relativistic method for large systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakai, Hiromi; Research Institute for Science and Engineering, Waseda University, Tokyo 169-8555; CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012

This paper reviews a series of theoretical studies to develop efficient two-component (2c) relativistic method for large systems by the author’s group. The basic theory is the infinite-order Douglas-Kroll-Hess (IODKH) method for many-electron Dirac-Coulomb Hamiltonian. The local unitary transformation (LUT) scheme can effectively produce the 2c relativistic Hamiltonian, and the divide-and-conquer (DC) method can achieve linear-scaling of Hartree-Fock and electron correlation methods. The frozen core potential (FCP) theoretically connects model potential calculations with the all-electron ones. The accompanying coordinate expansion with a transfer recurrence relation (ACE-TRR) scheme accelerates the computations of electron repulsion integrals with high angular momenta and longmore » contractions.« less

Generalization of the Bogoliubov-Zubarev Theorem for Dynamic Pressure to the Case of Compressibility

NASA Astrophysics Data System (ADS)

Rudoi, Yu. G.

2018-01-01

We present the motivation, formulation, and modified proof of the Bogoliubov-Zubarev theorem connecting the pressure of a dynamical object with its energy within the framework of a classical description and obtain a generalization of this theorem to the case of dynamical compressibility. In both cases, we introduce the volume of the object into consideration using a singular addition to the Hamiltonian function of the physical object, which allows using the concept of the Bogoliubov quasiaverage explicitly already on a dynamical level of description. We also discuss the relation to the same result known as the Hellmann-Feynman theorem in the framework of the quantum description of a physical object.

Low-rank factorization of electron integral tensors and its application in electronic structure theory

DOE PAGES

Peng, Bo; Kowalski, Karol

2017-01-25

In this paper, we apply reverse Cuthill-McKee (RCM) algorithm to transform two-electron integral tensors to their block diagonal forms. By further applying Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates low-rank factorizations of high-dimensional tensor contractions in post-Hartree-Fock calculations. Finally, we discuss the second-order Møller-Plesset (MP2) method and the linear coupled-cluster model with doubles (L-CCD) as examples to demonstrate the efficiency of this technique in representing the two-electron integrals in a compact form.

Low-rank factorization of electron integral tensors and its application in electronic structure theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peng, Bo; Kowalski, Karol

In this paper, we apply reverse Cuthill-McKee (RCM) algorithm to transform two-electron integral tensors to their block diagonal forms. By further applying Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates low-rank factorizations of high-dimensional tensor contractions in post-Hartree-Fock calculations. Finally, we discuss the second-order Møller-Plesset (MP2) method and the linear coupled-cluster model with doubles (L-CCD) as examples to demonstrate the efficiency of this technique in representing the two-electron integrals in a compact form.

The nuclear electric quadrupole moment of antimony from the molecular method.

PubMed

Haiduke, Roberto L A; da Silva, Albérico B F; Visscher, Lucas

2006-08-14

Relativistic Dirac-Coulomb (DC) Hartree-Fock calculations are employed to obtain the analytic electric field gradient (EFG) on the antimony nucleus in the SbN, SbP, SbF, and SbCl molecules. The electronic correlation contribution to the EFGs is included with the DC-CCSD(T) and DC-CCSD-T approaches, also in the four-component framework, using a finite-difference method. The total EFG results, along with the experimental nuclear quadrupole coupling constants from microwave spectroscopy, allow to derive the nuclear quadrupole moments of (121)Sb and (123)Sb, respectively, as -543(11) and -692(14) mb.

Weak-interaction rates in stellar conditions

NASA Astrophysics Data System (ADS)

Sarriguren, Pedro

2018-05-01

Weak-interaction rates, including β-decay and electron captures, are studied in several mass regions at various densities and temperatures of astrophysical interest. In particular, we study odd-A nuclei in the pf-shell region, which are involved in presupernova formations. Weak rates are relevant to understand the late stages of the stellar evolution, as well as the nucleosynthesis of heavy nuclei. The nuclear structure involved in the weak processes is studied within a quasiparticle proton-neutron random-phase approximation with residual interactions in both particle-hole and particle-particle channels on top of a deformed Skyrme Hartree-Fock mean field with pairing correlations. First, the energy distributions of the Gamow-Teller strength are discussed and compared with the available experimental information, measured under terrestrial conditions from charge-exchange reactions. Then, the sensitivity of the weak-interaction rates to both astrophysical densities and temperatures is studied. Special attention is paid to the relative contribution to these rates of thermally populated excited states in the decaying nucleus and to the electron captures from the degenerate electron plasma.

Diffeomorphism Group Representations in Relativistic Quantum Field Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goldin, Gerald A.; Sharp, David H.

We explore the role played by the di eomorphism group and its unitary representations in relativistic quantum eld theory. From the quantum kinematics of particles described by representations of the di eomorphism group of a space-like surface in an inertial reference frame, we reconstruct the local relativistic neutral scalar eld in the Fock representation. An explicit expression for the free Hamiltonian is obtained in terms of the Lie algebra generators (mass and momentum densities). We suggest that this approach can be generalized to elds whose quanta are spatially extended objects.

Semiempirical and DFT Investigations of the Dissociation of Alkyl Halides

ERIC Educational Resources Information Center

Waas, Jack R.

2006-01-01

Enthalpy changes corresponding to the gas phase heats of dissociation of 12 organic halides were calculated using two semiempirical methods, the Hartree-Fock method, and two DFT methods. These calculated values were compared to experimental values where possible. All five methods agreed generally with the expected empirically known trends in the…

Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory.

PubMed

Coriani, Sonia; Høst, Stinne; Jansík, Branislav; Thøgersen, Lea; Olsen, Jeppe; Jørgensen, Poul; Reine, Simen; Pawłowski, Filip; Helgaker, Trygve; Sałek, Paweł

2007-04-21

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms.

Scaled Hartree-Fock force field calculations for organothallium compounds: Normal-mode analysis for TlCH sub 3 Tl(CH sub 3 ) sub 2 sup + , Tl(CH sub 3 ) sub 3 , Tl(CH sub 3 ) sub 2 Br, and Tl(CH sub 3 ) sub 4 sup minus

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schwerdtfeger, P.; Bowmaker, G.A.; Boyd, P.D.W.

1990-02-01

In a recent paper we presented Hartree-Fock (HF) calculations for aliphatic organothallium compounds. The diagonal HF force constants obtained from a Fletcher-Powell geometry optimization are now used for a normal-mode analysis of TlCH{sub 3}, Tl(CH{sub 3}){sub 2}{sup +}, Tl(CH{sub 3}){sub 3}, Tl(CH{sub 3}){sub 2}Br, and Tl(CH{sub 3}){sub 4}{sup {minus}}. In order to calculate frequencies comparable to experimental values, the HF force field has been scaled by using scaling factors obtained from experimental infrared and Raman measurements on Tl(CH{sub 3}){sub 2}{sup +} and TlBr. The vibrational spectra of Tl(CH{sub 3}){sub 2}{sup +} were remeasured (infrared and Raman) in order to obtainmore » an accurate force field. Predictions are made for the vibrational spectrum of the as yet undetected TlCH{sub 3} molecule. Experimental infrared and Raman results for Tl(CH{sub 3}){sub 3} compare reasonably well with our calculated frequencies. Relativistic and correlation effects are analyzed for the vibrational frequencies of Tl(CH{sub 3}){sub 2}{sup +}.« less

Study of thermodynamic properties of liquid binary alloys by a pseudopotential method

NASA Astrophysics Data System (ADS)

Vora, Aditya M.

2010-11-01

On the basis of the Percus-Yevick hard-sphere model as a reference system and the Gibbs-Bogoliubov inequality, a thermodynamic perturbation method is applied with the use of the well-known model potential. By applying a variational method, the hard-core diameters are found which correspond to a minimum free energy. With this procedure, the thermodynamic properties such as the internal energy, entropy, Helmholtz free energy, entropy of mixing, and heat of mixing are computed for liquid NaK binary systems. The influence of the local-field correction functions of Hartree, Taylor, Ichimaru-Utsumi, Farid-Heine-Engel-Robertson, and Sarkar-Sen-Haldar-Roy is also investigated. The computed excess entropy is in agreement with available experimental data in the case of liquid alloys, whereas the agreement for the heat of mixing is poor. This may be due to the sensitivity of the latter to the potential parameters and dielectric function.

Stability conditions for exact-exchange Kohn-Sham methods and their relation to correlation energies from the adiabatic-connection fluctuation-dissipation theorem.

PubMed

Bleiziffer, Patrick; Schmidtel, Daniel; Görling, Andreas

2014-11-28

The occurrence of instabilities, in particular singlet-triplet and singlet-singlet instabilities, in the exact-exchange (EXX) Kohn-Sham method is investigated. Hessian matrices of the EXX electronic energy with respect to the expansion coefficients of the EXX effective Kohn-Sham potential in an auxiliary basis set are derived. The eigenvalues of these Hessian matrices determine whether or not instabilities are present. Similar as in the corresponding Hartree-Fock case instabilities in the EXX method are related to symmetry breaking of the Hamiltonian operator for the EXX orbitals. In the EXX methods symmetry breaking can easily be visualized by displaying the local multiplicative exchange potential. Examples (N2, O2, and the polyyne C10H2) for instabilities and symmetry breaking are discussed. The relation of the stability conditions for EXX methods to approaches calculating the Kohn-Sham correlation energy via the adiabatic-connection fluctuation-dissipation (ACFD) theorem is discussed. The existence or nonexistence of singlet-singlet instabilities in an EXX calculation is shown to indicate whether or not the frequency-integration in the evaluation of the correlation energy is singular in the EXX-ACFD method. This method calculates the Kohn-Sham correlation energy through the ACFD theorem theorem employing besides the Coulomb kernel also the full frequency-dependent exchange kernel and yields highly accurate electronic energies. For the case of singular frequency-integrands in the EXX-ACFD method a regularization is suggested. Finally, we present examples of molecular systems for which the self-consistent field procedure of the EXX as well as the Hartree-Fock method can converge to more than one local minimum depending on the initial conditions.

Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure.

PubMed

Hoy, Erik P; Mazziotti, David A

2015-08-14

Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory.

The Importance of Three-Body Interactions in Molecular Dynamics Simulations of Water with the Fragment Molecular Orbital Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pruitt, Spencer R.; Nakata, Hiroya; Nagata, Takeshi

2016-04-12

The analytic first derivative with respect to nuclear coordinates is formulated and implemented in the framework of the three-body fragment molecular orbital (FMO) method. The gradient has been derived and implemented for restricted Hartree-Fock, second-order Møller-Plesset perturbation, and density functional theories. The importance of the three-body fully analytic gradient is illustrated through the failure of the two-body FMO method during molecular dynamics simulations of a small water cluster. The parallel implementation of the fragment molecular orbital method, its parallel efficiency, and its scalability on the Blue Gene/Q architecture up to 262,144 CPU cores, are also discussed.

Electron correlation in Hooke's law atom in the high-density limit.

PubMed

Gill, P M W; O'Neill, D P

2005-03-01

Closed-form expressions for the first three terms in the perturbation expansion of the exact energy and Hartree-Fock energy of the lowest singlet and triplet states of the Hooke's law atom are found. These yield elementary formulas for the exact correlation energies (-49.7028 and -5.807 65 mE(h)) of the two states in the high-density limit and lead to a pair of necessary conditions on the exact correlation kernel G(w) in Hartree-Fock-Wigner theory.

Dependence of Excited State Potential Energy Surfaces on the Spatial Overlap of the Kohn-Sham Orbitals and the Amount of Nonlocal Hartree-Fock Exchange in Time-Dependent Density Functional Theory.

PubMed

Plötner, Jürgen; Tozer, David J; Dreuw, Andreas

2010-08-10

Time-dependent density functional theory (TDDFT) with standard GGA or hybrid exchange-correlation functionals is not capable of describing the potential energy surface of the S1 state of Pigment Yellow 101 correctly; an additional local minimum is observed at a twisted geometry with substantial charge transfer (CT) character. To investigate the influence of nonlocal exact orbital (Hartree-Fock) exchange on the shape of the potential energy surface of the S1 state in detail, it has been computed along the twisting coordinate employing the standard BP86, B3LYP, and BHLYP xc-functionals as well as the long-range separated (LRS) exchange-correlation (xc)-functionals LC-BOP, ωB97X, ωPBE, and CAM-B3LYP and compared to RI-CC2 benchmark results. Additionally, a recently suggested Λ-parameter has been employed that measures the amount of CT in an excited state by calculating the spatial overlap of the occupied and virtual molecular orbitals involved in the transition. Here, the error in the calculated S1 potential energy curves at BP86, B3LYP, and BHLYP can be clearly related to the Λ-parameter, i.e., to the extent of charge transfer. Additionally, it is demonstrated that the CT problem is largely alleviated when the BHLYP xc-functional is employed, although it still exhibits a weak tendency to underestimate the energy of CT states. The situation improves drastically when LRS-functionals are employed within TDDFT excited state calculations. All tested LRS-functionals give qualitatively the correct potential energy curves of the energetically lowest excited states of P. Y. 101 along the twisting coordinate. While LC-BOP and ωB97X overcorrect the CT problem and now tend to give too large excitation energies compared to other non-CT states, ωPBE and CAM-B3LYP are in excellent agreement with the RI-CC2 results, with respect to both the correct shape of the potential energy curve as well as the absolute values of the calculated excitation energies.

Ground-state properties of the three-band Hubbard model

NASA Astrophysics Data System (ADS)

Zhang, Shiwei; Vitali, Ettore; Chiciak, Adam; Shi, Hao

The three-band Hubbard model proposed by Emery describes the CuO2 plane in cuprate superconductors by retaining both Cu and O orbitals in a minimal sense. Applying the latest developments in the auxiliary-field quantum Monte Carlo (AFQMC) method, we investigate ground-state properties of this model at half-filling and when lightly (under-)doped. The AFQMC uses generalized Hartree-Fock (GHF) trial wave functions to control the sign problem. A self-consistent constraint is applied. We also determine the unrestricted Hartree-Fock (UHF) and GHF ground states and compare their predictions with those from AFQMC. Similarities and differences between the three-band model and one-band Hubbard model will be discussed. Supported by NSF, and the Simons Foundation. Computing is carried out at the Extreme Science and Engineering Discovery Environment(XSEDE).

Stiffness-constant variation in nickel-based alloys: Experiment and theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hennion, M.; Hennion, B.

1979-01-01

Recent measurements of the spin-wave stiffness constant in several nickel alloys at various concentrations are interpreted within a random-phase approximation, coherent-potential approximation (RPA-CPA) band model which uses the Hartree-Fock approximation to treat the intraatomic correlations. We give a theoretical description of the possible impurity states in the Hartree-Fock approximation. This allows the determination of the Hartree-Fock solutions which can account for the stiffness-constant behavior and the magnetic moment on the impurity for all the investigated alloys. For alloys such as NiCr, NiV, NiMo, and NiRu, the magnetizations of which deviate from the Slater-Pauling curve, our determination does not correspond tomore » previous works and is consequently discussed. The limits of the model appear mainly due to local-environment effects; in the case of NiMn, it is found that a ternary-alloy model with some Mn atoms in the antiferromagnetic state can account for both stiffness-constant and magnetization behaviors.« less

COMPARATIVE DOCKING STUDIES OF THE BINDING OF POLYCYCLIC AROMATIC HYDROCARBONS TO THE ESTROGEN RECEPTOR

EPA Science Inventory

The interactions of several PAHs, and some of their possible metabolites, with the ligand binding domain of the estrogen receptor have been examined using molecular docking and quantum mechanical methods. The geometries of the PAHs were optimized at the Hartree-Fock level and the...

Thouless-Valatin rotational moment of inertia from linear response theory

NASA Astrophysics Data System (ADS)

Petrík, Kristian; Kortelainen, Markus

2018-03-01

Spontaneous breaking of continuous symmetries of a nuclear many-body system results in the appearance of zero-energy restoration modes. These so-called spurious Nambu-Goldstone modes represent a special case of collective motion and are sources of important information about the Thouless-Valatin inertia. The main purpose of this work is to study the Thouless-Valatin rotational moment of inertia as extracted from the Nambu-Goldstone restoration mode that results from the zero-frequency response to the total-angular-momentum operator. We examine the role and effects of the pairing correlations on the rotational characteristics of heavy deformed nuclei in order to extend our understanding of superfluidity in general. We use the finite-amplitude method of the quasiparticle random-phase approximation on top of the Skyrme energy density functional framework with the Hartree-Fock-Bogoliubov theory. We have successfully extended this formalism and established a practical method for extracting the Thouless-Valatin rotational moment of inertia from the strength function calculated in the symmetry-restoration regime. Our results reveal the relation between the pairing correlations and the moment of inertia of axially deformed nuclei of rare-earth and actinide regions of the nuclear chart. We have also demonstrated the feasibility of the method for obtaining the moment of inertia for collective Hamiltonian models. We conclude that from the numerical and theoretical perspective, the finite-amplitude method can be widely used to effectively study rotational properties of deformed nuclei within modern density functional approaches.

Proceedings of US-Latin American Workshop on Molecular and Materials Sciences: Theoretical and Computational Aspects Held in Gainesville, Florida on 10-12 March 1993

DTIC Science & Technology

1994-08-09

City Josd Rdamier and R. Iterative Bogoliubov Transformations and Applications Jauregui Inst. de Fisica , Cuernavaca, Meiico Peter J. Reynolds Quantum...University, Provo, UT 84602 J. R•camier Instituto de Fisica , UNAM, Cuernavaca, Mor., MWxico Gamow states are solutions to the Schr6dinger equation with a...Coutinho Departamento de FAsica do UFPE 50732-910 Recife, PE, Brazil and Jnstituto de Fisica da USP, Czp 20516 01498-970 Sdo Paulo, SP, Brasil The

Direct Quantum Dynamics Using Grid-Based Wave Function Propagation and Machine-Learned Potential Energy Surfaces.

PubMed

Richings, Gareth W; Habershon, Scott

2017-09-12

We describe a method for performing nuclear quantum dynamics calculations using standard, grid-based algorithms, including the multiconfiguration time-dependent Hartree (MCTDH) method, where the potential energy surface (PES) is calculated "on-the-fly". The method of Gaussian process regression (GPR) is used to construct a global representation of the PES using values of the energy at points distributed in molecular configuration space during the course of the wavepacket propagation. We demonstrate this direct dynamics approach for both an analytical PES function describing 3-dimensional proton transfer dynamics in malonaldehyde and for 2- and 6-dimensional quantum dynamics simulations of proton transfer in salicylaldimine. In the case of salicylaldimine we also perform calculations in which the PES is constructed using Hartree-Fock calculations through an interface to an ab initio electronic structure code. In all cases, the results of the quantum dynamics simulations are in excellent agreement with previous simulations of both systems yet do not require prior fitting of a PES at any stage. Our approach (implemented in a development version of the Quantics package) opens a route to performing accurate quantum dynamics simulations via wave function propagation of many-dimensional molecular systems in a direct and efficient manner.

Variational Dirac-Hartree-Fock calculation of the Breit interaction

NASA Astrophysics Data System (ADS)

Goldman, S. P.

1988-04-01

The calculation of the retarded version of the Breit interaction in the context of the VDHF method is discussed. With the use of Slater-type basis functions, all the terms involved can be calculated in closed form. The results are expressed as an expansion in powers of one-electron energy differences and linear combinations of hypergeometric functions. Convergence is fast and high accuracy is obtained with a small number of terms in the expansion even for high values of the nuclear charge. An added advantage is that the lowest order cancellations occurring in the retardation terms are accounted for exactly a priori. A comparison of the number of terms in the total expansion needed for an accuracy of 12 significant digits in the total energy, as well as a comparison of the results with an without retardation and in the local potential approximation, are presented for the carbon isoelectronic sequence.

Big Data Meets Quantum Chemistry Approximations: The Δ-Machine Learning Approach.

PubMed

Ramakrishnan, Raghunathan; Dral, Pavlo O; Rupp, Matthias; von Lilienfeld, O Anatole

2015-05-12

Chemically accurate and comprehensive studies of the virtual space of all possible molecules are severely limited by the computational cost of quantum chemistry. We introduce a composite strategy that adds machine learning corrections to computationally inexpensive approximate legacy quantum methods. After training, highly accurate predictions of enthalpies, free energies, entropies, and electron correlation energies are possible, for significantly larger molecular sets than used for training. For thermochemical properties of up to 16k isomers of C7H10O2 we present numerical evidence that chemical accuracy can be reached. We also predict electron correlation energy in post Hartree-Fock methods, at the computational cost of Hartree-Fock, and we establish a qualitative relationship between molecular entropy and electron correlation. The transferability of our approach is demonstrated, using semiempirical quantum chemistry and machine learning models trained on 1 and 10% of 134k organic molecules, to reproduce enthalpies of all remaining molecules at density functional theory level of accuracy.

Approximate spin projection of three-component UHF wavefunctions - The states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O5/2-/

NASA Technical Reports Server (NTRS)

Phillips, D. H.; Schug, J. C.

1974-01-01

The approximate spin projection method of Amos et al. is extended to handle UHF wave functions having three significant components of differing multiplicity. An expression is given for the energy after single annihilation which differs from that of Amos and Hall. The new expression reproduces the results obtained from a previous exact calculation for which the weights and energies of the components are known. The extended approximate projection method is applied to the pi-electron UHF wave functions for the ground states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O5(2-). The results indicate a triplet ground state for the former and a singlet ground state for the latter, in agreement with experimental ESR susceptibility measurements for these molecular ions. C5C15(-) cannont be treated by restricted Hartree-Fock theory, due to its open-shell ground state. Incorrect results are obtained for the croconate dianion, if restricted Hartree-Fock theory and singly excited configuration interactions are utilized.

Evaluation of DFT methods for computing the interaction energies of homomolecular and heteromolecular dimers of monosubstituted benzene

NASA Astrophysics Data System (ADS)

Godfrey-Kittle, Andrew; Cafiero, Mauricio

We present density functional theory (DFT) interaction energies for the sandwich and T-shaped conformers of substituted benzene dimers. The DFT functionals studied include TPSS, HCTH407, B3LYP, and X3LYP. We also include Hartree-Fock (HF) and second-order Møller-Plesset perturbation theory calculations (MP2), as well as calculations using a new functional, P3LYP, which includes PBE and HF exchange and LYP correlation. Although DFT methods do not explicitly account for the dispersion interactions important in the benzene-dimer interactions, we find that our new method, P3LYP, as well as HCTH407 and TPSS, match MP2 and CCSD(T) calculations much better than the hybrid methods B3LYP and X3LYP methods do.

Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsuchiya, Shunji; Department of Physics, Waseda University, 3-4-1 Okubo, Tokyo 169-8555; Griffin, Allan

2005-11-15

We study the Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures, extending our recent work on one-dimensional (1D) optical lattices. We use a Bose-Hubbard tight-binding model and the Popov approximation to calculate the temperature dependence of the number of condensate atoms n{sup c0}(T) in each lattice well. As with 1D optical lattices, damping only occurs if the Bogoliubov excitations exhibit anomalous dispersion (i.e., the excitation energy bends upward at low momentum), analogous to the case of phonons in superfluid {sup 4}He. This leads to the disappearance of all damping processes in a D-dimensional simplemore » cubic optical lattice when Un{sup c0}{>=}6DJ, where U is the on-site interaction, and J is the hopping matrix element.« less

Asymptotics of small deviations of the Bogoliubov processes with respect to a quadratic norm

NASA Astrophysics Data System (ADS)

Pusev, R. S.

2010-10-01

We obtain results on small deviations of Bogoliubov’s Gaussian measure occurring in the theory of the statistical equilibrium of quantum systems. For some random processes related to Bogoliubov processes, we find the exact asymptotic probability of their small deviations with respect to a Hilbert norm.

The Fock-Schwinger gauge in the BFV formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barcelos-Neto, J.; Galvao, C.A.P.; Gaete, P.

1991-06-07

The authors consider the implementation of a properly modified form of the Fock-Schwinger gauge condition in a general non-Abelian gauge theory in the context of the BFV formalism. In this paper arguments are presented to justify the necessity of modifying the original Fock-Schwinger condition. The free field propagator and the general Ward identity are also calculated.

The multi-layer multi-configuration time-dependent Hartree method for bosons: theory, implementation, and applications.

PubMed

Cao, Lushuai; Krönke, Sven; Vendrell, Oriol; Schmelcher, Peter

2013-10-07

We develop the multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB), a variational numerically exact ab initio method for studying the quantum dynamics and stationary properties of general bosonic systems. ML-MCTDHB takes advantage of the permutation symmetry of identical bosons, which allows for investigations of the quantum dynamics from few to many-body systems. Moreover, the multi-layer feature enables ML-MCTDHB to describe mixed bosonic systems consisting of arbitrary many species. Multi-dimensional as well as mixed-dimensional systems can be accurately and efficiently simulated via the multi-layer expansion scheme. We provide a detailed account of the underlying theory and the corresponding implementation. We also demonstrate the superior performance by applying the method to the tunneling dynamics of bosonic ensembles in a one-dimensional double well potential, where a single-species bosonic ensemble of various correlation strengths and a weakly interacting two-species bosonic ensemble are considered.

Entropy generation in Gaussian quantum transformations: applying the replica method to continuous-variable quantum information theory

NASA Astrophysics Data System (ADS)

Gagatsos, Christos N.; Karanikas, Alexandros I.; Kordas, Georgios; Cerf, Nicolas J.

2016-02-01

In spite of their simple description in terms of rotations or symplectic transformations in phase space, quadratic Hamiltonians such as those modelling the most common Gaussian operations on bosonic modes remain poorly understood in terms of entropy production. For instance, determining the quantum entropy generated by a Bogoliubov transformation is notably a hard problem, with generally no known analytical solution, while it is vital to the characterisation of quantum communication via bosonic channels. Here we overcome this difficulty by adapting the replica method, a tool borrowed from statistical physics and quantum field theory. We exhibit a first application of this method to continuous-variable quantum information theory, where it enables accessing entropies in an optical parametric amplifier. As an illustration, we determine the entropy generated by amplifying a binary superposition of the vacuum and a Fock state, which yields a surprisingly simple, yet unknown analytical expression.

Semiclassical analysis for pseudo-relativistic Hartree equations

NASA Astrophysics Data System (ADS)

Cingolani, Silvia; Secchi, Simone

2015-06-01

In this paper we study the semiclassical limit for the pseudo-relativistic Hartree equation $\\sqrt{-\\varepsilon^2 \\Delta + m^2}u + V u = (I_\\alpha * |u|^{p}) |u|^{p-2}u$ in $\\mathbb{R}^N$ where $m>0$, $2 \\leq p < \\frac{2N}{N-1}$, $V \\colon \\mathbb{R}^N \\to \\mathbb{R}$ is an external scalar potential, $I_\\alpha (x) = \\frac{c_{N,\\alpha}}{|x|^{N-\\alpha}}$ is a convolution kernel, $c_{N,\\alpha}$ is a positive constant and $(N-1)p-N<\\alpha Hartree equation with Coulomb kernel.

The Hartree-Fock calculation of the magnetic properties of molecular solutes

NASA Astrophysics Data System (ADS)

Cammi, R.

1998-08-01

In this paper we set the formal bases for the calculation of the magnetic susceptibility and of the nuclear magnetic shielding tensors for molecular solutes described within the framework of the polarizable continuum model (PCM). The theory has been developed at self-consistent field (SCF) level and adapted to be used within the framework of some of the computational procedures of larger use, i.e., the gauge invariant atomic orbital method (GIAO) and the continuous set gauge transformation method (CSGT). The numerical results relative to the magnetizabilities and chemical shielding of acetonitrile and nitrometane in various solvents computed with the PCM-CSGT method are also presented.

Theoretical X-ray production cross sections at incident photon energies across Li (i=1-3) absorption edges of Br

NASA Astrophysics Data System (ADS)

Puri, Sanjiv

2015-08-01

The X-ray production (XRP) cross sections, σLk (k = l, η, α, β6, β1, β3, β4, β9,10, γ1,5, γ2,3) have been evaluated at incident photon energies across the Li(i=1-3) absorption edge energies of 35Br using theoretical data sets of different physical parameters, namely, the Li(i=1-3) sub-shell the X-ray emission rates based on the Dirac-Fock (DF) model, the fluorescence and Coster Kronig yields based on the Dirac-Hartree-Slater (DHS) model, and two sets of the photoionisation cross sections based on the relativistic Hartree-Fock-Slater (RHFS) model and the Dirac-Fock (DF) model, in order to highlight the importance of electron exchange effects at photon energies in vicinity of absorption edge energies.

LoFEx - A local framework for calculating excitation energies: Illustrations using RI-CC2 linear response theory.

PubMed

Baudin, Pablo; Kristensen, Kasper

2016-06-14

We present a local framework for the calculation of coupled cluster excitation energies of large molecules (LoFEx). The method utilizes time-dependent Hartree-Fock information about the transitions of interest through the concept of natural transition orbitals (NTOs). The NTOs are used in combination with localized occupied and virtual Hartree-Fock orbitals to generate a reduced excitation orbital space (XOS) specific to each transition where a standard coupled cluster calculation is carried out. Each XOS is optimized to ensure that the excitation energies are determined to a predefined precision. We apply LoFEx in combination with the RI-CC2 model to calculate the lowest excitation energies of a set of medium-sized organic molecules. The results demonstrate the black-box nature of the LoFEx approach and show that significant computational savings can be gained without affecting the accuracy of CC2 excitation energies.

Modeling molecule-plasmon interactions using quantized radiation fields within time-dependent electronic structure theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nascimento, Daniel R.; DePrince, A. Eugene, E-mail: deprince@chem.fsu.edu

2015-12-07

We present a combined cavity quantum electrodynamics/ab initio electronic structure approach for simulating plasmon-molecule interactions in the time domain. The simple Jaynes-Cummings-type model Hamiltonian typically utilized in such simulations is replaced with one in which the molecular component of the coupled system is treated in a fully ab initio way, resulting in a computationally efficient description of general plasmon-molecule interactions. Mutual polarization effects are easily incorporated within a standard ground-state Hartree-Fock computation, and time-dependent simulations carry the same formal computational scaling as real-time time-dependent Hartree-Fock theory. As a proof of principle, we apply this generalized method to the emergence ofmore » a Fano-like resonance in coupled molecule-plasmon systems; this feature is quite sensitive to the nanoparticle-molecule separation and the orientation of the molecule relative to the polarization of the external electric field.« less

Theoretical dissociation energies for the alkali and alkaline-earth monofluorides and monochlorides

NASA Technical Reports Server (NTRS)

Langhoff, S. R.; Bauschlicher, C. W., Jr.; Partridge, H.

1986-01-01

Spectroscopic parameters are accurately determined for the alkali and alkaline-earth monofluorides and monochlorides by means of ab initio self-consistent field and correlated wave function calculations. Numerical Hartree-Fock calculations are performed on selected systems to ensure that the extended Slater basis sets employed are near the Hartree-Fock limit. Since the bonding is predominantly electrostatic in origin, a strong correlation exists between the dissociation energy (to ions) and the spectroscopic parameter r(e). By dissociating to the ionic limits, most of the differential correlation effects can be embedded in the accurate experimental electron affinities and ionization potentials.

Neutron densities from a global analysis of medium-energy proton-nucleus elastic scattering

NASA Astrophysics Data System (ADS)

Clark, B. C.; Kerr, L. J.; Hama, S.

2003-05-01

A new method for extracting neutron densities from intermediate-energy elastic proton-nucleus scattering observables uses a global Dirac phenomenological approach based on the relativistic impulse approximation. Datasets for 40Ca, 48Ca, and 208Pb in the energy range from 500 MeV to 1040 MeV are considered. The global fits are successful in reproducing the data and in predicting datasets not included in the analysis. Using this global approach, energy-independent neutron densities are obtained. The vector point proton density distribution ρpv is determined from the empirical charge density after unfolding the proton form factor. The other densities, ρnv, ρps, ρns, are parametrized. This work provides energy-independent values for the rms neutron radius Rn and the neutron skin thickness Sn, in contrast to the energy-dependent values obtained by previous studies. In addition, the results presented in this paper show that the expected rms neutron radius and the skin thickness for 40Ca are accurately reproduced. The values of Rn and Sn obtained from the global fits that we consider to be the most reliable are given as follows: for 40Ca, 3.314>Rn>3.310 fm and -0.063>Sn >-0.067 fm; for 48Ca, 3.459>Rn>3.413 fm and 0.102>Sn>0.056 fm; and for 208Pb, 5.550>Rn>5.522 fm and 0.111>Sn>0.083 fm. These values are in reasonable agreement with nonrelativistic Skyrme-Hartree-Fock models and with relativistic Hartree-Bogoliubov models with density-dependent meson-nucleon couplings. The results from the global fits for 48Ca and 208Pb are generally not in agreement with the usual relativistic mean-field models.

Damping of Bogoliubov excitations in optical lattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsuchiya, Shunji; Department of Physics, Waseda University, 3-4-1 Okubo, Tokyo 169-8555; Griffin, Allan

2004-08-01

Extending recent work to finite temperatures, we calculate the Landau damping of a Bogoliubov excitation in an optical lattice, due to the coupling to a thermal cloud of such excitations. For simplicity, we consider a one-dimensional Bose-Hubbard model and restrict ourselves to the first energy band. For energy conservation to be satisfied, the excitations in the collision processes must exhibit ''anomalous dispersion,'' analogous to phonons in superfluid {sup 4}He. This leads to the disappearance of all damping processes when Un{sup c0}{>=}6J, where U is the on-site interaction, J is the hopping matrix element, and n{sup c0}(T) is the number ofmore » condensate atoms at a lattice site. This phenomenon also occurs in two-dimensional and three-dimensional optical lattices. The disappearance of Beliaev damping above a threshold wave vector is noted.« less

Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov approximation

NASA Astrophysics Data System (ADS)

Napiórkowski, M.; Reuvers, R.; Solovej, J. P.

2018-01-01

Following an earlier calculation in 3D, we calculate the 2D critical temperature of a dilute, translation-invariant Bose gas using a variational formulation of the Bogoliubov approximation introduced by Critchley and Solomon in 1976. This provides the first analytical calculation of the Kosterlitz-Thouless transition temperature that includes the constant in the logarithm.

Few-particle quantum dynamics-comparing nonequilibrium Green functions with the generalized Kadanoff-Baym ansatz to density operator theory

NASA Astrophysics Data System (ADS)

Hermanns, S.; Balzer, K.; Bonitz, M.

2013-03-01

The nonequilibrium description of quantum systems requires, for more than two or three particles, the use of a reduced description to be numerically tractable. Two possible approaches are based on either reduced density matrices or nonequilibrium Green functions (NEGF). Both concepts are formulated in terms of hierarchies of coupled equations—the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for the reduced density operators and the Martin-Schwinger-hierarchy (MS) for the Green functions, respectively. In both cases, similar approximations are introduced to decouple the hierarchy, yet still many questions regarding the correspondence of both approaches remain open. Here we analyze this correspondence by studying the generalized Kadanoff-Baym ansatz (GKBA) that reduces the NEGF to a single-time theory. Starting from the BBGKY-hierarchy we present the approximations that are necessary to recover the GKBA result both, with Hartree-Fock propagators (HF-GKBA) and propagators in second Born approximation. To test the quality of the HF-GKBA, we study the dynamics of a 4-electron Hubbard nanocluster starting from a strong nonequilibrium initial state and compare to exact results and the Wang-Cassing approximation to the BBGKY hierarchy presented recently by Akbari et al. [1].

Calculations of the β-decay half-lives of neutron-deficient nuclei

NASA Astrophysics Data System (ADS)

Tan, Wenjin; Ni, Dongdong; Ren, Zhongzhou

2017-05-01

In this work, β+/EC decays of some medium-mass nuclei are investigated within the extended quasiparticle random-phase approximation (QRPA), where neutron-neutron, proton-proton and neutron-proton (np) pairing correlations are taken into consideration in the specialized Hartree-Fock-Bogoliubov (HFB) transformation. In addition to the pairing interaction, the Brückner G-matrix obtained with the charge-dependent Bonn nucleon-nucleon force is used for the residual particle-particle and particle-hole interactions. Calculations are performed for even-even proton-rich isotopes ranging from Z=24 to Z=34. It is found that the np pairing interaction plays a significant role in β-decay for some nuclei far from stability. Compared with other theoretical calculations, our calculations show good agreement with the available experimental data. Predictions of β-decay half-lives for some very neutron-deficient nuclei are made for reference. Supported by National Nature Science Foundation of China (11535004, 11375086, 11120101005, 11175085 and 11235001), 973 Nation Major State Basic Research and Development of China (2013CB834400) and Science and Technology Development Fund of Macau (020/2014/A1 and 039/2013/A2)

Bose polaronic soliton-molecule and vector solitons in PT -symmetric potential

NASA Astrophysics Data System (ADS)

Boudjemâa, Abdelâali

2017-07-01

We study analytically and numerically the properties of polaronic soliton molecules and vector solitons of a trapped Bose-Einstein condensate (BEC)-impurity mixture subjected to a PT -symmetric potential in a quasi one-dimensional geometry employing our time-dependent Hartree-Fock-Bogoliubov equations. Analytical results, based on a variational approach and checked with direct numerical simulations reveal that the width, chirp, the vibration frequency and the profile of impurity solitons are enhanced by varying the strengths of real and imaginary parts of PT -symmetric potential as well as the boson-boson and boson-impurity interaction. We address the impact of the imaginary part of the potential, which represents a gain-loss mechanism, on the dynamics and on the stability of the impurity soliton-molecule. We show that for sufficiently strong complex part of the potential, the single soliton exhibits a snake instability and the molecule destroys analogous to the dissociation of a diatomic molecule. We discuss, on the other hand, the formation of several unusual families of three-component vector solitons in the BEC-impurity mixture. An unconventional dark (D)-bright (B) soliton conversion is found.

SO(8) fermion dynamical symmetry and strongly correlated quantum Hall states in monolayer graphene

NASA Astrophysics Data System (ADS)

Wu, Lian-Ao; Murphy, Matthew; Guidry, Mike

2017-03-01

A formalism is presented for treating strongly correlated graphene quantum Hall states in terms of an SO(8) fermion dynamical symmetry that includes pairing as well as particle-hole generators. The graphene SO(8) algebra is isomorphic to an SO(8) algebra that has found broad application in nuclear physics, albeit with physically very different generators, and exhibits a strong formal similarity to SU(4) symmetries that have been proposed to describe high-temperature superconductors. The well-known SU(4) symmetry of quantum Hall ferromagnetism for single-layer graphene is recovered as one subgroup of SO(8), but the dynamical symmetry structure associated with the full set of SO(8) subgroup chains extends quantum Hall ferromagnetism and allows analytical many-body solutions for a rich set of collective states exhibiting spontaneously broken symmetry that may be important for the low-energy physics of graphene in strong magnetic fields. The SO(8) symmetry permits a natural definition of generalized coherent states that correspond to symmetry-constrained Hartree-Fock-Bogoliubov solutions, or equivalently a microscopically derived Ginzburg-Landau formalism, exhibiting the interplay between competing spontaneously broken symmetries in determining the ground state.

Properties of nuclear matter from macroscopic-microscopic mass formulas

NASA Astrophysics Data System (ADS)

Wang, Ning; Liu, Min; Ou, Li; Zhang, Yingxun

2015-12-01

Based on the standard Skyrme energy density functionals together with the extended Thomas-Fermi approach, the properties of symmetric and asymmetric nuclear matter represented in two macroscopic-microscopic mass formulas: Lublin-Strasbourg nuclear drop energy (LSD) formula and Weizsäcker-Skyrme (WS*) formula, are extracted through matching the energy per particle of finite nuclei. For LSD and WS*, the obtained incompressibility coefficients of symmetric nuclear matter are K∞ = 230 ± 11 MeV and 235 ± 11 MeV, respectively. The slope parameter of symmetry energy at saturation density is L = 41.6 ± 7.6 MeV for LSD and 51.5 ± 9.6 MeV for WS*, respectively, which is compatible with the liquid-drop analysis of Lattimer and Lim [4]. The density dependence of the mean-field isoscalar and isovector effective mass, and the neutron-proton effective masses splitting for neutron matter are simultaneously investigated. The results are generally consistent with those from the Skyrme Hartree-Fock-Bogoliubov calculations and nucleon optical potentials, and the standard deviations are large and increase rapidly with density. A better constraint for the effective mass is helpful to reduce uncertainties of the depth of the mean-field potential.

An efficient MPI/OpenMP parallelization of the Hartree–Fock–Roothaan method for the first generation of Intel® Xeon Phi™ processor architecture

DOE PAGES

Mironov, Vladimir; Moskovsky, Alexander; D’Mello, Michael; ...

2017-10-04

The Hartree-Fock (HF) method in the quantum chemistry package GAMESS represents one of the most irregular algorithms in computation today. Major steps in the calculation are the irregular computation of electron repulsion integrals (ERIs) and the building of the Fock matrix. These are the central components of the main Self Consistent Field (SCF) loop, the key hotspot in Electronic Structure (ES) codes. By threading the MPI ranks in the official release of the GAMESS code, we not only speed up the main SCF loop (4x to 6x for large systems), but also achieve a significant (>2x) reduction in the overallmore » memory footprint. These improvements are a direct consequence of memory access optimizations within the MPI ranks. We benchmark our implementation against the official release of the GAMESS code on the Intel R Xeon PhiTM supercomputer. Here, scaling numbers are reported on up to 7,680 cores on Intel Xeon Phi coprocessors.« less

The giant Gamow-Teller resonance states

NASA Astrophysics Data System (ADS)

Suzuki, Toshio

1982-04-01

The mean energy of the giant Gamow-Teller resonance state (GTS) is studied, which is defined by the non-energy-weighted and the linearly energy-weighted sum of the strengths for ΣAi = 1 τi- σi- Using Bohr and Mottelson's hamiltonian with the ξl· σ force, the difference between the mean energies of GTS and the isobaric analog state (IAS) is expressed as E GTS -E IAS,≈ 2<π¦Σ Ai=1ξ il i· σ i¦π>/ (3T 0-4(k τ-k στ) T 0. The observed energy systematics is well explained by kτ- kστ≈ 4/ A MeV . The relationship between the mean energies and the excitation energies of the collective states in the random phase approximation for charge-exchange excitations is discussed in a simple model. From the excitation energy systematics of GTS, the values of kστ and the Migdal parameter g' are estimated to be about k στ = {(16-24)}/{A}MeV and g' = 0.49-0.72 , respectively.

Bogoliubov theory of acoustic Hawking radiation in Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Recati, A.; Physik-Department, Technische Universitaet Muenchen, D-85748 Garching; Pavloff, N.

2009-10-15

We apply the microscopic Bogoliubov theory of dilute Bose-Einstein condensates to analyze quantum and thermal fluctuations in a flowing atomic condensate in the presence of a sonic horizon. For the simplest case of a step-like horizon, closed-form analytical expressions are found for the spectral distribution of the analog Hawking radiation and for the density correlation function. The peculiar long-distance density correlations that appear as a consequence of the Hawking emission features turns out to be reinforced by a finite initial temperature of the condensate. The analytical results are in good quantitative agreement with first principle numerical calculations.

Applications of squeezed states: Bogoliubov transformations and wavelets to the statistical mechanics of water and its bubbles

NASA Technical Reports Server (NTRS)

Defacio, Brian; Kim, S.-H.; Vannevel, A.

1994-01-01

The squeezed states or Bogoliubov transformations and wavelets are applied to two problems in nonrelativistic statistical mechanics: the dielectric response of liquid water, epsilon(q-vector,w), and the bubble formation in water during insonnification. The wavelets are special phase-space windows which cover the domain and range of L(exp 1) intersection of L(exp 2) of classical causal, finite energy solutions. The multiresolution of discrete wavelets in phase space gives a decomposition into regions of time and scales of frequency thereby allowing the renormalization group to be applied to new systems in addition to the tired 'usual suspects' of the Ising models and lattice gasses. The Bogoliubov transformation: squeeze transformation is applied to the dipolaron collective mode in water and to the gas produced by the explosive cavitation process in bubble formation.

Calculation of UV, IR, and NMR Spectra of Diethyl 2,2'-[(1,1'-Biphenyl)-4,4'-Diylbis(Azanediyl)]Diacetate

NASA Astrophysics Data System (ADS)

Almodarresiyeh, H. A.; Shahab, S. N.; Zelenkovsky, V. M.; Ariko, N. G.; Filippovich, L. N.; Agabekov, V. E.

2014-03-01

The new substance diethyl 2,2'-[(1,1'-biphenyl)-4,4'-diylbis(azanediyl)]diacetate (M13) was modeled using the Hartree-Fock and density functional theory methods and then synthesized. The electronic absorption spectrum of M13 in dimethylformamide solution was calculated. The UV, IR, and NMR spectra of M13 were presented.

Temperature dependence of the symmetry energy and neutron skins in Ni, Sn, and Pb isotopic chains

NASA Astrophysics Data System (ADS)

Antonov, A. N.; Kadrev, D. N.; Gaidarov, M. K.; Sarriguren, P.; de Guerra, E. Moya

2017-02-01

The temperature dependence of the symmetry energy for isotopic chains of even-even Ni, Sn, and Pb nuclei is investigated in the framework of the local density approximation (LDA). The Skyrme energy density functional with two Skyrme-class effective interactions, SkM* and SLy4, is used in the calculations. The temperature-dependent proton and neutron densities are calculated through the hfbtho code that solves the nuclear Skyrme-Hartree-Fock-Bogoliubov problem by using the cylindrical transformed deformed harmonic-oscillator basis. In addition, two other density distributions of 208Pb, namely the Fermi-type density determined within the extended Thomas-Fermi (TF) method and symmetrized-Fermi local density obtained within the rigorous density functional approach, are used. The kinetic energy densities are calculated either by the hfbtho code or, for a comparison, by the extended TF method up to second order in temperature (with T2 term). Alternative ways to calculate the symmetry energy coefficient within the LDA are proposed. The results for the thermal evolution of the symmetry energy coefficient in the interval T =0 -4 MeV show that its values decrease with temperature. The temperature dependence of the neutron and proton root-mean-square radii and corresponding neutron skin thickness is also investigated, showing that the effect of temperature leads mainly to a substantial increase of the neutron radii and skins, especially in the more neutron-rich nuclei, a feature that may have consequences on astrophysical processes and neutron stars.

Low-rank factorization of electron integral tensors and its application in electronic structure theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peng, Bo; Kowalski, Karol

In this letter, we introduce the reverse Cuthill-McKee (RCM) algorithm, which is often used for the bandwidth reduction of sparse tensors, to transform the two-electron integral tensors to their block diagonal forms. By further applying the pivoted Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates the low-rank factorization of the high-dimensional tensor contractions that are usually encountered in post-Hartree-Fock calculations. In this letter, we discuss the second-order Møller-Plesset (MP2) method and linear coupled- cluster model with doublesmore » (L-CCD) as two simple examples to demonstrate the efficiency of the RCM-CD technique in representing two-electron integrals in a compact form.« less

Physics in Screening Environments

NASA Astrophysics Data System (ADS)

Certik, Ondrej

In the current study, we investigated atoms in screening environments like plasmas. It is common practice to extract physical data, such as temperature and electron densities, from plasma experiments. We present results that address inherent computational difficulties that arise when the screening approach is extended to include the interaction between the atomic electrons. We show that there may arise an ambiguity in the interpretation of physical properties, such as temperature and charge density, from experimental data due to the opposing effects of electron-nucleus screening and electron-electron screening. The focus of the work, however, is on the resolution of inherent computational challenges that appear in the computation of two-particle matrix elements. Those enter already at the Hartree-Fock level. Furthermore, as examples of post Hartree-Fock calculations, we show second-order Green's function results and many body perturbation theory results of second order. A self-contained derivation of all necessary equations has been included. The accuracy of the implementation of the method is established by comparing standard unscreened results for various atoms and molecules against literature for Hartree-Fock as well as Green's function and many body perturbation theory. The main results of the thesis are presented in the chapter called Screened Results, where the behavior of several atomic systems depending on electron-electron and electron-nucleus Debye screening was studied. The computer code that we have developed has been made available for anybody to use. Finally, we present and discuss results obtained for screened interactions. We also examine thoroughly the computational details of the calculations and particular implementations of the method.

Hartree and Exchange in Ensemble Density Functional Theory: Avoiding the Nonuniqueness Disaster.

PubMed

Gould, Tim; Pittalis, Stefano

2017-12-15

Ensemble density functional theory is a promising method for the efficient and accurate calculation of excitations of quantum systems, at least if useful functionals can be developed to broaden its domain of practical applicability. Here, we introduce a guaranteed single-valued "Hartree-exchange" ensemble density functional, E_{Hx}[n], in terms of the right derivative of the universal ensemble density functional with respect to the coupling constant at vanishing interaction. We show that E_{Hx}[n] is straightforwardly expressible using block eigenvalues of a simple matrix [Eq. (14)]. Specialized expressions for E_{Hx}[n] from the literature, including those involving superpositions of Slater determinants, can now be regarded as originating from the unifying picture presented here. We thus establish a clear and practical description for Hartree and exchange in ensemble systems.

Wave-function-based approach to quasiparticle bands: Insight into the electronic structure of c-ZnS

NASA Astrophysics Data System (ADS)

Stoyanova, A.; Hozoi, L.; Fulde, P.; Stoll, H.

2011-05-01

Ab initio wave-function-based methods are employed for the study of quasiparticle energy bands of zinc-blende ZnS, with focus on the Zn 3d “semicore” states. The relative energies of these states with respect to the top of the S 3p valence bands appear to be poorly described as compared to experimental values not only within the local density approximation (LDA), but also when many-body corrections within the GW approximation are applied to the LDA or LDA + U mean-field solutions [T. Miyake, P. Zhang, M. L. Cohen, and S. G. Louie, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.74.245213 74, 245213 (2006)]. In the present study, we show that for the accurate description of the Zn 3d states a correlation treatment based on wave-function methods is needed. Our study rests on a local Hamiltonian approach which rigorously describes the short-range polarization and charge redistribution effects around an extra hole or electron placed into the valence respective conduction bands of semiconductors and insulators. The method also facilitates the computation of electron correlation effects beyond relaxation and polarization. The electron correlation treatment is performed on finite clusters cut off the infinite system. The formalism makes use of localized Wannier functions and embedding potentials derived explicitly from prior periodic Hartree-Fock calculations. The on-site and nearest-neighbor charge relaxation lead to corrections of several eV to the Hartree-Fock band energies and gap. Corrections due to long-range polarization are of the order of 1.0 eV. The dispersion of the Hartree-Fock bands is only slightly affected by electron correlations. We find the Zn 3d “semicore” states to lie ~9.0 eV below the top of the S 3p valence bands, in very good agreement with values from valence-band x-ray photoemission.

Electronic Structure and Absorption Spectra of Sodium 2-Hydroxy-5-({2-Methoxy-4[(4-Sulfophenyl)Diazenyl]Phenyl}Diazenyl)Benzoate

NASA Astrophysics Data System (ADS)

Almodarresiyeh, H. A.; Shahab, S. N.; Zelenkovsky, V. M.; Agabekov, V. E.

2014-03-01

The electronic structure and geometry of the synthesized azodye sodium 2-hydroxy-5-({2-methoxy-4[(4-sulfophenyl) diazenyl]phenyl}diazenyl)benzoate (M12) were calculated theoretically by an ab initio Hartree-Fock method in basis set 6-31G. The nature of absorption bands in the visible and near-UV spectral regions was interpreted.

Relativistic effects on magnetic circular dichroism studied by GUHF/SECI method

NASA Astrophysics Data System (ADS)

Honda, Y.; Hada, M.; Ehara, M.; Nakatsuji, H.; Downing, J.; Michl, J.

2002-04-01

Quasi-relativistic formulation of the Magnetic circular dichroism (MCD) Faraday terms are presented using the generalized unrestricted Hartree-Fock (GUHF)/single excitation configuration interaction (SECI) method combined with the finite perturbation method and applied to the MCD of the three n-σ ∗ states ( 3Q1, 3Q0, 1Q1) of CH 3I. The Faraday B term for the 1Q1 state was 0.1976( Debye) 2( Bohr magneton )/(10 3 cm-1) in the non-relativistic theory, but was dramatically improved by the relativistic effect and became 0.0184 in agreement with the experimental values, 0.014 and 0.0257. This change was mainly due to the one-electron spin-orbit (SO1) term rather than the spin-free relativistic (SFR) and the two-electron spin-orbit (SO2) terms.

On the physical interpretation of the nuclear molecular orbital energy.

PubMed

Charry, Jorge; Pedraza-González, Laura; Reyes, Andrés

2017-06-07

Recently, several groups have extended and implemented molecular orbital (MO) schemes to simultaneously obtain wave functions for electrons and selected nuclei. Many of these schemes employ an extended Hartree-Fock approach as a first step to find approximate electron-nuclear wave functions and energies. Numerous studies conducted with these extended MO methodologies have explored various effects of quantum nuclei on physical and chemical properties. However, to the best of our knowledge no physical interpretation has been assigned to the nuclear molecular orbital energy (NMOE) resulting after solving extended Hartree-Fock equations. This study confirms that the NMOE is directly related to the molecular electrostatic potential at the position of the nucleus.

Average Nuclear Potentials from Selfconsistent Semiclassical Calculations

NASA Astrophysics Data System (ADS)

Bartel, J.

1999-03-01

Using the selfconsistent semiclassical Extended Thomas-Fermi (ETF) method up to 4th order in connection with Skyrme forces it is demonstrated that the neutron and proton average potentials obtained using the semiclassical functionals τ (ETF)[ρ] and vec {J}(ETF)[ρ] reproduce the corresponding Hartree-Fock fields extremely well, except for shell oscillations in the nuclear center.

Basis set and electron correlation effects on the polarizability and second hyperpolarizability of model open-shell π-conjugated systems

NASA Astrophysics Data System (ADS)

Champagne, Benoı̂t; Botek, Edith; Nakano, Masayoshi; Nitta, Tomoshige; Yamaguchi, Kizashi

2005-03-01

The basis set and electron correlation effects on the static polarizability (α) and second hyperpolarizability (γ) are investigated ab initio for two model open-shell π-conjugated systems, the C5H7 radical and the C6H8 radical cation in their doublet state. Basis set investigations evidence that the linear and nonlinear responses of the radical cation necessitate the use of a less extended basis set than its neutral analog. Indeed, double-zeta-type basis sets supplemented by a set of d polarization functions but no diffuse functions already provide accurate (hyper)polarizabilities for C6H8 whereas diffuse functions are compulsory for C5H7, in particular, p diffuse functions. In addition to the 6-31G*+pd basis set, basis sets resulting from removing not necessary diffuse functions from the augmented correlation consistent polarized valence double zeta basis set have been shown to provide (hyper)polarizability values of similar quality as more extended basis sets such as augmented correlation consistent polarized valence triple zeta and doubly augmented correlation consistent polarized valence double zeta. Using the selected atomic basis sets, the (hyper)polarizabilities of these two model compounds are calculated at different levels of approximation in order to assess the impact of including electron correlation. As a function of the method of calculation antiparallel and parallel variations have been demonstrated for α and γ of the two model compounds, respectively. For the polarizability, the unrestricted Hartree-Fock and unrestricted second-order Møller-Plesset methods bracket the reference value obtained at the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples level whereas the projected unrestricted second-order Møller-Plesset results are in much closer agreement with the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples values than the projected unrestricted Hartree-Fock

Self-Attractive Hartree Decomposition: Partitioning Electron Density into Smooth Localized Fragments.

PubMed

Zhu, Tianyu; de Silva, Piotr; Van Voorhis, Troy

2018-01-09

Chemical bonding plays a central role in the description and understanding of chemistry. Many methods have been proposed to extract information about bonding from quantum chemical calculations, the majority of them resorting to molecular orbitals as basic descriptors. Here, we present a method called self-attractive Hartree (SAH) decomposition to unravel pairs of electrons directly from the electron density, which unlike molecular orbitals is a well-defined observable that can be accessed experimentally. The key idea is to partition the density into a sum of one-electron fragments that simultaneously maximize the self-repulsion and maintain regular shapes. This leads to a set of rather unusual equations in which every electron experiences self-attractive Hartree potential in addition to an external potential common for all the electrons. The resulting symmetry breaking and localization are surprisingly consistent with chemical intuition. SAH decomposition is also shown to be effective in visualization of single/multiple bonds, lone pairs, and unusual bonds due to the smooth nature of fragment densities. Furthermore, we demonstrate that it can be used to identify specific chemical bonds in molecular complexes and provides a simple and accurate electrostatic model of hydrogen bonding.

Theoretical X-ray production cross sections at incident photon energies across L{sub i} (i=1-3) absorption edges of Br

DOE Office of Scientific and Technical Information (OSTI.GOV)

Puri, Sanjiv

The X-ray production (XRP) cross sections, σ{sub Lk} (k = l, η, α, β{sub 6}, β{sub 1}, β{sub 3}, β{sub 4}, β{sub 9,10}, γ{sub 1,5}, γ{sub 2,3}) have been evaluated at incident photon energies across the L{sub i}(i=1-3) absorption edge energies of {sub 35}Br using theoretical data sets of different physical parameters, namely, the L{sub i}(i=1-3) sub-shell the X-ray emission rates based on the Dirac-Fock (DF) model, the fluorescence and Coster Kronig yields based on the Dirac-Hartree-Slater (DHS) model, and two sets of the photoionisation cross sections based on the relativistic Hartree-Fock-Slater (RHFS) model and the Dirac-Fock (DF) model, inmore » order to highlight the importance of electron exchange effects at photon energies in vicinity of absorption edge energies.« less

Multipole expansions and Fock symmetry of the hydrogen atom

NASA Astrophysics Data System (ADS)

Meremianin, A. V.; Rost, J.-M.

2006-10-01

The main difficulty in utilizing the O(4) symmetry of the hydrogen atom in practical calculations is the dependence of the Fock stereographic projection on energy. This is due to the fact that the wavefunctions of the states with different energies are proportional to the hyperspherical harmonics (HSH) corresponding to different points on the hypersphere. Thus, the calculation of the matrix elements reduces to the problem of re-expanding HSH in terms of HSH depending on different points on the hypersphere. We solve this problem by applying the technique of multipole expansions for four-dimensional HSH. As a result, we obtain the multipole expansions whose coefficients are the matrix elements of the boost operator taken between hydrogen wavefunctions (i.e., hydrogen form factors). The explicit expressions for those coefficients are derived. It is shown that the hydrogen matrix elements can be presented as derivatives of an elementary function. Such an operator representation is convenient for the derivation of recurrence relations connecting matrix elements between states corresponding to different values of the quantum numbers n and l.

Immediate estimation of correlation energy for molecular systems from the partial charges on atoms in the molecule

NASA Astrophysics Data System (ADS)

Kristyán, Sándor

1997-11-01

In the author's previous work (Chem. Phys. Lett. 247 (1995) 101 and Chem. Phys. Lett. 256 (1996) 229) a simple quasi-linear relationship was introduced between the number of electrons, N, participating in any molecular system and the correlation energy: -0.035 ( N - 1) > Ecorr[hartree] > - 0.045( N -1). This relationship was developed to estimate more accurately correlation energy immediately in ab initio calculations by using the partial charges of atoms in the molecule, easily obtained after Hartree-Fock self-consistent field (HF-SCF) calculations. The method is compared to the well-known B3LYP, MP2, CCSD and G2M methods. Correlation energy estimations for negatively (-1) charged atomic ions are also reported.

BRST quantization of Yang-Mills theory: A purely Hamiltonian approach on Fock space

NASA Astrophysics Data System (ADS)

Öttinger, Hans Christian

2018-04-01

We develop the basic ideas and equations for the BRST quantization of Yang-Mills theories in an explicit Hamiltonian approach, without any reference to the Lagrangian approach at any stage of the development. We present a new representation of ghost fields that combines desirable self-adjointness properties with canonical anticommutation relations for ghost creation and annihilation operators, thus enabling us to characterize the physical states on a well-defined Fock space. The Hamiltonian is constructed by piecing together simple BRST invariant operators to obtain a minimal invariant extension of the free theory. It is verified that the evolution equations implied by the resulting minimal Hamiltonian provide a quantum version of the classical Yang-Mills equations. The modifications and requirements for the inclusion of matter are discussed in detail.

Particle-hole symmetry in many-body theories of electron correlation

NASA Astrophysics Data System (ADS)

Kats, Daniel; Usvyat, Denis; Manby, Frederick R.

2018-06-01

Second-quantised creation and annihilation operators for fermionic particles anticommute, but the same is true for the creation and annihilation operators for holes. This introduces a symmetry into the quantum theory of fermions that is absent for bosons. In ab initio electronic structure theory, it is common to classify methods by the number of electrons for which the method returns exact results: for example Hartree-Fock theory is exact for one-electron systems, whereas coupled-cluster theory with single and double excitations is exact for two-electron systems. Here, we discuss the generalisation: methods based on approximate wavefunctions that are exact for n-particle systems are also exact for n-hole systems. Novel electron correlation methods that attempt to improve on the coupled-cluster framework sometimes retain this property, and sometimes lose it. Here, we argue for retaining particle-hole symmetry as a desirable design criterion of approximate electron correlation methods. Dispensing with it might lead to loss of n-representability of density matrices, and this in turn can lead to spurious long-range behaviour in the correlation energy.

The vibrational spectroscopic studies and molecular property analysis of L-Phenylalanine using quantum chemical method

NASA Astrophysics Data System (ADS)

Borah, Mukunda Madhab; Devi, Th. Gomti

2017-05-01

In the present work, L-phenylalanine is studied using the experimental and theoretical methods. The spectral characterization of the molecule has been done using Raman, FTIR, Hartee-Fock(HF), density functional theory (DFT) and vibrational energy distribution analysis (VEDA) calculation. The optimization of the molecule has been studied using basis set HF/6-31G(d,p) and B3LYP/6-31G(d,p) for Hartree Fock and density functional theory calculation. The complete vibrational assignment of the molecule in monomer and dimer states have been attempted. The potential energy distribution and normal mode analysis are also carried out to determine the contributions of bond oscillators in each normal mode. The molecular geometry, HOMO-LUMO energy gap, molecular hardness (η), ionization energy (IE), electron affinity (EA), total energy and dipole moment were determined from the calculated data. The observed experimental and the scaled theoretical results are compared and found to be in good agreement. The vibrational assignment of molecule in different dimer states has also been done using SERS data and better correlated Raman peaks are observed as compare to normal Raman technique.

Theoretical L-shell Coster-Kronig energies 11 or equal to z or equal to 103

NASA Technical Reports Server (NTRS)

Chen, M. H.; Crasemann, B.; Huang, K. N.; Aoyagi, M.; Mark, H.

1976-01-01

Relativistic relaxed-orbital calculations of L-shell Coster-Kronig transition energies have been performed for all possible transitions in atoms with atomic numbers. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order approximation to the local approximation was thus included. Quantum-electrodynamic corrections were made. Each transition energy was computed as the difference between results of separate self-consistent-field calculations for the initial, singly ionized state and the final two-hole state. The following quantities are listed: total transition energy, 'electric' (Dirac-Hartree-Fock-Slater) contribution, magnetic and retardation contributions, and contributions due to vacuum polarization and self energy.

Interacting Electrons in Graphene: Fermi Velocity Renormalization and Optical Response

NASA Astrophysics Data System (ADS)

Stauber, T.; Parida, P.; Trushin, M.; Ulybyshev, M. V.; Boyda, D. L.; Schliemann, J.

2017-06-01

We have developed a Hartree-Fock theory for electrons on a honeycomb lattice aiming to solve a long-standing problem of the Fermi velocity renormalization in graphene. Our model employs no fitting parameters (like an unknown band cutoff) but relies on a topological invariant (crystal structure function) that makes the Hartree-Fock sublattice spinor independent of the electron-electron interaction. Agreement with the experimental data is obtained assuming static self-screening including local field effects. As an application of the model, we derive an explicit expression for the optical conductivity and discuss the renormalization of the Drude weight. The optical conductivity is also obtained via precise quantum Monte Carlo calculations which compares well to our mean-field approach.

Vibrational Spectral Studies of Gemfibrozil

NASA Astrophysics Data System (ADS)

Benitta, T. Asenath; Balendiran, G. K.; James, C.

2008-11-01

The Fourier Transform Raman and infrared spectra of the crystallized drug molecule 5-(2,5-Dimethylphenoxy)-2,2-dimethylpentanoic acid (Gemfibrozil) have been recorded and analyzed. Quantum chemical computational methods have been employed using Gaussian 03 software package based on Hartree Fock method for theoretically modeling the grown molecule. The optimized geometry and vibrational frequencies have been predicted. Observed vibrational modes have been assigned with the aid of normal coordinate analysis.

Non-expanded dispersion energies and damping functions for Ar 2 and Li 2

NASA Astrophysics Data System (ADS)

Knowles, Peter J.; Meath, William J.

1986-02-01

The non-expanded second-order dispersion energies and damping functions associated with the long-range dispersion energies varying as R-6, R-8and R-10 have been calculated for Ar 2 and Li 2 with the time-dependent Hartree-Fock method, using extended Gaussian basis sets. These results are used to discuss the difficulties associated with ab initio computations of these quantities.

Energy-consistent small-core pseudopotentials for 3d-transition metals adapted to quantum Monte Carlo calculations.

PubMed

Burkatzki, M; Filippi, Claudia; Dolg, M

2008-10-28

We extend our recently published set of energy-consistent scalar-relativistic Hartree-Fock pseudopotentials by the 3d-transition metal elements, scandium through zinc. The pseudopotentials do not exhibit a singularity at the nucleus and are therefore suitable for quantum Monte Carlo (QMC) calculations. The pseudopotentials and the accompanying basis sets (VnZ with n=T,Q) are given in standard Gaussian representation and their parameter sets are presented. Coupled cluster, configuration interaction, and QMC studies are carried out for the scandium and titanium atoms and their oxides, demonstrating the good performance of the pseudopotentials. Even though the choice of pseudopotential form is motivated by QMC, these pseudopotentials can also be employed in other quantum chemical approaches.

Interpretation of the silver L X-ray spectrum

NASA Technical Reports Server (NTRS)

Chen, M. H.; Crasemann, B.; Aoyagi, M.; Mark, H.

1977-01-01

Silver L X-ray energies were calculated using theoretical binding energies from relaxed orbital relativistic Hartree-Fock-Slater calculations. Theoretical X-ray energies are compared with experimental results.

A Well-Tempered Hybrid Method for Solving Challenging Time-Dependent Density Functional Theory (TDDFT) Systems.

PubMed

Kasper, Joseph M; Williams-Young, David B; Vecharynski, Eugene; Yang, Chao; Li, Xiaosong

2018-04-10

The time-dependent Hartree-Fock (TDHF) and time-dependent density functional theory (TDDFT) equations allow one to probe electronic resonances of a system quickly and inexpensively. However, the iterative solution of the eigenvalue problem can be challenging or impossible to converge, using standard methods such as the Davidson algorithm for spectrally dense regions in the interior of the spectrum, as are common in X-ray absorption spectroscopy (XAS). More robust solvers, such as the generalized preconditioned locally harmonic residual (GPLHR) method, can alleviate this problem, but at the expense of higher average computational cost. A hybrid method is proposed which adapts to the problem in order to maximize computational performance while providing the superior convergence of GPLHR. In addition, a modification to the GPLHR algorithm is proposed to adaptively choose the shift parameter to enforce a convergence of states above a predefined energy threshold.

Theoretical study of the electron affinities of MF6 and MF - 6 (M=Cr, Mo, and W) using a model potential method

NASA Astrophysics Data System (ADS)

Sakai, Yoshiko; Miyoshi, Eisaku

1987-09-01

Electronic structures of MF6, MF-6, and MF2-6 (M=Cr, Mo, and W) were calculated using a model potential method in the Hartree-Fock-Roothaan scheme. Major relativistic effects were taken into account for the calculations on MoFq6 and WFq6 (q=0, -1, and -2). It is shown that the calculated electron affinities (EAs) are extremely high for all the MF6 molecules, and that the CrF-6 and MoF-6 anions also have positive EAs, whereas the WF-6 anion has a slightly negative EA. The behaviors of the EAs are interpreted with reference to the electronic structures of the MFq6 systems.

Superintegrability of the Fock-Darwin system

NASA Astrophysics Data System (ADS)

Drigho-Filho, E.; Kuru, Ş.; Negro, J.; Nieto, L. M.

2017-08-01

The Fock-Darwin system is analyzed from the point of view of its symmetry properties in the quantum and classical frameworks. The quantum Fock-Darwin system is known to have two sets of ladder operators, a fact which guarantees its solvability. We show that for rational values of the quotient of two relevant frequencies, this system is superintegrable, the quantum symmetries being responsible for the degeneracy of the energy levels. These symmetries are of higher order and close a polynomial algebra. In the classical case, the ladder operators are replaced by ladder functions and the symmetries by constants of motion. We also prove that the rational classical system is superintegrable and its trajectories are closed. The constants of motion are also generators of symmetry transformations in the phase space that have been integrated for some special cases. These transformations connect different trajectories with the same energy. The coherent states of the quantum superintegrable system are found and they reproduce the closed trajectories of the classical one.

On the classification of the spectrally stable standing waves of the Hartree problem

NASA Astrophysics Data System (ADS)

Georgiev, Vladimir; Stefanov, Atanas

2018-05-01

We consider the fractional Hartree model, with general power non-linearity and arbitrary spatial dimension. We construct variationally the "normalized" solutions for the corresponding Choquard-Pekar model-in particular a number of key properties, like smoothness and bell-shapedness are established. As a consequence of the construction, we show that these solitons are spectrally stable as solutions to the time-dependent Hartree model. In addition, we analyze the spectral stability of the Moroz-Van Schaftingen solitons of the classical Hartree problem, in any dimensions and power non-linearity. A full classification is obtained, the main conclusion of which is that only and exactly the "normalized" solutions (which exist only in a portion of the range) are spectrally stable.

Identification of DNA-Binding Proteins Using Mixed Feature Representation Methods.

PubMed

Qu, Kaiyang; Han, Ke; Wu, Song; Wang, Guohua; Wei, Leyi

2017-09-22

DNA-binding proteins play vital roles in cellular processes, such as DNA packaging, replication, transcription, regulation, and other DNA-associated activities. The current main prediction method is based on machine learning, and its accuracy mainly depends on the features extraction method. Therefore, using an efficient feature representation method is important to enhance the classification accuracy. However, existing feature representation methods cannot efficiently distinguish DNA-binding proteins from non-DNA-binding proteins. In this paper, a multi-feature representation method, which combines three feature representation methods, namely, K-Skip-N-Grams, Information theory, and Sequential and structural features (SSF), is used to represent the protein sequences and improve feature representation ability. In addition, the classifier is a support vector machine. The mixed-feature representation method is evaluated using 10-fold cross-validation and a test set. Feature vectors, which are obtained from a combination of three feature extractions, show the best performance in 10-fold cross-validation both under non-dimensional reduction and dimensional reduction by max-relevance-max-distance. Moreover, the reduced mixed feature method performs better than the non-reduced mixed feature technique. The feature vectors, which are a combination of SSF and K-Skip-N-Grams, show the best performance in the test set. Among these methods, mixed features exhibit superiority over the single features.

Comment on atomic independent-particle models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Doda, D.D.; Gravey, R.H.; Green, A.E.S.

1975-08-01

The Hartree-Fock-Slater (HFS) independent-particle model in the form developed by Hermann and Skillman (HS) and the Green, Sellin, and Zachor (GSZ) analytic independent-particle model are being used for many types of applications of atomic theory to avoid cumbersome, albeit more rigorous, many-body calculations. The single-electron eigenvalues obtained with these models are examined and it is found that the GSZ model is capable of yielding energy eigenvalues for valence electrons which are substantially closer to experimental values than are the results of HS-HFS calculations. With the aid of an analytic representation of the equivalent HS-HFS screening function, the difficulty with thismore » model is identified as a weakness of the potential in the neighborhood of the valence shell. Accurate representations of valence states are important in most atomic applications of the independent-particle model. (auth)« less

Angular distribution of photoelectrons from atomic oxygen, nitrogen and carbon. [in upper atmosphere

NASA Technical Reports Server (NTRS)

Manson, S. J.; Kennedy, D. J.; Starace, A. F.; Dill, D.

1974-01-01

The angular distributions of photoelectrons from atomic oxygen, nitrogen, and carbon are calculated. Both Hartree-Fock and Hartree-Slater (Herman-Skillman) wave functions are used for oxygen, and the agreement is excellent; thus only Hartree-Slater functions are used for carbon and nitrogen. The pitch-angle distribution of photoelectrons is discussed, and it is shown that previous approximations of energy-independent isotropic or sin squared theta distributions are at odds with the authors' results, which vary with energy. This variation with energy is discussed, as is the reliability of these calculations.

The AB Initio Mia Method: Theoretical Development and Practical Applications

NASA Astrophysics Data System (ADS)

Peeters, Anik

The bottleneck in conventional ab initio Hartree -Fock calculations is the storage of the electron repulsion integrals because their number increases with the fourth power of the number of basis functions. This problem can be solved by a combination of the multiplicative integral approximation (MIA) and the direct SCF method. The MIA approach was successfully applied in the geometry optimisation of some biologically interesting compounds like the neurolepticum Haloperidol and two TIBO derivatives, inactivators of HIV1. In this thesis the potency of the MIA-method is shown by the application of this method in the calculation of the forces on the nuclei. In addition, the MIA method enabled the development of a new model for performing crystal field studies: the supermolecule model. The results for this model are in better agreement with experimental data than the results for the point charge model. This is illustrated by the study of some small molecules in the solid state: 2,3-diketopiperazine, formamide oxime and two polymorphic forms of glycine, alpha-glycine and beta-glycine.

Simultaneous analytical optimization of variational parameters in Gaussian-type functions with full configuration interaction of multicomponent molecular orbital method by elimination of translational and rotational motions: application to isotopomers of the hydrogen molecule.

PubMed

Ishimoto, Takayoshi; Tachikawa, Masanori; Nagashima, Umpei

2008-04-28

We have extended the multicomponent molecular orbital (MCMO) method to the full-configuration interaction (full-CI) fully variational molecular orbital method by elimination of translational and rotational motion components from total Hamiltonian. In the MCMO scheme, the quantum effects of protons and deuterons as well as electrons can be directly taken into account. All variational parameters in the full-CI scheme, i.e., exponents and centers (alpha and R) in the Gaussian-type function (GTF) basis set as well as the CI coefficients, are simultaneously optimized by using their analytical gradients. The total energy of the H(2) molecule calculated using the electronic [6s3p2d1f] and nuclear [1s1p1d1f] GTFs is -1.161 726 hartree, which can be compared to the energy of -1.164 025 hartree reported using a 512 term-explicitly correlated GTF calculation. Although the d- and f-type nuclear GTFs contribute to the improvement of energy convergence, the convergence of electron-nucleus correlation energy is slower than that of electron-electron one. The nuclear wave functions are delocalized due to the electron-nucleus correlation effect compared to the result of Hartree-Fock level of MCMO method. In addition, the average internuclear distances of all diatomic molecules are within 0.001 A of the previously reported experimental results. The dipole moment of the HD molecule estimated by our method is 8.4 x 10(-4) D, which is in excellent agreement with the experimental result of (8-10) x 10(-4) D.

High-resolution study of Gamow-Teller excitations in the 42Ca(3He,t )42Sc reaction and the observation of a "low-energy super-Gamow-Teller state"

NASA Astrophysics Data System (ADS)

Fujita, Y.; Fujita, H.; Adachi, T.; Susoy, G.; Algora, A.; Bai, C. L.; Colò, G.; Csatlós, M.; Deaven, J. M.; Estevez-Aguado, E.; Guess, C. J.; Gulyás, J.; Hatanaka, K.; Hirota, K.; Honma, M.; Ishikawa, D.; Krasznahorkay, A.; Matsubara, H.; Meharchand, R.; Molina, F.; Nakada, H.; Okamura, H.; Ong, H. J.; Otsuka, T.; Perdikakis, G.; Rubio, B.; Sagawa, H.; Sarriguren, P.; Scholl, C.; Shimbara, Y.; Stephenson, E. J.; Suzuki, T.; Tamii, A.; Thies, J. H.; Yoshida, K.; Zegers, R. G. T.; Zenihiro, J.

2015-06-01

To study the Gamow-Teller (GT) transitions from the Tz=+1 nucleus 42Ca to the Tz=0 nucleus 42Sc, where Tz is the z component of isospin T , we performed a (p ,n )-type (3He,t ) charge-exchange reaction at 140 MeV/nucleon and scattering angles around 0∘. With an energy resolution of 29 keV, states excited by GT transitions (GT states) could be studied accurately. The reduced GT transition strengths B (GT) were derived up to the excitation energy of 13 MeV, assuming the proportionality between the cross sections at 0∘ and B (GT) values. The main part of the observed GT transition strength is concentrated in the lowest 0.611-MeV, Jπ=1+ GT state. All the other states at higher energies are weakly excited. Shell-model calculations could reproduce the gross feature of the experimental B (GT) distribution, and random-phase-approximation calculations including an attractive isoscalar interaction showed that the 0.611-MeV state has a collective nature. It was found that this state has all of the properties of a "low-energy super-Gamow-Teller state." It is expected that low-lying Jπ=1+ GT states have T =0 in the Tz=0 nucleus 42Sc. However, T =1 states are situated in a higher energy region. Assuming an isospin-analogous structure in A =42 isobars, analogous T =1 , 1+ states are also expected in 42Ca. Comparing the (3He 42,tCa) 42Sc and 42Ca(p ,p') spectra measured at 0∘, candidates for T =1 GT states could be found in the 10 -12 -MeV region of 42Sc. They were all weakly excited. The mass dependence of the GT strength distributions in Sc isotopes is also discussed.

Generalization of the Kohn-Sham system that can represent arbitrary one-electron density matrices

DOE PAGES

Hubertus J. J. van Dam

2016-04-27

Density functional theory is currently the most widely applied method in electronic structure theory. The Kohn-Sham method, based on a fictitious system of noninteracting particles, is the workhorse of the theory. The particular form of the Kohn-Sham wave function admits only idempotent one-electron density matrices whereas wave functions of correlated electrons in post-Hartree-Fock methods invariably have fractional occupation numbers. Here we show that by generalizing the orbital concept and introducing a suitable dot product as well as a probability density, a noninteracting system can be chosen that can represent the one-electron density matrix of any system, even one with fractionalmore » occupation numbers. This fictitious system ensures that the exact electron density is accessible within density functional theory. It can also serve as the basis for reduced density matrix functional theory. Moreover, to aid the analysis of the results the orbitals may be assigned energies from a mean-field Hamiltonian. This produces energy levels that are akin to Hartree-Fock orbital energies such that conventional analyses based on Koopmans' theorem are available. Lastly, this system is convenient in formalisms that depend on creation and annihilation operators as they are trivially applied to single-determinant wave functions.« less

Non-perturbative calculation of orbital and spin effects in molecules subject to non-uniform magnetic fields

NASA Astrophysics Data System (ADS)

Sen, Sangita; Tellgren, Erik I.

2018-05-01

External non-uniform magnetic fields acting on molecules induce non-collinear spin densities and spin-symmetry breaking. This necessitates a general two-component Pauli spinor representation. In this paper, we report the implementation of a general Hartree-Fock method, without any spin constraints, for non-perturbative calculations with finite non-uniform fields. London atomic orbitals are used to ensure faster basis convergence as well as invariance under constant gauge shifts of the magnetic vector potential. The implementation has been applied to investigate the joint orbital and spin response to a field gradient—quantified through the anapole moments—of a set of small molecules. The relative contributions of orbital and spin-Zeeman interaction terms have been studied both theoretically and computationally. Spin effects are stronger and show a general paramagnetic behavior for closed shell molecules while orbital effects can have either direction. Basis set convergence and size effects of anapole susceptibility tensors have been reported. The relation of the mixed anapole susceptibility tensor to chirality is also demonstrated.

Gamow-Teller transitions and neutron-proton-pair transfer reactions

NASA Astrophysics Data System (ADS)

Van Isacker, P.; Macchiavelli, A. O.

2018-05-01

We propose a schematic model of nucleons moving in spin-orbit partner levels, j = l ± 1/2, to explain Gamow-Teller and two-nucleon transfer data in N = Z nuclei above 40Ca. Use of the LS coupling scheme provides a more transparent approach to interpret the structure and reaction data. We apply the model to the analysis of charge-exchange, 42Ca(3He,t)42Sc, and np-transfer, 40Ca(3He,p)42Sc, reactions data to define the elementary modes of excitation in terms of both isovector and isoscalar pairs, whose properties can be determined by adjusting the parameters of the model (spin-orbit splitting, isovector pairing strength and quadrupole matrix element) to the available data. The overall agreement with experiment suggests that the approach captures the main physics ingredients and provides the basis for a boson approximation that can be extended to heavier nuclei. Our analysis also reveals that the SU(4)-symmetry limit is not realized in 42Sc.

Measurement of Kα and Kβ fluorescence cross sections for elements in the range 44<=Z<=68 at 59.5 keV

NASA Astrophysics Data System (ADS)

Budak, G.; Karabulut, A.; Demir, L.; Sahin, Y.

1999-09-01

The Kα and Kβ x-ray fluorescence cross sections have been measured for elements in the range 44<=Z<=68 at an excitation energy of 59.5-keV γ ray from 241Am radioisotope with a Si(Li) detector. A reasonable agreement is found between the present experimental results and the theoretically calculated values based on photoionization cross sections by Scofield using Hartree-Slater and Hartree-Fock central potential theory.

Analytical energy gradient based on spin-free infinite-order Douglas-Kroll-Hess method with local unitary transformation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakajima, Yuya; Seino, Junji; Nakai, Hiromi, E-mail: nakai@waseda.jp

In this study, the analytical energy gradient for the spin-free infinite-order Douglas-Kroll-Hess (IODKH) method at the levels of the Hartree-Fock (HF), density functional theory (DFT), and second-order Møller-Plesset perturbation theory (MP2) is developed. Furthermore, adopting the local unitary transformation (LUT) scheme for the IODKH method improves the efficiency in computation of the analytical energy gradient. Numerical assessments of the present gradient method are performed at the HF, DFT, and MP2 levels for the IODKH with and without the LUT scheme. The accuracies are examined for diatomic molecules such as hydrogen halides, halogen dimers, coinage metal (Cu, Ag, and Au) halides,more » and coinage metal dimers, and 20 metal complexes, including the fourth–sixth row transition metals. In addition, the efficiencies are investigated for one-, two-, and three-dimensional silver clusters. The numerical results confirm the accuracy and efficiency of the present method.« less

A long-range-corrected density functional that performs well for both ground-state properties and time-dependent density functional theory excitation energies, including charge-transfer excited states.

PubMed

Rohrdanz, Mary A; Martins, Katie M; Herbert, John M

2009-02-07

We introduce a hybrid density functional that asymptotically incorporates full Hartree-Fock exchange, based on the long-range-corrected exchange-hole model of Henderson et al. [J. Chem. Phys. 128, 194105 (2008)]. The performance of this functional, for ground-state properties and for vertical excitation energies within time-dependent density functional theory, is systematically evaluated, and optimal values are determined for the range-separation parameter, omega, and for the fraction of short-range Hartree-Fock exchange. We denote the new functional as LRC-omegaPBEh, since it reduces to the standard PBEh hybrid functional (also known as PBE0 or PBE1PBE) for a certain choice of its two parameters. Upon optimization of these parameters against a set of ground- and excited-state benchmarks, the LRC-omegaPBEh functional fulfills three important requirements: (i) It outperforms the PBEh hybrid functional for ground-state atomization energies and reaction barrier heights; (ii) it yields statistical errors comparable to PBEh for valence excitation energies in both small and medium-sized molecules; and (iii) its performance for charge-transfer excitations is comparable to its performance for valence excitations. LRC-omegaPBEh, with the parameters determined herein, is the first density functional that satisfies all three criteria. Notably, short-range Hartree-Fock exchange appears to be necessary in order to obtain accurate ground-state properties and vertical excitation energies using the same value of omega.

Towards Efficient and Accurate Description of Many-Electron Problems: Developments of Static and Time-Dependent Electronic Structure Methods

NASA Astrophysics Data System (ADS)

Ding, Feizhi

Understanding electronic behavior in molecular and nano-scale systems is fundamental to the development and design of novel technologies and materials for application in a variety of scientific contexts from fundamental research to energy conversion. This dissertation aims to provide insights into this goal by developing novel methods and applications of first-principle electronic structure theory. Specifically, we will present new methods and applications of excited state multi-electron dynamics based on the real-time (RT) time-dependent Hartree-Fock (TDHF) and time-dependent density functional theory (TDDFT) formalism, and new development of the multi-configuration self-consist field theory (MCSCF) for modeling ground-state electronic structure. The RT-TDHF/TDDFT based developments and applications can be categorized into three broad and coherently integrated research areas: (1) modeling of the interaction between moleculars and external electromagnetic perturbations. In this part we will first prove both analytically and numerically the gauge invariance of the TDHF/TDDFT formalisms, then we will present a novel, efficient method for calculating molecular nonlinear optical properties, and last we will study quantum coherent plasmon in metal namowires using RT-TDDFT; (2) modeling of excited-state charge transfer in molecules. In this part, we will investigate the mechanisms of bridge-mediated electron transfer, and then we will introduce a newly developed non-equilibrium quantum/continuum embedding method for studying charge transfer dynamics in solution; (3) developments of first-principles spin-dependent many-electron dynamics. In this part, we will present an ab initio non-relativistic spin dynamics method based on the two-component generalized Hartree-Fock approach, and then we will generalized it to the two-component TDDFT framework and combine it with the Ehrenfest molecular dynamics approach for modeling the interaction between electron spins and nuclear

Decay of Bogoliubov excitations in one-dimensional Bose gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ristivojevic, Zoran; Matveev, K. A.

For this research, we study the decay of Bogoliubov quasiparticles in one-dimensional Bose gases. Starting from the hydrodynamic Hamiltonian, we develop a microscopic theory that enables one to systematically study both the excitations and their decay. At zero temperature, the leading mechanism of decay of a quasiparticle is disintegration into three others. We find that low-energy quasiparticles (phonons) decay with the rate that scales with the seventh power of momentum, whereas the rate of decay of the high-energy quasiparticles does not depend on momentum. In addition, our approach allows us to study analytically the quasiparticle decay in the whole crossovermore » region between the two limiting cases. When applied to integrable models, including the Lieb-Liniger model of bosons with contact repulsion, our theory confirms the absence of the decay of quasiparticle excitations. Finally, we account for two types of integrability-breaking perturbations that enable finite decay: three-body interaction between the bosons and two-body interaction of finite range.« less

Decay of Bogoliubov excitations in one-dimensional Bose gases

DOE PAGES

Ristivojevic, Zoran; Matveev, K. A.

2016-07-11

For this research, we study the decay of Bogoliubov quasiparticles in one-dimensional Bose gases. Starting from the hydrodynamic Hamiltonian, we develop a microscopic theory that enables one to systematically study both the excitations and their decay. At zero temperature, the leading mechanism of decay of a quasiparticle is disintegration into three others. We find that low-energy quasiparticles (phonons) decay with the rate that scales with the seventh power of momentum, whereas the rate of decay of the high-energy quasiparticles does not depend on momentum. In addition, our approach allows us to study analytically the quasiparticle decay in the whole crossovermore » region between the two limiting cases. When applied to integrable models, including the Lieb-Liniger model of bosons with contact repulsion, our theory confirms the absence of the decay of quasiparticle excitations. Finally, we account for two types of integrability-breaking perturbations that enable finite decay: three-body interaction between the bosons and two-body interaction of finite range.« less

Fock space, symbolic algebra, and analytical solutions for small stochastic systems.

PubMed

Santos, Fernando A N; Gadêlha, Hermes; Gaffney, Eamonn A

2015-12-01

Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.

Direct Delta-MBPT(2) method for ionization potentials, electron affinities, and excitation energies using fractional occupation numbers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Beste, Ariana; Vazquez-Mayagoitia, Alvaro; Ortiz, J. Vincent

2013-01-01

A direct method (D-Delta-MBPT(2)) to calculate second-order ionization potentials (IPs), electron affinities (EAs), and excitation energies is developed. The Delta-MBPT(2) method is defined as the correlated extension of the Delta-HF method. Energy differences are obtained by integrating the energy derivative with respect to occupation numbers over the appropriate parameter range. This is made possible by writing the second-order energy as a function of the occupation numbers. Relaxation effects are fully included at the SCF level. This is in contrast to linear response theory, which makes the D-Delta-MBPT(2) applicable not only to single excited but also higher excited states. We showmore » the relationship of the D-Delta-MBPT(2) method for IPs and EAs to a second-order approximation of the effective Fock-space coupled-cluster Hamiltonian and a second-order electron propagator method. We also discuss the connection between the D-Delta-MBPT(2) method for excitation energies and the CIS-MP2 method. Finally, as a proof of principle, we apply our method to calculate ionization potentials and excitation energies of some small molecules. For IPs, the Delta-MBPT(2) results compare well to the second-order solution of the Dyson equation. For excitation energies, the deviation from EOM-CCSD increases when correlation becomes more important. When using the numerical integration technique, we encounter difficulties that prevented us from reaching the Delta-MBPT(2) values. Most importantly, relaxation beyond the Hartree Fock level is significant and needs to be included in future research.« less

Mouvements collectifs de grandes amplitudes dans les noyaux : une approche microscopique

NASA Astrophysics Data System (ADS)

Giannoni, M.-J.

Various aspects of the adiabatic limit of the time-dependent Hartree-Fock approximation are studied. This formalism is a mean field theory for nuclear collective motion which provides microscopical foundations to the successful phenomenological collective models, and whose validity is not restricted to small amplitude phenomena. Emphasis is put on the classical Hamiltonian-like structure of the dynamical equations. Several limiting cases of the general formalism are considered : Random Phase Approximation, Nuclear Hydrodynamics, case of a single collective variable. Applications to low-lying vibrational modes are described. Results are discussed in terms of sum rules. A quantitative comparison between self-consistent and Inglis cranking mass parameters is made. Important dynamical corrections to the Hartree-Fock ground state are expected for soft nuclei. On étudie divers aspects de l'approximation de Hartree-Fock dépendant du temps à la limite adiabatique. Ce formalisme est une théorie de champ moyen adaptée à la description de phénomènes collectifs dans les noyaux, et dont le domaine de validité n'est pas limité aux mouvements de faibles amplitudes ; d'autre part il permet, grâce à l'approximation adiabatique, de comprendre en termes microscopiques les modèles collectifs purement phénoménologiques. La structure Hamiltonienne classique des équations de mouvement, est étudiée en détail. On considère plusieurs cas limites du formalisme général : approximation des phases au hasard (RPA), limite hydrodynamique, réduction à une seule variable collective. Dans le cadre de ce dernier cas limite, on calcule les paramètres de masse pour les modes vibrationnels quadrupolaires de plusieurs noyaux. Les résultats sont discutés en termes de règle de somme. On compare les paramètres de masse autocohérents aux paramètres de masse d'Inglis. Le formalisme conduit à d'importantes corrections, d'origine dynamique, à l'état fondamental de Hartree-Fock

International Conference on Quantum Chemical Calculations of NMR and EPR Parameters Held in Castle Smolenice, Slovak Republic on September 14-18 1998

DTIC Science & Technology

1998-10-21

site. The electric-field- induced linear shift is also observed in the hyperfine splitting of nuclear quadrupole resonance ( NQR ) spectrum of a nucleus...located at a noncentrosymmetric site in a molecule or in crystal lattice. Thus, the linear electric field effect on the ESR and NQR hyperfine splitting...the electric field effects on ESR and NQR hyperfine couplings. Theoretical methods to calculate the electric field effects within Hartree-Fock

A minimal multiconfigurational technique.

PubMed

Fernández Rico, J; Paniagua, M; GarcíA De La Vega, J M; Fernández-Alonso, J I; Fantucci, P

1986-04-01

A direct minimization method previously presented by the authors is applied here to biconfigurational wave functions. A very moderate increasing in the time by iteration with respect to the one-determinant calculation and good convergence properties have been found. So qualitatively correct studies on singlet systems with strong biradical character can be performed with a cost similar to that required by Hartree-Fock calculations. Copyright © 1986 John Wiley & Sons, Inc.

Gamow-Teller strength observed in the 48Ti(n, p) 48Sc reaction: Implications for the double beta decay of 48Ca

NASA Astrophysics Data System (ADS)

Alford, W. P.; Helmer, R. L.; Abegg, R.; Celler, A.; Frekers, D.; Green, P.; Häusser, O.; Henderson, R.; Hicks, K.; Jackson, K. P.; Jeppesen, R.; Miller, C. A.; Trudel, A.; Vetterli, M.; Yen, S.; Pourang, R.; Watson, J.; Brown, B. A.; Engel, J.

1990-07-01

Cross sections for the 48Ti(n, p) reaction have been measured at angles of 0°, 6°, and 12° at an energy of 200 MeV. The measurements are compared with results of DWIA calculations to obtain estimates of transition strengths for L = 0, 1, and ⩾2 up to an excitation energy of 25 MeV. Gamow-Teller strength ( L = 0) is peaked between 3 and 4 MeV excitation energy, with a significant distribution extending to about 12 MeV. The L = 1 strength is found mainly between 6 and 20 MeV while the cross section for transitions with L ⩾2 increases from 10 MeV to the upper limit of the measurements. The distribution of Gamow-Teller strength is in poor agreement with theoretical distributions used to calculate the lifetime for double beta decay of 48Ca.

Assessing the performance of dispersionless and dispersion-accounting methods: helium interaction with cluster models of the TiO2(110) surface.

PubMed

de Lara-Castells, María Pilar; Stoll, Hermann; Mitrushchenkov, Alexander O

2014-08-21

As a prototypical dispersion-dominated physisorption problem, we analyze here the performance of dispersionless and dispersion-accounting methodologies on the helium interaction with cluster models of the TiO2(110) surface. A special focus has been given to the dispersionless density functional dlDF and the dlDF+Das construction for the total interaction energy (K. Pernal, R. Podeswa, K. Patkowski, and K. Szalewicz, Phys. Rev. Lett. 2009, 109, 263201), where Das is an effective interatomic pairwise functional form for the dispersion. Likewise, the performance of symmetry-adapted perturbation theory (SAPT) method is evaluated, where the interacting monomers are described by density functional theory (DFT) with the dlDF, PBE, and PBE0 functionals. Our benchmarks include CCSD(T)-F12b calculations and comparative analysis on the nuclear bound states supported by the He-cluster potentials. Moreover, intra- and intermonomer correlation contributions to the physisorption interaction are analyzed through the method of increments (H. Stoll, J. Chem. Phys. 1992, 97, 8449) at the CCSD(T) level of theory. This method is further applied in conjunction with a partitioning of the Hartree-Fock interaction energy to estimate individual interaction energy components, comparing them with those obtained using the different SAPT(DFT) approaches. The cluster size evolution of dispersionless and dispersion-accounting energy components is then discussed, revealing the reduced role of the dispersionless interaction and intramonomer correlation when the extended nature of the surface is better accounted for. On the contrary, both post-Hartree-Fock and SAPT(DFT) results clearly demonstrate the high-transferability character of the effective pairwise dispersion interaction whatever the cluster model is. Our contribution also illustrates how the method of increments can be used as a valuable tool not only to achieve the accuracy of CCSD(T) calculations using large cluster models but also to

Higher order alchemical derivatives from coupled perturbed self-consistent field theory.

PubMed

Lesiuk, Michał; Balawender, Robert; Zachara, Janusz

2012-01-21

We present an analytical approach to treat higher order derivatives of Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory energy in the Born-Oppenheimer approximation with respect to the nuclear charge distribution (so-called alchemical derivatives). Modified coupled perturbed self-consistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of Kohn-Sham energy and up to the third derivative of Hartree-Fock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the "surrounding" molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals. © 2012 American Institute of Physics

Rayleigh scattering of x-ray and γ-ray by 1s and 2s electrons in ions and neutral atoms

NASA Astrophysics Data System (ADS)

Costescu, A.; Karim, K.; Moldovan, M.; Spanulescu, S.; Stoica, C.

2011-02-01

Using the Coulomb-Green function method and considering the nonrelativistic limit for the two-photon S-matrix element, the right nonrelativistic 2s Rayleigh scattering amplitudes are obtained. Our result takes into account all multipoles, retardation and relativistic kinematics contributions, and the old dipole approximation result of Costescu [1] is retrieved as a limit case. The total photoeffect cross-section which is related to the imaginary part of the Rayleigh forward scattering amplitude through the optical theorem is also obtained. Our Coulombian formulae are used in the more realistic case of elastic scattering of photons by bound 1s and 2s electrons in ions and neutral atoms. Screening effects are considered in the independent particle approximation through the Hartree-Fock method. The effective charge Zeff is obtained by fitting the Hartree-Fock charge distribution by a Coulombian one. Good agreement (within 10%) is found when comparing the numerical predictions given by our nonrelativistic formulae with the full relativistic numerical results of Kissel [2] in the case of elastic scattering of photons by 1s and 2s electrons and Scofield [3] in the case of K-shell and 2s subshell photoionization for neutral atoms with 18 <= Z <= 92 and photon energies ω <= αZm.

The s-Ordered Fock Space Projectors Gained by the General Ordering Theorem

NASA Astrophysics Data System (ADS)

Farid, Shähandeh; Mohammad, Reza Bazrafkan; Mahmoud, Ashrafi

2012-09-01

Employing the general ordering theorem (GOT), operational methods and incomplete 2-D Hermite polynomials, we derive the t-ordered expansion of Fock space projectors. Using the result, the general ordered form of the coherent state projectors is obtained. This indeed gives a new integration formula regarding incomplete 2-D Hermite polynomials. In addition, the orthogonality relation of the incomplete 2-D Hermite polynomials is derived to resolve Dattoli's failure.

Systematic shell-model study of β -decay properties and Gamow-Teller strength distributions in A ≈40 neutron-rich nuclei

NASA Astrophysics Data System (ADS)

Yoshida, Sota; Utsuno, Yutaka; Shimizu, Noritaka; Otsuka, Takaharu

2018-05-01

We perform large-scale shell-model calculations of β -decay properties for neutron-rich nuclei with 13 ≤Z ≤18 and 22 ≤N ≤34 , taking the first-forbidden transitions into account. The natural-parity and unnatural-parity states are calculated in the 0 ℏ ω and 1 ℏ ω model spaces, respectively, within the full s d +p f +s d g valence shell. The calculated β -decay half-lives and β -delayed neutron emission probabilities show good agreement with the experimental data. The first-forbidden transitions make a non-negligible contribution to the half-lives of N ≳28 nuclei. The low-lying Gamow-Teller strengths of even-even nuclei are considerably larger than those of the neighboring odd-A and odd-odd nuclei, strongly affecting the half-lives and neutron emission probabilities. It is shown that this even-odd effect is caused by the Jπ=1+ proton-neutron pairing interaction. We derive a formula to represent the positions of the Gamow-Teller giant resonances from the calculated strength distributions.

Breit interaction contribution to parity violating potentials in chiral molecules containing light nuclei.

PubMed

Berger, Robert

2008-10-21

The importance of the Breit interaction for an accurate prediction of parity violating energy differences between enantiomers is studied within electroweak quantum chemical frameworks. Besides two-electron orbit-orbit and spin-spin coupling contributions, the Breit interaction gives rise to the spin-other-orbit coupling term of the Breit-Pauli Hamiltonian. The present numerical study demonstrates that neglect of this latter term leads in hydrogen peroxide (H(2)O(2)) to relative deviations in the parity violating potential (V(pv)) by about 10%, whereas further relativistic corrections accounted for within a four-component Dirac-Hartree-Fock-Coulomb (DHFC) framework remain smaller, below 5%. Thus, the main source of discrepancy between previous one-component based (coupled perturbed) Hartree-Fock (HF) and four-component Dirac-Hartree-Fock results for parity violating potentials in H(2)O(2) is the neglect of the Breit contribution in DHFC. In heavier homologs of hydrogen peroxide the relative contribution of the spin-other-orbit coupling term to V(pv) decreases with increasing nuclear charge, whereas other relativistic effects become increasingly important. As shown for the H(2)X(2) (X = O,S,Se,Te,Po) series of molecules and for CHBrClF, to a good approximation these other relativistic influences on V(pv) can be accounted for in one-component based HF calculations with the help of relativistic enhancement factors proposed earlier in the theory of atomic parity violation.

Computational Studies of Strongly Correlated Quantum Matter

NASA Astrophysics Data System (ADS)

Shi, Hao

The study of strongly correlated quantum many-body systems is an outstanding challenge. Highly accurate results are needed for the understanding of practical and fundamental problems in condensed-matter physics, high energy physics, material science, quantum chemistry and so on. Our familiar mean-field or perturbative methods tend to be ineffective. Numerical simulations provide a promising approach for studying such systems. The fundamental difficulty of numerical simulation is that the dimension of the Hilbert space needed to describe interacting systems increases exponentially with the system size. Quantum Monte Carlo (QMC) methods are one of the best approaches to tackle the problem of enormous Hilbert space. They have been highly successful for boson systems and unfrustrated spin models. For systems with fermions, the exchange symmetry in general causes the infamous sign problem, making the statistical noise in the computed results grow exponentially with the system size. This hinders our understanding of interesting physics such as high-temperature superconductivity, metal-insulator phase transition. In this thesis, we present a variety of new developments in the auxiliary-field quantum Monte Carlo (AFQMC) methods, including the incorporation of symmetry in both the trial wave function and the projector, developing the constraint release method, using the force-bias to drastically improve the efficiency in Metropolis framework, identifying and solving the infinite variance problem, and sampling Hartree-Fock-Bogoliubov wave function. With these developments, some of the most challenging many-electron problems are now under control. We obtain an exact numerical solution of two-dimensional strongly interacting Fermi atomic gas, determine the ground state properties of the 2D Fermi gas with Rashba spin-orbit coupling, provide benchmark results for the ground state of the two-dimensional Hubbard model, and establish that the Hubbard model has a stripe order in the

Low-frequency analogue Hawking radiation: The Bogoliubov-de Gennes model

NASA Astrophysics Data System (ADS)

Coutant, Antonin; Weinfurtner, Silke

2018-01-01

We analytically study the low-frequency properties of the analogue Hawking effect in Bose-Einstein condensates. We show that in one-dimensional flows displaying an analogue horizon, the Hawking effect is dominant in the low-frequency regime. This happens despite nonvanishing grey-body factors, that is, the coupling of the Hawking mode and its partner to the mode propagating with the flow. To show this, we obtained analytical expressions for the scattering coefficients, in general flows and taking into account the full Bogoliubov dispersion relation. We discuss the obtained expressions for the grey-body factors. In particular, we show that they can be significantly decreased if the flow obeys a conformal coupling condition. We argue that in the presence of a small but non-zero temperature, reducing grey-body factors greatly facilitates the observation of entanglement, that is, establishing that the state of the Hawking mode and its partner is non-separable.

Nonadiabatic electron wavepacket dynamics behind molecular autoionization

NASA Astrophysics Data System (ADS)

Matsuoka, Takahide; Takatsuka, Kazuo

2018-01-01

A theoretical method for real-time dynamics of nonadiabatic reorganization of electronic configurations in molecules is developed, with dual aim that the intramolecular electron dynamics can be probed by means of direct and/or indirect photoionizations and that the physical origins behind photoionization signals attained in the time domain can be identified in terms of the language of time-dependent quantum chemistry. In doing so, we first formulate and implement a new computational scheme for nonadiabatic electron dynamics associated with molecular ionization, which well fits in the general theory of nonadiabatic electron dynamics. In this method, the total nonadiabatic electron wavepackets are propagated in time directly with complex natural orbitals without referring to Hartree-Fock molecular orbitals, and the amount of electron flux from a molecular region leading to ionization is evaluated in terms of the relevant complex natural orbitals. In the second half of this paper, we apply the method to electron dynamics in the elementary processes consisting of the Auger decay to demonstrate the methodological significance. An illustrative example is taken from an Auger decay starting from the 2a1 orbital hole-state of H2O+. The roles of nuclear momentum (kinetic) couplings in electronic-state mixing during the decay process are analyzed in terms of complex natural orbitals, which are schematically represented in the conventional language of molecular symmetry of the Hartree-Fock orbitals.

X-ray production cross sections at incident photon energies across the M{sub i} (i=1-5) edges of {sub 90}Th

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaur, Rajnish; Shehla,; Kumar, Anil

2015-08-28

The X-ray production cross sections for the M{sub k} (k= ξ, δ, α, β, ζ, γ, m{sub 1}, m{sub 2}) groups of X-rays have been evaluated at incident photon energies across the M{sub i} (i =1-5) edges of {sub 90}Th using the relativistic Hartree-Fock-Slater model based photoionisation cross sections and recently reported values of the M-shell X-ray emission rates, fluorescence and Coster Kronig yields. Further, the energies of the prominent (M{sub i}-S{sub j}) (S{sub j}=N{sub j}, O{sub j} and i =1-3, j =1-7) resonant Raman scattered (RRS) peaks at different incident photon energies have also been evaluated using the neutral-atommore » electron binding energies (E{sub sj}) based on the relaxed orbital relativistic Hartree-Fock-Slater model.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Robledo, L. M.; Baldo, M.; Schuck, P.

We discuss the octupole deformation properties of the recently proposed Barcelona-Catania-Paris (BCP) energy density functionals for two sets of isotopes, those of radium and barium, in which it is believed that octupole deformation plays a role in the description of the ground state. The analysis is carried out in the mean field framework (Hartree-Fock-Bogoliubov approximation) by using the axially symmetric octupole moment as a constraint. The main ingredients entering the octupole collective Hamiltonian are evaluated and the lowest-lying octupole eigenstates are obtained. In this way we restore, in an approximate way, the parity symmetry spontaneously broken by the mean fieldmore » and also incorporate octupole fluctuations around the ground-state solution. For each isotope the energy of the lowest lying 1{sup -} state and the B(E1) and B(E3) transition probabilities have been computed and compared to both the experimental data and the results obtained in the same framework with the Gogny D1S interaction, which are used here as a well-established benchmark. Finally, the octupolarity of the configurations involved in the way down to fission of {sup 240}Pu, which is strongly connected to the asymmetric fragment mass distribution, is studied. We confirm with this thorough study the suitability of the BCP functionals to describe octupole-related phenomena.« less

Microscopic description of fission in odd-mass uranium and plutonium nuclei with the Gogny energy density functional

NASA Astrophysics Data System (ADS)

Rodrıguez-Guzmán, R.; Robledo, L. M.

2017-12-01

The parametrization D1M of the Gogny energy density functional is used to study fission in the odd-mass Uranium and Plutonium isotopes with A=233, \\ldots , 249 within the framework of the Hartree-Fock-Bogoliubov (HFB) Equal Filling Approximation (EFA). Ground state quantum numbers and deformations, pairing energies, one-neutron separation energies, barrier heights and fission isomer excitation energies are given. Fission paths, collective masses and zero point rotational and vibrational quantum corrections are used to compute the systematic of the spontaneous fission half-lives t_{SF}, the masses and charges of the fission fragments as well as their intrinsic shapes. Although there exits a strong variance of the predicted fission rates with respect to the details involved in their computation, it is shown that both the specialization energy and the pairing quenching effects, taken into account fully variationally within the HFB-EFA blocking scheme, lead to larger spontaneous fission half-lives in odd-mass U and Pu nuclei as compared with the corresponding even-even neighbors. It is shown that modifications of a few percent in the strengths of the neutron and proton pairing fields can have a significant impact on the collective masses leading to uncertainties of several orders of magnitude in the predicted t_{SF} values. Alpha-decay lifetimes have also been computed using a parametrization of the Viola-Seaborg formula.

Thermal and quantum fluctuations of confined Bose–Einstein condensate beyond the Bogoliubov approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakamura, Y., E-mail: yusuke.n@asagi.waseda.jp; Nagano Prefectural Kiso Seiho High School, Nagano 397-8571; Kawaguchi, T., E-mail: pionelish30@toki.waseda.jp

The formulation for zero mode of a Bose–Einstein condensate beyond the Bogoliubov approximation at zero temperature [Y. Nakamura et al., Phys. Rev. A 89 (2014) 013613] is extended to finite temperature. Both thermal and quantum fluctuations are considered in a manner consistent with a concept of spontaneous symmetry breakdown for a finite-size system. Therefore, we need a proper treatment of the zero mode operators, which invoke non-trivial enhancements in depletion condensate and thermodynamical quantities such as the specific heat. The enhancements are visible in the weak interaction case. Our approach reproduces the results of a homogeneous system in the Bogoliubovmore » approximation in a large particle number limit.« less

Quantum chemical approach for positron annihilation spectra of atoms and molecules beyond plane-wave approximation

NASA Astrophysics Data System (ADS)

Ikabata, Yasuhiro; Aiba, Risa; Iwanade, Toru; Nishizawa, Hiroaki; Wang, Feng; Nakai, Hiromi

2018-05-01

We report theoretical calculations of positron-electron annihilation spectra of noble gas atoms and small molecules using the nuclear orbital plus molecular orbital method. Instead of a nuclear wavefunction, the positronic wavefunction is obtained as the solution of the coupled Hartree-Fock or Kohn-Sham equation for a positron and the electrons. The molecular field is included in the positronic Fock operator, which allows an appropriate treatment of the positron-molecule repulsion. The present treatment succeeds in reproducing the Doppler shift, i.e., full width at half maximum (FWHM) of experimentally measured annihilation (γ-ray) spectra for molecules with a mean absolute error less than 10%. The numerical results indicate that the interpretation of the FWHM in terms of a specific molecular orbital is not appropriate.

Development of efficient time-evolution method based on three-term recurrence relation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akama, Tomoko, E-mail: a.tomo---s-b-l-r@suou.waseda.jp; Kobayashi, Osamu; Nanbu, Shinkoh, E-mail: shinkoh.nanbu@sophia.ac.jp

The advantage of the real-time (RT) propagation method is a direct solution of the time-dependent Schrödinger equation which describes frequency properties as well as all dynamics of a molecular system composed of electrons and nuclei in quantum physics and chemistry. Its applications have been limited by computational feasibility, as the evaluation of the time-evolution operator is computationally demanding. In this article, a new efficient time-evolution method based on the three-term recurrence relation (3TRR) was proposed to reduce the time-consuming numerical procedure. The basic formula of this approach was derived by introducing a transformation of the operator using the arcsine function.more » Since this operator transformation causes transformation of time, we derived the relation between original and transformed time. The formula was adapted to assess the performance of the RT time-dependent Hartree-Fock (RT-TDHF) method and the time-dependent density functional theory. Compared to the commonly used fourth-order Runge-Kutta method, our new approach decreased computational time of the RT-TDHF calculation by about factor of four, showing the 3TRR formula to be an efficient time-evolution method for reducing computational cost.« less

Trial densities for the extended Thomas-Fermi model

NASA Astrophysics Data System (ADS)

Yu, An; Jimin, Hu

1996-02-01

A new and simplified form of nuclear densities is proposed for the extended Thomas-Fermi method (ETF) and applied to calculate the ground-state properties of several spherical nuclei, with results comparable or even better than other conventional density profiles. With the expectation value method (EVM) for microscopic corrections we checked our new densities for spherical nuclei. The binding energies of ground states almost reproduce the Hartree-Fock (HF) calculations exactly. Further applications to nuclei far away from the β-stability line are discussed.

Analytic second derivatives of the energy in the fragment molecular orbital method

NASA Astrophysics Data System (ADS)

Nakata, Hiroya; Nagata, Takeshi; Fedorov, Dmitri G.; Yokojima, Satoshi; Kitaura, Kazuo; Nakamura, Shinichiro

2013-04-01

We developed the analytic second derivatives of the energy for the fragment molecular orbital (FMO) method. First we derived the analytic expressions and then introduced some approximations related to the first and second order coupled perturbed Hartree-Fock equations. We developed a parallel program for the FMO Hessian with approximations in GAMESS and used it to calculate infrared (IR) spectra and Gibbs free energies and to locate the transition states in SN2 reactions. The accuracy of the Hessian is demonstrated in comparison to ab initio results for polypeptides and a water cluster. By using the two residues per fragment division, we achieved the accuracy of 3 cm-1 in the reduced mean square deviation of vibrational frequencies from ab initio for all three polyalanine isomers, while the zero point energy had the error not exceeding 0.3 kcal/mol. The role of the secondary structure on IR spectra, zero point energies, and Gibbs free energies is discussed.

Computation of energy states of hydrogenic quantum dot with two-electrons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yakar, Y., E-mail: yuyakar@yahoo.com; Özmen, A., E-mail: aozmen@selcuk.edu.tr; Çakır, B., E-mail: bcakir@selcuk.edu.tr

2016-03-25

In this study we have investigated the electronic structure of the hydrogenic quantum dot with two electrons inside an impenetrable potential surface. The energy eigenvalues and wavefunctions of the ground and excited states of spherical quantum dot have been calculated by using the Quantum Genetic Algorithm (QGA) and Hartree-Fock Roothaan (HFR) method, and the energies are investigated as a function of dot radius. The results show that as dot radius increases, the energy of quantum dot decreases.

Using a pruned, nondirect product basis in conjunction with the multi-configuration time-dependent Hartree (MCTDH) method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wodraszka, Robert, E-mail: Robert.Wodraszka@chem.queensu.ca; Carrington, Tucker, E-mail: Tucker.Carrington@queensu.ca

In this paper, we propose a pruned, nondirect product multi-configuration time dependent Hartree (MCTDH) method for solving the Schrödinger equation. MCTDH uses optimized 1D basis functions, called single particle functions, but the size of the standard direct product MCTDH basis scales exponentially with D, the number of coordinates. We compare the pruned approach to standard MCTDH calculations for basis sizes small enough that the latter are possible and demonstrate that pruning the basis reduces the CPU cost of computing vibrational energy levels of acetonitrile (D = 12) by more than two orders of magnitude. Using the pruned method, it ismore » possible to do calculations with larger bases, for which the cost of standard MCTDH calculations is prohibitive. Pruning the basis complicates the evaluation of matrix-vector products. In this paper, they are done term by term for a sum-of-products Hamiltonian. When no attempt is made to exploit the fact that matrices representing some of the factors of a term are identity matrices, one needs only to carefully constrain indices. In this paper, we develop new ideas that make it possible to further reduce the CPU time by exploiting identity matrices.« less

Modeling electron fractionalization with unconventional Fock spaces.

PubMed

Cobanera, Emilio

2017-08-02

It is shown that certain fractionally-charged quasiparticles can be modeled on D-dimensional lattices in terms of unconventional yet simple Fock algebras of creation and annihilation operators. These unconventional Fock algebras are derived from the usual fermionic algebra by taking roots (the square root, cubic root, etc) of the usual fermionic creation and annihilation operators. If the fermions carry non-Abelian charges, then this approach fractionalizes the Abelian charges only. In particular, the mth-root of a spinful fermion carries charge e/m and spin 1/2. Just like taking a root of a complex number, taking a root of a fermion yields a mildly non-unique result. As a consequence, there are several possible choices of quantum exchange statistics for fermion-root quasiparticles. These choices are tied to the dimensionality [Formula: see text] of the lattice by basic physical considerations. One particular family of fermion-root quasiparticles is directly connected to the parafermion zero-energy modes expected to emerge in certain mesoscopic devices involving fractional quantum Hall states. Hence, as an application of potential mesoscopic interest, I investigate numerically the hybridization of Majorana and parafermion zero-energy edge modes caused by fractionalizing but charge-conserving tunneling.

Theoretical dissociation energies for ionic molecules

NASA Technical Reports Server (NTRS)

Langhoff, S. R.; Bauschlicher, C. W., Jr.; Partridge, H.

1986-01-01

Ab initio calculations at the self-consistent-field and singles plus doubles configuration-interaction level are used to determine accurate spectroscopic parameters for most of the alkali and alkaline-earth fluorides, chlorides, oxides, sulfides, hydroxides, and isocyanides. Numerical Hartree-Fock (NHF) calculations are performed on selected systems to ensure that the extended Slater basis sets employed for the diatomic systems are near the Hartree-Fock limit. Extended Gaussian basis sets of at least triple-zeta plus double polarization equality are employed for the triatomic system. With this model, correlation effects are relatively small, but invariably increase the theoretical dissociation energies. The importance of correlating the electrons on both the anion and the metal is discussed. The theoretical dissociation energies are critically compared with the literature to rule out disparate experimental values. Theoretical (sup 2)Pi - (sup 2)Sigma (sup +) energy separations are presented for the alkali oxides and sulfides.

Compton scattering study of electron momentum distribution in lithium fluoride using 662 keV gamma radiations

NASA Astrophysics Data System (ADS)

Vijayakumar, R.; Shivaramu; Ramamurthy, N.; Ford, M. J.

2008-12-01

Here we report the first ever 137Cs Compton spectroscopy study of lithium fluoride. The spherical average Compton profiles of lithium fluoride are deduced from Compton scattering measurements on poly crystalline sample at gamma ray energy of 662 keV. To compare the experimental data, we have computed the spherical average Compton profiles using self-consistent Hartree-Fock wave functions employed on linear combination of atomic orbital (HF-LCAO) approximation. The directional Compton profiles and their anisotropic effects are also calculated using the same HF-LCAO approximation. The experimental spherical average profiles are found to be in good agreement with the corresponding HF-LCAO calculations and in qualitative agreement with Hartree-Fock free atom values. The present experimental isotropic and calculated directional profiles are also compared with the available experimental isotropic and directional Compton profiles using 59.54 and 159 keV γ-rays.

Spin Contamination Error in Optimized Geometry of Singlet Carbene (1A1) by Broken-Symmetry Method

NASA Astrophysics Data System (ADS)

Kitagawa, Yasutaka; Saito, Toru; Nakanishi, Yasuyuki; Kataoka, Yusuke; Matsui, Toru; Kawakami, Takashi; Okumura, Mitsutaka; Yamaguchi, Kizashi

2009-10-01

Spin contamination errors of a broken-symmetry (BS) method in optimized structural parameters of the singlet methylene (1A1) molecule are quantitatively estimated for the Hartree-Fock (HF) method, post-HF methods (CID, CCD, MP2, MP3, MP4(SDQ)), and a hybrid DFT (B3LYP) method. For the purpose, the optimized geometry by the BS method is compared with that of an approximate spin projection (AP) method. The difference between the BS and the AP methods is about 10-20° in the HCH angle. In order to examine the basis set dependency of the spin contamination error, calculated results by STO-3G, 6-31G*, and 6-311++G** are compared. The error depends on the basis sets, but the tendencies of each method are classified into two types. Calculated energy splitting values between the triplet and the singlet states (ST gap) indicate that the contamination of the stable triplet state makes the BS singlet solution stable and the ST gap becomes small. The energy order of the spin contamination error in the ST gap is estimated to be 10-1 eV.

The effective local potential method: Implementation for molecules and relation to approximate optimized effective potential techniques

NASA Astrophysics Data System (ADS)

Izmaylov, Artur F.; Staroverov, Viktor N.; Scuseria, Gustavo E.; Davidson, Ernest R.; Stoltz, Gabriel; Cancès, Eric

2007-02-01

We have recently formulated a new approach, named the effective local potential (ELP) method, for calculating local exchange-correlation potentials for orbital-dependent functionals based on minimizing the variance of the difference between a given nonlocal potential and its desired local counterpart [V. N. Staroverov et al., J. Chem. Phys. 125, 081104 (2006)]. Here we show that under a mildly simplifying assumption of frozen molecular orbitals, the equation defining the ELP has a unique analytic solution which is identical with the expression arising in the localized Hartree-Fock (LHF) and common energy denominator approximations (CEDA) to the optimized effective potential. The ELP procedure differs from the CEDA and LHF in that it yields the target potential as an expansion in auxiliary basis functions. We report extensive calculations of atomic and molecular properties using the frozen-orbital ELP method and its iterative generalization to prove that ELP results agree with the corresponding LHF and CEDA values, as they should. Finally, we make the case for extending the iterative frozen-orbital ELP method to full orbital relaxation.

Rapid calculation of accurate atomic charges for proteins via the electronegativity equalization method.

PubMed

Ionescu, Crina-Maria; Geidl, Stanislav; Svobodová Vařeková, Radka; Koča, Jaroslav

2013-10-28

We focused on the parametrization and evaluation of empirical models for fast and accurate calculation of conformationally dependent atomic charges in proteins. The models were based on the electronegativity equalization method (EEM), and the parametrization procedure was tailored to proteins. We used large protein fragments as reference structures and fitted the EEM model parameters using atomic charges computed by three population analyses (Mulliken, Natural, iterative Hirshfeld), at the Hartree-Fock level with two basis sets (6-31G*, 6-31G**) and in two environments (gas phase, implicit solvation). We parametrized and successfully validated 24 EEM models. When tested on insulin and ubiquitin, all models reproduced quantum mechanics level charges well and were consistent with respect to population analysis and basis set. Specifically, the models showed on average a correlation of 0.961, RMSD 0.097 e, and average absolute error per atom 0.072 e. The EEM models can be used with the freely available EEM implementation EEM_SOLVER.

Outstanding performance of configuration interaction singles and doubles using exact exchange Kohn-Sham orbitals in real-space numerical grid method

NASA Astrophysics Data System (ADS)

Lim, Jaechang; Choi, Sunghwan; Kim, Jaewook; Kim, Woo Youn

2016-12-01

To assess the performance of multi-configuration methods using exact exchange Kohn-Sham (KS) orbitals, we implemented configuration interaction singles and doubles (CISD) in a real-space numerical grid code. We obtained KS orbitals with the exchange-only optimized effective potential under the Krieger-Li-Iafrate (KLI) approximation. Thanks to the distinctive features of KLI orbitals against Hartree-Fock (HF), such as bound virtual orbitals with compact shapes and orbital energy gaps similar to excitation energies; KLI-CISD for small molecules shows much faster convergence as a function of simulation box size and active space (i.e., the number of virtual orbitals) than HF-CISD. The former also gives more accurate excitation energies with a few dominant configurations than the latter, even with many more configurations. The systematic control of basis set errors is straightforward in grid bases. Therefore, grid-based multi-configuration methods using exact exchange KS orbitals provide a promising new way to make accurate electronic structure calculations.

Nondiffracting wave beams in non-Hermitian Glauber-Fock lattice

NASA Astrophysics Data System (ADS)

Oztas, Z.

2018-05-01

We theoretically study non-Hermitian Glauber-Fock lattice with nonuniform hopping. We show how to engineer this lattice to get nondiffracting wave beams and find an exact analytical solution to nondiffracting localized waves. The exceptional points in the energy spectrum are also analyzed.

Computational Prediction of Kinetic Rate Constants

DTIC Science & Technology

2009-02-01

best experimental estimates are in kcal/mol. RMcdoo l> Uil. . 1 -.In 1 1 II. lei ,. »rrsnn • emu rtvm . « snfi. !>ii K.IIHlMi’ \\i . St"WTi H...straightforward extensions the HF energy and gradient expressions. For example, the energy and the gradient HF-DFT ’ dE designated as E r-IIF DF1 and...8217’ Coulomb Electron Electron «P Hartr » . pBecke-LYP I ^Hartree-Fock \\7 n ’ Exchange correlation \\H ’ r llarlree-Fock Contract

Semiclassical perturbation Stark widths of singly charged argon spectral lines

NASA Astrophysics Data System (ADS)

Hamdi, Rafik; Ben Nessib, Nabil; Sahal-Bréchot, Sylvie; Dimitrijević, Milan S.

2018-03-01

Using a semiclassical perturbation approach with the impact approximation, Stark widths for singly charged argon (Ar II) spectral lines have been calculated. Energy levels and oscillator strengths needed for this calculation have been determined using the Hartree-Fock method with relativistic corrections. Our Stark widths are compared with experimental results for 178 spectral lines. Our results may be of interest not only for laboratory plasma, lasers and technological plasmas but also for white dwarfs and A- and B-type stars.

σ -SCF: A Direct Energy-targeting Method To Mean-field Excited States

NASA Astrophysics Data System (ADS)

Ye, Hongzhou; Welborn, Matthew; Ricke, Nathan; van Voorhis, Troy

The mean-field solutions of electronic excited states are much less accessible than ground state (e.g. Hartree-Fock) solutions. Energy-based optimization methods for excited states, like Δ-SCF, tend to fall into the lowest solution consistent with a given symmetry - a problem known as ``variational collapse''. In this work, we combine the ideas of direct energy-targeting and variance-based optimization in order to describe excited states at the mean-field level. The resulting method, σ-SCF, has several advantages. First, it allows one to target any desired excited state by specifying a single parameter: a guess of the energy of that state. It can therefore, in principle, find all excited states. Second, it avoids variational collapse by using a variance-based, unconstrained local minimization. As a consequence, all states - ground or excited - are treated on an equal footing. Third, it provides an alternate approach to locate Δ-SCF solutions that are otherwise hardly accessible by the usual non-aufbau configuration initial guess. We present results for this new method for small atoms (He, Be) and molecules (H2, HF). This work was funded by a Grant from NSF (CHE-1464804).

Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cortez, Jerónimo, E-mail: jacq@ciencias.unam.mx; Elizaga Navascués, Beatriz, E-mail: beatriz.elizaga@iem.cfmac.csic.es; Martín-Benito, Mercedes, E-mail: m.martin@hef.ru.nl

We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under themore » symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed.« less

Impact of New Gamow-Teller Strengths on Explosive Type Ia Supernova Nucleosynthesis

NASA Astrophysics Data System (ADS)

Mori, Kanji; Famiano, Michael A.; Kajino, Toshitaka; Suzuki, Toshio; Hidaka, Jun; Honma, Michio; Iwamoto, Koichi; Nomoto, Ken'ichi; Otsuka, Takaharu

2016-12-01

Recent experimental results have confirmed a possible reduction in the Gamow-Teller (GT+) strengths of pf-shell nuclei. These proton-rich nuclei are of relevance in the deflagration and explosive burning phases of SNe Ia. While prior GT strengths result in nucleosynthesis predictions with a lower-than-expected electron fraction, a reduction in the GT+ strength can result in a slightly increased electron fraction compared to previous shell model predictions, though the enhancement is not as large as previous enhancements in going from rates computed by Fuller, Fowler, and Newman based on an independent particle model. A shell model parametrization has been developed that more closely matches experimental GT strengths. The resultant electron-capture rates are used in nucleosynthesis calculations for carbon deflagration and explosion phases of SNe Ia, and the final mass fractions are compared to those obtained using more commonly used rates.

Equation-of-motion coupled cluster method for the description of the high spin excited states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Musiał, Monika, E-mail: musial@ich.us.edu.pl; Lupa, Łukasz; Kucharski, Stanisław A.

2016-04-21

The equation-of-motion (EOM) coupled cluster (CC) approach in the version applicable for the excitation energy (EE) calculations has been formulated for high spin components. The EE-EOM-CC scheme based on the restricted Hartree-Fock reference and standard amplitude equations as used in the Davidson diagonalization procedure yields the singlet states. The triplet and higher spin components require separate amplitude equations. In the case of quintets, the relevant equations are much simpler and easier to solve. Out of 26 diagrammatic terms contributing to the R{sub 1} and R{sub 2} singlet equations in the case of quintets, only R{sub 2} operator survives with 5more » diagrammatic terms present. In addition all terms engaging three body elements of the similarity transformed Hamiltonian disappear. This indicates a substantial simplification of the theory. The implemented method has been applied to the pilot study of the excited states of the C{sub 2} molecule and quintet states of C and Si atoms.« less

Ultrafast Processes in Atoms and Molecules: Integrated treatment of electronic and nuclear motion in ultrashort XUV pulses

DOE Office of Scientific and Technical Information (OSTI.GOV)

McCurdy, C. William

This project made use of Multiconfiguration Time-Dependent Hartree-Fock method developed earlier in the McCurdy group in a series of novel applications of the method to ultrafast spectroscopic processes. MCTDHF treats the dynamics of a molecule or atom under the influence of an external field in manner that has all electrons active. That property distinguishes this method from the more popular (and much less computationally demanding) approaches for treating the electron dynamics of atoms and molecules in fields, such as the time-dependent “Configuration Interaction Singles” approximation or approaches that limit the treatment to either one or two-electron models.

Towards a multiconfigurational method of increments

NASA Astrophysics Data System (ADS)

Fertitta, E.; Koch, D.; Paulus, B.; Barcza, G.; Legeza, Ö.

2018-06-01

The method of increments (MoI) allows one to successfully calculate cohesive energies of bulk materials with high accuracy, but it encounters difficulties when calculating dissociation curves. The reason is that its standard formalism is based on a single Hartree-Fock (HF) configuration whose orbitals are localised and used for the many-body expansion. In situations where HF does not allow a size-consistent description of the dissociation, the MoI cannot be guaranteed to yield proper results either. Herein, we address the problem by employing a size-consistent multiconfigurational reference for the MoI formalism. This leads to a matrix equation where a coupling derived by the reference itself is employed. In principle, such an approach allows one to evaluate approximate values for the ground as well as excited states energies. While the latter are accurate close to the avoided crossing only, the ground state results are very promising for the whole dissociation curve, as shown by the comparison with density matrix renormalisation group benchmarks. We tested this two-state constant-coupling MoI on beryllium rings of different sizes and studied the error introduced by the constant coupling.

Simulation of multivariate stationary stochastic processes using dimension-reduction representation methods

NASA Astrophysics Data System (ADS)

Liu, Zhangjun; Liu, Zenghui; Peng, Yongbo

2018-03-01

In view of the Fourier-Stieltjes integral formula of multivariate stationary stochastic processes, a unified formulation accommodating spectral representation method (SRM) and proper orthogonal decomposition (POD) is deduced. By introducing random functions as constraints correlating the orthogonal random variables involved in the unified formulation, the dimension-reduction spectral representation method (DR-SRM) and the dimension-reduction proper orthogonal decomposition (DR-POD) are addressed. The proposed schemes are capable of representing the multivariate stationary stochastic process with a few elementary random variables, bypassing the challenges of high-dimensional random variables inherent in the conventional Monte Carlo methods. In order to accelerate the numerical simulation, the technique of Fast Fourier Transform (FFT) is integrated with the proposed schemes. For illustrative purposes, the simulation of horizontal wind velocity field along the deck of a large-span bridge is proceeded using the proposed methods containing 2 and 3 elementary random variables. Numerical simulation reveals the usefulness of the dimension-reduction representation methods.

Ab initio effective core potentials including relativistic effects and their application to the electronic structure calculations of heavy atoms and molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Y.S.

1977-11-01

The effects of the 4f shell of electrons and the relativity of valence electrons are compared. The effect of 4f shell (lanthanide contraction) is estimated from the numerical Hartree-Fock (HF) calculations of pseudo-atoms corresponding to Hf, Re, Au, Hg, Tl, Pb and Bi without 4f electrons and with atomic numbers reduced by 14. The relativistic effect estimated from the numerical Dirac-Hartree-Fock (DHF) calculations of those atoms is comparable in the magnitude with that of the 4f shell of electrons. Both are larger for 6s than for 5d or 6p electrons. The various relativistic effects on valence electrons are discussed inmore » detail to determine the proper level of the approximation for the valence electron calculations of systems with heavy elements. An effective core potential system has been developed for heavy atoms in which relativistic effects are included in the effective potentials.« less

Influence of the plasma environment on atomic structure using an ion-sphere model

DOE PAGES

Belkhiri, Madeny Jean; Fontes, Christopher John; Poirier, Michel

2015-09-03

Plasma environment effects on atomic structure are analyzed using various atomic structure codes. To monitor the effect of high free-electron density or low temperatures, Fermi-Dirac and Maxwell-Boltzmann statistics are compared. After a discussion of the implementation of the Fermi-Dirac approach within the ion-sphere model, several applications are considered. In order to check the consistency of the modifications brought here to extant codes, calculations have been performed using the Los Alamos Cowan Atomic Structure (cats) code in its Hartree-Fock or Hartree-Fock-Slater form and the parametric potential Flexible Atomic Code (fac). The ground-state energy shifts due to the plasma effects for themore » six most ionized aluminum ions have been calculated using the fac and cats codes and fairly agree. For the intercombination resonance line in Fe 22+, the plasma effect within the uniform electron gas model results in a positive shift that agrees with the MCDF value of B. Saha et al.« less

Influence of the plasma environment on atomic structure using an ion-sphere model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Belkhiri, Madeny Jean; Fontes, Christopher John; Poirier, Michel

Plasma environment effects on atomic structure are analyzed using various atomic structure codes. To monitor the effect of high free-electron density or low temperatures, Fermi-Dirac and Maxwell-Boltzmann statistics are compared. After a discussion of the implementation of the Fermi-Dirac approach within the ion-sphere model, several applications are considered. In order to check the consistency of the modifications brought here to extant codes, calculations have been performed using the Los Alamos Cowan Atomic Structure (cats) code in its Hartree-Fock or Hartree-Fock-Slater form and the parametric potential Flexible Atomic Code (fac). The ground-state energy shifts due to the plasma effects for themore » six most ionized aluminum ions have been calculated using the fac and cats codes and fairly agree. For the intercombination resonance line in Fe 22+, the plasma effect within the uniform electron gas model results in a positive shift that agrees with the MCDF value of B. Saha et al.« less

On the validity of microscopic calculations of double-quantum-dot spin qubits based on Fock-Darwin states

NASA Astrophysics Data System (ADS)

Chan, GuoXuan; Wang, Xin

2018-04-01

We consider two typical approximations that are used in the microscopic calculations of double-quantum dot spin qubits, namely, the Heitler-London (HL) and the Hund-Mulliken (HM) approximations, which use linear combinations of Fock-Darwin states to approximate the two-electron states under the double-well confinement potential. We compared these results to a case in which the solution to a one-dimensional Schr¨odinger equation was exactly known and found that typical microscopic calculations based on Fock-Darwin states substantially underestimate the value of the exchange interaction, which is the key parameter that controls the quantum dot spin qubits. This underestimation originates from the lack of tunneling of Fock-Darwin states, which is accurate only in the case with a single potential well. Our results suggest that the accuracies of the current two-dimensional molecular- orbit-theoretical calculations based on Fock-Darwin states should be revisited since underestimation could only deteriorate in dimensions that are higher than one.

Phase diagram of an extended Agassi model

NASA Astrophysics Data System (ADS)

García-Ramos, J. E.; Dukelsky, J.; Pérez-Fernández, P.; Arias, J. M.

2018-05-01

Background: The Agassi model [D. Agassi, Nucl. Phys. A 116, 49 (1968), 10.1016/0375-9474(68)90482-X] is an extension of the Lipkin-Meshkov-Glick (LMG) model [H. J. Lipkin, N. Meshkov, and A. J. Glick, Nucl. Phys. 62, 188 (1965), 10.1016/0029-5582(65)90862-X] that incorporates the pairing interaction. It is a schematic model that describes the interplay between particle-hole and pair correlations. It was proposed in the 1960s by D. Agassi as a model to simulate the properties of the quadrupole plus pairing model. Purpose: The aim of this work is to extend a previous study by Davis and Heiss [J. Phys. G: Nucl. Phys. 12, 805 (1986), 10.1088/0305-4616/12/9/006] generalizing the Agassi model and analyze in detail the phase diagram of the model as well as the different regions with coexistence of several phases. Method: We solve the model Hamiltonian through the Hartree-Fock-Bogoliubov (HFB) approximation, introducing two variational parameters that play the role of order parameters. We also compare the HFB calculations with the exact ones. Results: We obtain the phase diagram of the model and classify the order of the different quantum phase transitions appearing in the diagram. The phase diagram presents broad regions where several phases, up to three, coexist. Moreover, there is also a line and a point where four and five phases are degenerated, respectively. Conclusions: The phase diagram of the extended Agassi model presents a rich variety of phases. Phase coexistence is present in extended areas of the parameter space. The model could be an important tool for benchmarking novel many-body approximations.

Influence of the plasma environment on atomic structure using an ion-sphere model

NASA Astrophysics Data System (ADS)

Belkhiri, Madeny; Fontes, Christopher J.; Poirier, Michel

2015-09-01

Plasma environment effects on atomic structure are analyzed using various atomic structure codes. To monitor the effect of high free-electron density or low temperatures, Fermi-Dirac and Maxwell-Boltzmann statistics are compared. After a discussion of the implementation of the Fermi-Dirac approach within the ion-sphere model, several applications are considered. In order to check the consistency of the modifications brought here to extant codes, calculations have been performed using the Los Alamos Cowan Atomic Structure (cats) code in its Hartree-Fock or Hartree-Fock-Slater form and the parametric potential Flexible Atomic Code (fac). The ground-state energy shifts due to the plasma effects for the six most ionized aluminum ions have been calculated using the fac and cats codes and fairly agree. For the intercombination resonance line in Fe22 +, the plasma effect within the uniform electron gas model results in a positive shift that agrees with the multiconfiguration Dirac-Fock value of B. Saha and S. Fritzsche [J. Phys. B 40, 259 (2007), 10.1088/0953-4075/40/2/002]. Last, the present model is compared to experimental data in titanium measured on the terawatt Astra facility and provides values for electron temperature and density in agreement with the maria code.

Gamow-Teller Strength in the Continuum Studied via the (p,n) Reaction

NASA Astrophysics Data System (ADS)

Wakasa, T.; Hatanaka, K.; Sakai, H.; Fujita, S.; Nonaka, T.; Ohnishi, T.; Yako, K.; Sekiguchi, K.; Okamura, H.; Otsu, H.; Ishida, S.; Sakamoto, N.; Uesaka, T.; Satou, Y.; Greenfield, M. B.

2002-09-01

The double differential cross sections for θ1ab between 0.0° and 14.7° and the polarization transfer coefficient DNN(0°) for the 27 Al(vec {p},vec {n}) reaction have been measured at a bombarding energy of 295 MeV. A multipole decomposition technique is applied for the cross section data to extract L = 0, 1, 2, and 3 contributions. The Gamow-Teller (GT) strength B(GT) deduced from the L = 0 contribution is compared with the B(GT) values calculated in a full sd shell-model space. The sum of B(GT) values up to 20 MeV excitation is Sβ- = 4.0 ± 0.1 ± 0.1. A fairly large L = 0 contribution is observed in the continuum region up to 50 MeV, which could be in part ascribed to the quenched GT strength. A limit on the effect that the Δ(1232)-isobar nucleon-hole admixture has upon the GT strength is estimated.

Beyond mean-field description of Gamow-Teller resonances and β-decay

NASA Astrophysics Data System (ADS)

Niu, Yifei; Colò, Gianluca; Vigezzi, Enrico; Bai, Chunlin; Niu, Zhongming; Sagawa, Hiroyuki

2018-02-01

β-decay half-lives set the time scale of the rapid neutron capture process, and are therefore essential for understanding the origin of heavy elements in the universe. The random-phase approximation (RPA) based on Skyrme energy density functionals is widely used to calculate the properties of Gamow-Teller (GT) transitions, which play a dominant role in β-decay half-lives. However, the RPA model has its limitations in reproducing the resonance width and often overestimates β-decay half-lives. To overcome these problems, effects beyond mean-field can be included on top of the RPA model. In particular, this can be obtained by taking into account the particle-vibration coupling (PVC). Within the RPA+PVC model, we successfully reproduce the experimental GT resonance width and β-decay half-lives in magic nuclei. We then extend the formalism to superfluid nuclei and apply it to the GT resonance in 120Sn, obtaining a good reproduction of the experimental strength distribution. The effect of isoscalar pairing is also discussed.

Connection between the regular approximation and the normalized elimination of the small component in relativistic quantum theory

NASA Astrophysics Data System (ADS)

Filatov, Michael; Cremer, Dieter

2005-02-01

The regular approximation to the normalized elimination of the small component (NESC) in the modified Dirac equation has been developed and presented in matrix form. The matrix form of the infinite-order regular approximation (IORA) expressions, obtained in [Filatov and Cremer, J. Chem. Phys. 118, 6741 (2003)] using the resolution of the identity, is the exact matrix representation and corresponds to the zeroth-order regular approximation to NESC (NESC-ZORA). Because IORA (=NESC-ZORA) is a variationally stable method, it was used as a suitable starting point for the development of the second-order regular approximation to NESC (NESC-SORA). As shown for hydrogenlike ions, NESC-SORA energies are closer to the exact Dirac energies than the energies from the fifth-order Douglas-Kroll approximation, which is much more computationally demanding than NESC-SORA. For the application of IORA (=NESC-ZORA) and NESC-SORA to many-electron systems, the number of the two-electron integrals that need to be evaluated (identical to the number of the two-electron integrals of a full Dirac-Hartree-Fock calculation) was drastically reduced by using the resolution of the identity technique. An approximation was derived, which requires only the two-electron integrals of a nonrelativistic calculation. The accuracy of this approach was demonstrated for heliumlike ions. The total energy based on the approximate integrals deviates from the energy calculated with the exact integrals by less than 5×10-9hartree units. NESC-ZORA and NESC-SORA can easily be implemented in any nonrelativistic quantum chemical program. Their application is comparable in cost with that of nonrelativistic methods. The methods can be run with density functional theory and any wave function method. NESC-SORA has the advantage that it does not imply a picture change.

Different equation-of-motion coupled cluster methods with different reference functions: The formyl radical

NASA Astrophysics Data System (ADS)

Kuś, Tomasz; Bartlett, Rodney J.

2008-09-01

The doublet and quartet excited states of the formyl radical have been studied by the equation-of-motion (EOM) coupled cluster (CC) method. The Sz spin-conserving singles and doubles (EOM-EE-CCSD) and singles, doubles, and triples (EOM-EE-CCSDT) approaches, as well as the spin-flipped singles and doubles (EOM-SF-CCSD) method have been applied, subject to unrestricted Hartree-Fock (HF), restricted open-shell HF, and quasirestricted HF references. The structural parameters, vertical and adiabatic excitation energies, and harmonic vibrational frequencies have been calculated. The issue of the reference function choice for the spin-flipped (SF) method and its impact on the results has been discussed using the experimental data and theoretical results available. The results show that if the appropriate reference function is chosen so that target states differ from the reference by only single excitations, then EOM-EE-CCSD and EOM-SF-CCSD methods give a very good description of the excited states. For the states that have a non-negligible contribution of the doubly excited configurations one is able to use the SF method with such a reference function, that in most cases the performance of the EOM-SF-CCSD method is better than that of the EOM-EE-CCSD approach.

Atomic data of intermediate autoionzing Rydberg series nf[K]J (n = 4, 5), nd[K]J (n = 5, 6), np[K]J (n = 6, 7) and ns[K]J (n = 7, 8) of neutral argon atom in the multiconfiguration Dirac-Hartree-Fock framework

NASA Astrophysics Data System (ADS)

Hassouneh, Ola; Salah, Wa'el

2017-07-01

We report the results of an accurate computation of the energy levels, oscillator strengths f_{ij}, the radiative transition rates A_{ij}, the Landé g-factor, the magnetic dipole and the electric quadrupole hyperfine constants of the intermediate Rydberg series nf[K]J (n = 4, 5), nd[K]J (n = 5, 6), np[K]J (n = 6, 7) and ns[K]J (n = 7, 8) relative to the ground state 3p6 1S0 for neutral argon atom spectra based on the multiconfiguration Dirac-Hartree-Fock (MCDHF) approach. In this approach, the quantum electrodynamics (QED) effects with transverse photon Breit interaction and vacuum photon polarization self-energy corrections are included. Moreover, the perturbation due to the core-polarization and electron correlation effects are taken into account. We also reported the oscillator strengths and transition rates in Coulomb and Babushkin gauges for the 3p5(2P)3d-3p5(2P)4f, 3p5(2P)3d-3p5(2P)5f, 3p5(2P)4d-3p5(2P)4f, 3p5(2P)4d-3p5(2P)5f, 3p5(2P)5d-3p5(2P)4f, 3p5(2P)5d-3p5(2P)5f, 3p5(2P)6d-3p5(2P)4f and 3p5(2P)6d-3p5(2P)5f transition arrays as well as the 3p5(2P)5d-3p5(2P)6p, 3p5(2P)7s-3p5(2P)6p, 3p5(2P)7s-3p5(2P)7p and 3p5(2P)8s-3p5(2P)7p transition arrays. Insofar as experimental or theoretical values by other authors exist, comparison is made with those values; it turns out that, for most of the levels, a rather satisfying agreement with these experimental and theoretical results is obtained, thus confirming the reliability of our data.

Pseudospin-orbit splitting and its consequences for the central depression in nuclear density

NASA Astrophysics Data System (ADS)

Li, Jia Jie; Long, Wen Hui; Song, Jun Ling; Zhao, Qiang

2016-05-01

The occurrence of the bubble-like structure has been studied, in the light of pseudospin degeneracy, within the relativistic Hartree-Fock-Bogoliubov (RHFB) theory. It is concluded that the charge/neutron bubble-like structure is predicted to occur in the mirror system of {34Si,34Ca } commonly by the selected Lagrangians, due to the persistence of Z (N )=14 subshell gaps above which the π (ν ) 2 s1 /2 states are not occupied. However, for the popular candidate 46Ar, the RHFB Lagrangian PKA1 does not support the occurrence of the bubble-like structure in the charge (proton) density profiles, due to the almost degenerate pseudospin doublet {π 2 s1 /2,π 1 d3 /2} and coherent pairing effects. The formation of a semibubble in heavy nuclei is less possible as a result of small pseudospin-orbit (PSO) splitting, while it tends to appear at Z =120 superheavy systems which coincides with large PSO splitting of the doublet {π 3 p3 /2,π 2 f5 /2} and couples with significant shell effects. Pairing correlations, which can work against bubble formation, significantly affect the PSO splitting. Furthermore, we found that the influence on semibubble formation due to different types of pairing interactions is negligible. The quenching of the spin-orbit splitting in the p orbit has been also stressed, and it may be considered the hallmark for semibubble nuclei.

Kohn's theorem in a superfluid Fermi gas with a Feshbach resonance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ohashi, Y.

2004-12-01

We investigate the dipole mode in a superfluid gas of Fermi atoms trapped in a harmonic potential. According to Kohn's theorem, the frequency of this collective mode is not affected by an interaction between the atoms and is always equal to the trap frequency. This remarkable property, however, does not necessarily hold in an approximate theory. We explicitly prove that the Hartree-Fock-Bogoliubov generalized random phase approximation (HFB-GRPA), including a coupling between fluctuations in the density and Cooper channels, is consistent with both Kohn's theorem as well as Goldstone's theorem. This proof can be immediately extended to the strong-coupling superfluid theorymore » developed by Nozieres and Schmitt-Rink (NSR), where the effect of superfluid fluctuations is included within the Gaussian level. As a result, the NSR-GRPA formalism can be used to study collective modes in the BCS-BEC crossover region in a manner which is consistent with Kohn's theorem. We also include the effect of a Feshbach resonance and a condensate of the associated molecular bound states. A detailed discussion is given of the unusual nature of the Kohn mode eigenfunctions in a Fermi superfluid, in the presence and absence of a Feshbach resonance. When the molecular bosons feel a different trap frequency from the Fermi atoms, the dipole frequency is shown to depend on the strength of effective interaction associated with the Feshbach resonance.« less

Accurate and Efficient Approximation to the Optimized Effective Potential for Exchange

NASA Astrophysics Data System (ADS)

Ryabinkin, Ilya G.; Kananenka, Alexei A.; Staroverov, Viktor N.

2013-07-01

We devise an efficient practical method for computing the Kohn-Sham exchange-correlation potential corresponding to a Hartree-Fock electron density. This potential is almost indistinguishable from the exact-exchange optimized effective potential (OEP) and, when used as an approximation to the OEP, is vastly better than all existing models. Using our method one can obtain unambiguous, nearly exact OEPs for any reasonable finite one-electron basis set at the same low cost as the Krieger-Li-Iafrate and Becke-Johnson potentials. For all practical purposes, this solves the long-standing problem of black-box construction of OEPs in exact-exchange calculations.

Effects of nitrogenous substituent groups on the benzene dication

NASA Astrophysics Data System (ADS)

Forgy, C. C.; Schlimgen, A. W.; Mazziotti, D. A.

2018-05-01

The benzene dication possesses a pentagonal-pyramidal structure with a hexacoordinated carbon. In contrast, halogenated benzene dications retain a similar structure to their parent molecules. In this work, we report on theoretical studies of the structures of the dications of benzene with nitrogenous substituents. We find that the nitrobenzene dication favours a near ideal pentagonal-pyramidal structure, while the aniline dication favours a flat, hexagonal structure. Reduced-density-matrices methods give predictions in agreement with available ab initio calculations and experiment. These results are also compared with those from the Hartree-Fock method and density functional theory.

Adaptation of the projector-augmented-wave formalism to the treatment of orbital-dependent exchange-correlation functionals

NASA Astrophysics Data System (ADS)

Xu, Xiao; Holzwarth, N. A. W.

2011-10-01

This paper presents the formulation and numerical implementation of a self-consistent treatment of orbital-dependent exchange-correlation functionals within the projector-augmented-wave method of Blöchl [Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.50.17953 50, 17953 (1994)] for electronic structure calculations. The methodology is illustrated with binding energy curves for C in the diamond structure and LiF in the rock salt structure, by comparing results from the Hartree-Fock (HF) formalism and the optimized effective potential formalism in the so-called KLI approximation [Krieger, Li, and Iafrate, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.45.101 45, 101 (1992)] with those of the local density approximation. While the work here uses pure Fock exchange only, the formalism can be extended to treat orbital-dependent functionals more generally.

Developmental psycholinguistics teaches us that we need multi-method, not single-method, approaches to the study of linguistic representation.

PubMed

Rowland, Caroline F; Monaghan, Padraic

2017-01-01

In developmental psycholinguistics, we have, for many years, been generating and testing theories that propose both descriptions of adult representations and explanations of how those representations develop. We have learnt that restricting ourselves to any one methodology yields only incomplete data about the nature of linguistic representations. We argue that we need a multi-method approach to the study of representation.

Gamow-Teller transitions in the 64Ni(3He, t)64Cu reaction

NASA Astrophysics Data System (ADS)

Popescu, L.; Adachi, T.; Berg, G. P. A.; von Brentano, P.; De Frenne, D.; Fujita, K.; Fujita, Y.; Hatanaka, K.; Jacobs, E.; Negret, A.; Nakanishi, K.; Sakemi, Y.; Shimbara, Y.; Shimizu, Y.; Tameshige, Y.; Tamii, A.; Uchida, M.; Yosoi, M.

2005-10-01

In order to study the Gamow-Teller (GT) transitions in the fp-shell nucleus 64Cu, the 64Ni(3He, t)64Cu charge-exchange reaction was investigated at E3He= 140 MeV/nucleon [1]. The outgoing tritons were momentum analysed by the Grand Raiden spectrometer at 0°. The very high energy resolution of 35 keV (FWHM) allowed the separation of individual levels in the excitation energy region from 0 to 3.5 MeV. An angular distribution analysis was performed for the observed transitions to these states. In addition to the ground state (g.s.), known to be a Jπ = 1+ GT state, several excited states showed L = 0 nature, making them candidates of GT states. At higher excitation energies, the level density becomes very high and a bump-like structure, the so-called GT Giant Resonance, dominates the spectrum.

From Hartree Dynamics to the Relativistic Vlasov Equation

NASA Astrophysics Data System (ADS)

Dietler, Elia; Rademacher, Simone; Schlein, Benjamin

2018-02-01

We derive the relativistic Vlasov equation from quantum Hartree dynamics for fermions with relativistic dispersion in the mean-field scaling, which is naturally linked with an effective semiclassic limit. Similar results in the non-relativistic setting have been recently obtained in Benedikter et al. (Arch Rat Mech Anal 221(1): 273-334, 2016). The new challenge that we have to face here, in the relativistic setting, consists in controlling the difference between the quantum kinetic energy and the relativistic transport term appearing in the Vlasov equation.

Progesterone and testosterone studies by neutron-scattering methods and quantum chemistry calculations

NASA Astrophysics Data System (ADS)

Holderna-Natkaniec, K.; Szyczewski, A.; Natkaniec, I.; Khavryutchenko, V. D.; Pawlukojc, A.

Inelastic incoherent neutron scattering (IINS) and neutron diffraction spectra of progesterone and testosterone were measured simultaneously on the NERA spectrometer at the IBR-2 pulsed reactor in Dubna. Both studied samples do not indicate any phase transition in the temperature range from 20 to 290K. The IINS spectra have been transformed to the phonon density of states (PDS) in the one-phonon scattering approximation. The PDS spectra display well-resolved peaks of low-frequency internal vibration modes up to 600cm-1. The assignment of these modes was proposed taking into account the results of calculations of the structure and dynamics of isolated molecules of the investigated substances. The quantum chemistry calculations were performed by the semi-empirical PM3 method and at the restricted Hartree-Fock level with the 6-31* basis set. The lower internal modes assigned to torsional vibration of the androstane skeleton mix with the lattice vibrations. The intense bands in the PDS spectra in the frequency range from 150 to 300cm-1 are related to librations of structurally inequivalent methyl groups.

Dielectronic satellite spectra of hydrogen-like titanium (Ti XXII)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bitter, M.; von Goeler, S.; Cohen, S.

High resolution spectra of the Ly ..cap alpha../sub 1/ and Ly ..cap alpha../sub 2/ lines of hydrogenlike titanium, TiXXII, and the associated dielectronic satellites which are due to transitions 1snl-2pnl with n greater than or equal to 2, have been observed from tokamak discharges with auxiliary ion cyclotron heating (ICRH) with central electron temperatures of 2 keV and central electron densities of 8 x 10/sup 13/ cm/sup -3/ on the Princeton Large Torus (PLT). The data have been used for a detailed comparison with theoretical predictions based on the Z - expansion method and Hartree - Fock calculations. The resultsmore » obtained with the Z - expansion method are in excellent agreement with the observed spectral data except for minor discrepancies between the theoretical and experimental wavelengths of 0.0003 A for the n = 2 satellites and of 0.0001 A for the separation of the Ly ..cap alpha../sub 1/ and Ly ..cap alpha../sub 2/ lines. Very good agreement with the experimental data is also obtained for the results from the Hartree - Fock calculations though somewhat larger discrepancies (approx. = 0.0009 A) exist between experimental and theoretical wavelengths which are systematically too small. The observed spectra are used for diagnosis of the central ion and electron temperatures of the PLT discharges and for a measurement of the dielectronic recombination rate coefficient of TiXXII.« less

Local unitary transformation method for large-scale two-component relativistic calculations. II. Extension to two-electron Coulomb interaction.

PubMed

Seino, Junji; Nakai, Hiromi

2012-10-14

The local unitary transformation (LUT) scheme at the spin-free infinite-order Douglas-Kroll-Hess (IODKH) level [J. Seino and H. Nakai, J. Chem. Phys. 136, 244102 (2012)], which is based on the locality of relativistic effects, has been extended to a four-component Dirac-Coulomb Hamiltonian. In the previous study, the LUT scheme was applied only to a one-particle IODKH Hamiltonian with non-relativistic two-electron Coulomb interaction, termed IODKH/C. The current study extends the LUT scheme to a two-particle IODKH Hamiltonian as well as one-particle one, termed IODKH/IODKH, which has been a real bottleneck in numerical calculation. The LUT scheme with the IODKH/IODKH Hamiltonian was numerically assessed in the diatomic molecules HX and X(2) and hydrogen halide molecules, (HX)(n) (X = F, Cl, Br, and I). The total Hartree-Fock energies calculated by the LUT method agree well with conventional IODKH/IODKH results. The computational cost of the LUT method is reduced drastically compared with that of the conventional method. In addition, the LUT method achieves linear-scaling with respect to the system size and a small prefactor.

Select-divide-and-conquer method for large-scale configuration interaction

NASA Astrophysics Data System (ADS)

Bunge, Carlos F.; Carbó-Dorca, Ramon

2006-07-01

A select-divide-and-conquer variational method to approximate configuration interaction (CI) is presented. Given an orthonormal set made up of occupied orbitals (Hartree-Fock or similar) and suitable correlation orbitals (natural or localized orbitals), a large N-electron target space S is split into subspaces S0,S1,S2,…,SR. S0, of dimension d0, contains all configurations K with attributes (energy contributions, etc.) above thresholds T0≡{T0egy,T0etc.}; the CI coefficients in S0 remain always free to vary. S1 accommodates Ks with attributes above T1⩽T0. An eigenproblem of dimension d0+d1 for S0+S1 is solved first, after which the last d1 rows and columns are contracted into a single row and column, thus freezing the last d1 CI coefficients hereinafter. The process is repeated with successive Sj(j ⩾2) chosen so that corresponding CI matrices fit random access memory (RAM). Davidson's eigensolver is used R times. The final energy eigenvalue (lowest or excited one) is always above the corresponding exact eigenvalue in S. Threshold values {Tj;j=0,1,2,…,R} regulate accuracy; for large-dimensional S, high accuracy requires S0+S1 to be solved outside RAM. From there on, however, usually a few Davidson iterations in RAM are needed for each step, so that Hamiltonian matrix-element evaluation becomes rate determining. One μhartree accuracy is achieved for an eigenproblem of order 24×106, involving 1.2×1012 nonzero matrix elements, and 8.4×109 Slater determinants.

Calculations of atomic magnetic nuclear shielding constants based on the two-component normalized elimination of the small component method

NASA Astrophysics Data System (ADS)

Yoshizawa, Terutaka; Zou, Wenli; Cremer, Dieter

2017-04-01

A new method for calculating nuclear magnetic resonance shielding constants of relativistic atoms based on the two-component (2c), spin-orbit coupling including Dirac-exact NESC (Normalized Elimination of the Small Component) approach is developed where each term of the diamagnetic and paramagnetic contribution to the isotropic shielding constant σi s o is expressed in terms of analytical energy derivatives with regard to the magnetic field B and the nuclear magnetic moment 𝝁 . The picture change caused by renormalization of the wave function is correctly described. 2c-NESC/HF (Hartree-Fock) results for the σiso values of 13 atoms with a closed shell ground state reveal a deviation from 4c-DHF (Dirac-HF) values by 0.01%-0.76%. Since the 2-electron part is effectively calculated using a modified screened nuclear shielding approach, the calculation is efficient and based on a series of matrix manipulations scaling with (2M)3 (M: number of basis functions).

Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method

NASA Astrophysics Data System (ADS)

Nakata, Hiroya; Fedorov, Dmitri G.; Zahariev, Federico; Schmidt, Michael W.; Kitaura, Kazuo; Gordon, Mark S.; Nakamura, Shinichiro

2015-03-01

Analytic second derivatives of the energy with respect to nuclear coordinates have been developed for spin restricted density functional theory (DFT) based on the fragment molecular orbital method (FMO). The derivations were carried out for the three-body expansion (FMO3), and the two-body expressions can be obtained by neglecting the three-body corrections. Also, the restricted Hartree-Fock (RHF) Hessian for FMO3 can be obtained by neglecting the density-functional related terms. In both the FMO-RHF and FMO-DFT Hessians, certain terms with small magnitudes are neglected for computational efficiency. The accuracy of the FMO-DFT Hessian in terms of the Gibbs free energy is evaluated for a set of polypeptides and water clusters and found to be within 1 kcal/mol of the corresponding full (non-fragmented) ab initio calculation. The FMO-DFT method is also applied to transition states in SN2 reactions and for the computation of the IR and Raman spectra of a small Trp-cage protein (PDB: 1L2Y). Some computational timing analysis is also presented.

Method for making 2-electron response reduced density matrices approximately N-representable

NASA Astrophysics Data System (ADS)

Lanssens, Caitlin; Ayers, Paul W.; Van Neck, Dimitri; De Baerdemacker, Stijn; Gunst, Klaas; Bultinck, Patrick

2018-02-01

In methods like geminal-based approaches or coupled cluster that are solved using the projected Schrödinger equation, direct computation of the 2-electron reduced density matrix (2-RDM) is impractical and one falls back to a 2-RDM based on response theory. However, the 2-RDMs from response theory are not N-representable. That is, the response 2-RDM does not correspond to an actual physical N-electron wave function. We present a new algorithm for making these non-N-representable 2-RDMs approximately N-representable, i.e., it has the right symmetry and normalization and it fulfills the P-, Q-, and G-conditions. Next to an algorithm which can be applied to any 2-RDM, we have also developed a 2-RDM optimization procedure specifically for seniority-zero 2-RDMs. We aim to find the 2-RDM with the right properties which is the closest (in the sense of the Frobenius norm) to the non-N-representable 2-RDM by minimizing the square norm of the difference between this initial response 2-RDM and the targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM, Q-matrix, and G-matrix are positive semidefinite, i.e., their eigenvalues are non-negative. Our method is suitable for fixing non-N-representable 2-RDMs which are close to being N-representable. Through the N-representability optimization algorithm we add a small correction to the initial 2-RDM such that it fulfills the most important N-representability conditions.

Modified Fourth-Order Kinetic Energy Gradient Expansion with Hartree Potential-Dependent Coefficients.

PubMed

Constantin, Lucian A; Fabiano, Eduardo; Della Sala, Fabio

2017-09-12

Using the semiclassical neutral atom theory, we developed a modified fourth-order kinetic energy (KE) gradient expansion (GE4m) that keeps unchanged all the linear-response terms of the uniform electron gas and gives a significant improvement with respect to the known semilocal functionals for both large atoms and jellium surfaces. On the other hand, GE4m is not accurate for light atoms; thus, we modified the GE4m coefficients making them dependent on a novel ingredient, the reduced Hartree potential, recently introduced in the Journal of Chemical Physics 2016, 145, 084110, in the context of exchange functionals. The resulting KE gradient expansion functional, named uGE4m, belongs to the novel class of u-meta-generalized-gradient-approximations (uMGGA) whose members depend on the conventional ingredients (i.e., the reduced gradient and Laplacian of the density) as well as on the reduced Hartree potential. To test uGE4m, we defined an appropriate benchmark (including total KE and KE differences for atoms, molecules and jellium clusters) for gradient expansion functionals, that is, including only those systems which are mainly described by a slowly varying density regime. While most of the GGA and meta-GGA KE functionals (we tested 18 of them) are accurate for some properties and inaccurate for others, uGE4m shows a consistently good performance for all the properties considered. This represents a qualitative boost in the KE functional development and highlights the importance of the reduced Hartree potential for the construction of next-generation KE functionals.

Polariton biexciton transitions in a ZnSe-based microcavity

NASA Astrophysics Data System (ADS)

Neukirch, U.; Bolton, S. R.; Fromer, N. A.; Sham, L. J.; Chemla, D. S.

2000-06-01

The optical third-order nonlinearity of a ZnSe-based microcavity is investigated by the pump-and-probe method. In the specially designed non-monolithic sample the biexciton binding energy exceeds all damping constants and the normal-mode splitting between exciton and cavity photon. For counter-circular polarized beams the nonlinear response exhibits strong oscillatory structures in the spectral vicinity of the polariton-biexciton transition. Comparison to model calculations shows that in this case the coherent nonlinearity is completely dominated by biexciton-exciton interactions beyond the Hartree-Fock approximation.

Level Energies, Oscillator Strengths and Lifetimes for Transitions in Pb IV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Colon, C.; Alonso-Medina, A.; Zanon, A.

2008-10-22

Oscillator strengths for several lines of astrophysical interest arising from some configurations and some levels radiative lifetimes of Pb IV have been calculated. These values were obtained in intermediate coupling (IC) and using ab initio relativistic Hartree-Fock calculations. We use for the IC calculations the standard method of least square fitting of experimental energy levels by means of computer codes from Cowan. Transition Probabilities and oscillator strengths obtained, although in general agreement with the rare experimental data, do present some noticeable discrepancies that are studied in the text.

On the way to a microscopic derivation of covariant density functionals in nuclei

NASA Astrophysics Data System (ADS)

Ring, Peter

2018-02-01

Several methods are discussed to derive covariant density functionals from the microscopic input of bare nuclear forces. In a first step there are semi-microscopic functionals, which are fitted to ab-initio calculations of nuclear matter and depend in addition on very few phenomenological parameters. They are able to describe nuclear properties with the same precision as fully phenomenological functionals. In a second step we present first relativistic Brueckner-Hartree-Fock calculations in finite nuclei in order to study properties of such functionals, which cannot be obtained from nuclear matter calculations.

M sub shell X-ray emission cross section measurements for Pt, Au, Hg, Pb, Th and U at 8 and 10 keV synchrotron photons

NASA Astrophysics Data System (ADS)

Kaur, Gurpreet; Gupta, Sheenu; Tiwari, M. K.; Mittal, Raj

2014-02-01

M sub shell X-ray emission cross sections of Pt, Au, Hg, Pb, Th and U at 8 and 10 keV photon energies have been determined with linearly polarized photon beam from Indus-2 synchrotron source. The measured cross sections have been reported for the first time and were used to check the available theoretical Dirac-Hartree-Slater (DHS) and Dirac-Fock (DF) values reported in literature and also the presently derived Non Relativistic Hartree-Slater (NRHS), DF and DHS values for Mξ, Mδ, Mα, Mβ, Mγ, Mm1 and Mm2 group of X-rays.

Electronic structure investigations of 4-aminophthal hydrazide by UV-visible, NMR spectral studies and HOMO-LUMO analysis by ab initio and DFT calculations.

PubMed

Sambathkumar, K; Jeyavijayan, S; Arivazhagan, M

2015-08-05

Combined experimental and theoretical studies were conducted on the molecular structure and vibrational spectra of 4-AminoPhthalhydrazide (APH). The FT-IR and FT-Raman spectra of APH were recorded in the solid phase. The molecular geometry and vibrational frequencies of APH in the ground state have been calculated by using the ab initio HF (Hartree-Fock) and density functional methods (B3LYP) invoking 6-311+G(d,p) basis set. The optimized geometric bond lengths and bond angles obtained by HF and B3LYP method show best agreement with the experimental values. Comparison of the observed fundamental vibrational frequencies of APH with calculated results by HF and density functional methods indicates that B3LYP is superior to the scaled Hartree-Fock approach for molecular vibrational problems. The difference between the observed and scaled wave number values of most of the fundamentals is very small. A detailed interpretation of the NMR spectra of APH was also reported. The theoretical spectrograms for infrared and Raman spectra of the title molecule have been constructed. UV-vis spectrum of the compound was recorded and the electronic properties, such as HOMO and LUMO energies, were performed by time dependent density functional theory (TD-DFT) approach. Finally the calculations results were applied to simulated infrared and Raman spectra of the title compound which show good agreement with observed spectra. And the temperature dependence of the thermodynamic properties of constant pressure (Cp), entropy (S) and enthalpy change (ΔH0→T) for APH were also determined. Copyright © 2015 Elsevier B.V. All rights reserved.

On the photoisomerization of 5-hydroxytropolone: An ab initio and nuclear wave function study

NASA Astrophysics Data System (ADS)

Paz, Juan J.; Moreno, Miquel; Lluch, José M.

1997-10-01

In this paper we perform ab initio calculations for the stable conformations and the transition states for the isomerization processes in 5-hydroxytropolone in both the ground (S0) and first excited (S1) singlet electronic states. The Hartree-Fock self-consistent field (SCF) level and a complete active space SCF (CASSCF) level for S0 are considered, whereas the configuration interaction all single excitation method (CIS) and the CASSCF levels are used to deal with the S1 state. Energies are reevaluated at all levels through perturbation theory up to second order: Møller-Plesset for the Hartree-Fock and CIS methods, and the CASPT2 method for CAS results. The ab initio results are then used to perform different monodimensional fits to the potential energy surfaces in order to analyze the wave functions for the nuclear motions in both electronic states. Our best results predict that for the S0 state two stable conformers, syn and anti, can exist in thermal equilibrium. In accordance with experimental expectations the syn isomer is the most stable. As for the S1 state, and again in accord with experimental spectroscopical data, the order of stability reverses, the anti being the most stable. A more interesting result is that analysis of the nuclear wave functions shows an important syn-anti mixing in the S1 state that does not appear in S0. This result explains the appearance of syn-anti and anti-syn crossover transitions observed in the electronic spectra of 5-hydroxytropolone so that syn-anti reaction may take place through photoisomerization.

VizieR Online Data Catalog: Energy levels & transition rates for F-like ions (Si+, 2016)

NASA Astrophysics Data System (ADS)

Si, R.; Li, S.; Guo, X. L.; Chen, Z. B.; Brage, T.; Jonsson, P.; Wang, K.; Yan, J.; Chen, C. Y.; Zou, Y. M.

2017-01-01

For the multiconfiguration Dirac-Hartree-Fock (MCDHF) calculation we use the latest version of the GRASP2K code (Jonsson+ 2013CoPhC.184.2197J), while the many-body perturbation theory (MBPT) calculation is performed using the Flexible Atomic Code (FAC; Gu 2008CaJPh..86..675G). (2 data files).

SU-E-I-43: Photoelectric Cross Section Revisited

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haga, A; Nakagawa, K; Kotoku, J

2015-06-15

Purpose: The importance of the precision in photoelectric cross-section value increases for recent developed technology such as dual energy computed tomography, in which some reconstruction algorithms require the energy dependence of the photo-absorption in each material composition of human being. In this study, we revisited the photoelectric cross-section calculation by self-consistent relativistic Hartree-Fock (HF) atomic model and compared with that widely distributed as “XCOM database” in National Institute of Standards and Technology, which was evaluated with localdensity approximation for electron-exchange (Fock)z potential. Methods: The photoelectric cross section can be calculated with the electron wave functions in initial atomic state (boundmore » electron) and final continuum state (photoelectron). These electron states were constructed based on the selfconsistent HF calculation, where the repulsive Coulomb potential from the electron charge distribution (Hartree term) and the electron exchange potential with full electromagnetic interaction (Fock term) were included for the electron-electron interaction. The photoelectric cross sections were evaluated for He (Z=2), Be (Z=4), C (Z=6), O (Z=8), and Ne (Z=10) in energy range of 10keV to 1MeV. The Result was compared with XCOM database. Results: The difference of the photoelectric cross section between the present calculation and XCOM database was 8% at a maximum (in 10keV for Be). The agreement tends to be better as the atomic number increases. The contribution from each atomic shell has a considerable discrepancy with XCOM database except for K-shell. However, because the photoelectric cross section arising from K-shell is dominant, the net photoelectric cross section was almost insensitive to the different handling in Fock potential. Conclusion: The photoelectric cross-section program has been developed based on the fully self-consistent relativistic HF atomic model. Due to small effect on the

Thermodynamic Properties of Low-Density {}^{132}Xe Gas in the Temperature Range 165-275 K

NASA Astrophysics Data System (ADS)

Akour, Abdulrahman

2018-01-01

The method of static fluctuation approximation was used to calculate selected thermodynamic properties (internal energy, entropy, energy capacity, and pressure) for xenon in a particularly low-temperature range (165-270 K) under different conditions. This integrated microscopic study started from an initial basic assumption as the main input. The basic assumption in this method was to replace the local field operator with its mean value, then numerically solve a closed set of nonlinear equations using an iterative method, considering the Hartree-Fock B2-type dispersion potential as the most appropriate potential for xenon. The results are in very good agreement with those of an ideal gas.

Accuracy of electron densities obtained via Koopmans-compliant hybrid functionals

NASA Astrophysics Data System (ADS)

Elmaslmane, A. R.; Wetherell, J.; Hodgson, M. J. P.; McKenna, K. P.; Godby, R. W.

2018-04-01

We evaluate the accuracy of electron densities and quasiparticle energy gaps given by hybrid functionals by directly comparing these to the exact quantities obtained from solving the many-electron Schrödinger equation. We determine the admixture of Hartree-Fock exchange to approximate exchange-correlation in our hybrid functional via one of several physically justified constraints, including the generalized Koopmans' theorem. We find that hybrid functionals yield strikingly accurate electron densities and gaps in both exchange-dominated and correlated systems. We also discuss the role of the screened Fock operator in the success of hybrid functionals.

An Accurate Projector Calibration Method Based on Polynomial Distortion Representation

PubMed Central

Liu, Miao; Sun, Changku; Huang, Shujun; Zhang, Zonghua

2015-01-01

In structure light measurement systems or 3D printing systems, the errors caused by optical distortion of a digital projector always affect the precision performance and cannot be ignored. Existing methods to calibrate the projection distortion rely on calibration plate and photogrammetry, so the calibration performance is largely affected by the quality of the plate and the imaging system. This paper proposes a new projector calibration approach that makes use of photodiodes to directly detect the light emitted from a digital projector. By analyzing the output sequence of the photoelectric module, the pixel coordinates can be accurately obtained by the curve fitting method. A polynomial distortion representation is employed to reduce the residuals of the traditional distortion representation model. Experimental results and performance evaluation show that the proposed calibration method is able to avoid most of the disadvantages in traditional methods and achieves a higher accuracy. This proposed method is also practically applicable to evaluate the geometric optical performance of other optical projection system. PMID:26492247

Baryons as Fock states of 3,5,... Quarks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dmitri Diakonov; Victor Petrov

2004-09-01

We present a generating functional producing quark wave functions of all Fock states in the octet, decuplet and antidecuplet baryons in the mean field approximation, both in the rest and infinite momentum frames. In particular, for the usual octet and decuplet baryons we get the SU(6)-symmetric wave functions for their 3-quark component but with specific corrections from relativism and from additional quark-antiquark pairs. For the exotic antidecuplet baryons we obtain the 5-quark wave function.

Calculations of electric dipole moments and static dipole polarizabilities based on the two-component normalized elimination of the small component method.

PubMed

Yoshizawa, Terutaka; Zou, Wenli; Cremer, Dieter

2016-11-14

The analytical energy gradient and Hessian of the two-component Normalized Elimination of the Small Component (2c-NESC) method with regard to the components of the electric field are derived and used to calculate spin-orbit coupling (SOC) corrected dipole moments and dipole polarizabilities of molecules, which contain elements with high atomic number. Calculated 2c-NESC dipole moments and isotropic polarizabilities agree well with the corresponding four-component-Dirac Hartree-Fock or density functional theory values. SOC corrections for the electrical properties are in general small, but become relevant for the accurate prediction of these properties when the molecules in question contain sixth and/or seventh period elements (e.g., the SO effect for At 2 is about 10% of the 2c-NESC polarizability). The 2c-NESC changes in the electric molecular properties are rationalized in terms of spin-orbit splitting and SOC-induced mixing of frontier orbitals with the same j = l + s quantum numbers.

Calculations of electric dipole moments and static dipole polarizabilities based on the two-component normalized elimination of the small component method

NASA Astrophysics Data System (ADS)

Yoshizawa, Terutaka; Zou, Wenli; Cremer, Dieter

2016-11-01

The analytical energy gradient and Hessian of the two-component Normalized Elimination of the Small Component (2c-NESC) method with regard to the components of the electric field are derived and used to calculate spin-orbit coupling (SOC) corrected dipole moments and dipole polarizabilities of molecules, which contain elements with high atomic number. Calculated 2c-NESC dipole moments and isotropic polarizabilities agree well with the corresponding four-component-Dirac Hartree-Fock or density functional theory values. SOC corrections for the electrical properties are in general small, but become relevant for the accurate prediction of these properties when the molecules in question contain sixth and/or seventh period elements (e.g., the SO effect for At2 is about 10% of the 2c-NESC polarizability). The 2c-NESC changes in the electric molecular properties are rationalized in terms of spin-orbit splitting and SOC-induced mixing of frontier orbitals with the same j = l + s quantum numbers.

Double Gamow-Teller Transitions and its Relation to Neutrinoless β β Decay

NASA Astrophysics Data System (ADS)

Shimizu, Noritaka; Menéndez, Javier; Yako, Kentaro

2018-04-01

We study the double Gamow-Teller (DGT) strength distribution of 48Ca with state-of-the-art large-scale nuclear shell model calculations. Our analysis shows that the centroid energy of the DGT giant resonance depends mostly on the isovector pairing interaction, while the resonance width is more sensitive to isoscalar pairing. Pairing correlations are also key in neutrinoless β β (0 ν β β ) decay. We find a simple relation between the centroid energy of the 48Ca DGT giant resonance and the 0 ν β β decay nuclear matrix element. More generally, we observe a very good linear correlation between the DGT transition to the ground state of the final nucleus and the 0 ν β β decay matrix element. The correlation, which originates on the dominant short-range character of both transitions, extends to heavier systems including several β β emitters and also holds in energy-density functional results. Our findings suggest that DGT experiments can be a very valuable tool to obtain information on the value of 0 ν β β decay nuclear matrix elements.

Application of relativistic distorted-wave method to electron-impact excitation of highly charged Fe XXIV ion embedded in weakly coupled plasmas

NASA Astrophysics Data System (ADS)

Chen, Zhanbin

2018-05-01

The process of excitation of highly charged Fe XXIV ion embedded in weakly coupled plasmas by electron impact is studied, together with the subsequent radiative decay. For the target structure, the calculation is performed using the multiconfiguration Dirac-Hartree-Fock method incorporating the Debye-Hückel potential for the electron-nucleus interaction. Fine-structure levels of the 1s22p and 1s2s2p configurations and the transition properties among these levels are presented over a wide range of screening parameters. For the collision dynamics, the distorted-wave method in the relativistic frame is adopted to include the effect of plasma background, in which the interparticle interactions in the system are described by screened interactions of the Debye-Hückel type. The continuum wave function of the projectile electron is obtained by solving the modified Dirac equations. The influence of plasma strength on the cross section, the linear polarization, and the angular distribution of x-ray photon emission are investigated in detail. Comparison of the present results with experimental data and other theoretical predictions, when available, is made.

Charge and Spin Currents in Open-Shell Molecules:  A Unified Description of NMR and EPR Observables.

PubMed

Soncini, Alessandro

2007-11-01

The theory of EPR hyperfine coupling tensors and NMR nuclear magnetic shielding tensors of open-shell molecules in the limit of vanishing spin-orbit coupling (e.g., for organic radicals) is analyzed in terms of spin and charge current density vector fields. The ab initio calculation of the spin and charge current density response has been implemented at the Restricted Open-Shell Hartree-Fock, Unrestricted Hartree-Fock, and unrestricted GGA-DFT level of theory. On the basis of this formalism, we introduce the definition of nuclear hyperfine coupling density, a scalar function of position providing a partition of the EPR observable over the molecular domain. Ab initio maps of spin and charge current density and hyperfine coupling density for small radicals are presented and discussed in order to illustrate the interpretative advantages of the newly introduced approach. Recent NMR experiments providing evidence for the existence of diatropic ring currents in the open-shell singlet pancake-bonded dimer of the neutral phenalenyl radical are directly assessed via the visualization of the induced current density.

Global hybrids from the semiclassical atom theory satisfying the local density linear response.

PubMed

Fabiano, Eduardo; Constantin, Lucian A; Cortona, Pietro; Della Sala, Fabio

2015-01-13

We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 2011, 106, 186406] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetic and structural testing, including thermochemistry and geometry, transition metal complexes, noncovalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semiempirical dispersion corrections are also provided.

Wentzel-Kramers-Brillouin method in the Bargmann representation. [of quantum mechanics

NASA Technical Reports Server (NTRS)

Voros, A.

1989-01-01

It is demonstrated that the Bargmann representation of quantum mechanics is ideally suited for semiclassical analysis, using as an example the WKB method applied to the bound-state problem in a single well of one degree of freedom. For the harmonic oscillator, this WKB method trivially gives the exact eigenfunctions in addition to the exact eigenvalues. For an anharmonic well, a self-consistent variational choice of the representation greatly improves the accuracy of the semiclassical ground state. Also, a simple change of scale illuminates the relationship of semiclassical versus linear perturbative expansions, allowing a variety of multidimensional extensions.

Towards "Inverse" Character Tables? A One-Step Method for Decomposing Reducible Representations

ERIC Educational Resources Information Center

Piquemal, J.-Y.; Losno, R.; Ancian, B.

2009-01-01

In the framework of group theory, a new procedure is described for a one-step automated reduction of reducible representations. The matrix inversion tool, provided by standard spreadsheet software, is applied to the central part of the character table that contains the characters of the irreducible representation. This method is not restricted to…

Effect of gauge-field interaction on fermion transport in two dimensions: Hartree conductivity correction and dephasing

NASA Astrophysics Data System (ADS)

Ludwig, T.; Gornyi, I. V.; Mirlin, A. D.; Wölfle, P.

2008-06-01

We consider the quantum corrections to the conductivity of fermions interacting via a Chern Simons gauge field and concentrate on the Hartree-type contributions. The first-order Hartree approximation is only valid in the limit of weak coupling λ≪g-1/2 to the gauge field ( g≫1 is the dimensionless conductance) and results in an antilocalizing conductivity correction ˜λ2gln2T . In the case of strong coupling, an infinite summation of higher-order terms is necessary, which includes both the virtual (renormalization of the frequency) and real (dephasing) processes. At intermediate temperatures, T0≪T≪gT0 , where T0˜1/g2τ and τ is the elastic scattering time, the T dependence of the conductivity is determined by the Hartree correction, δσH(T)-δσH(gT0)∝g1/2-(T/T0)1/2[1+ln(gT0/T)1/2] , so that σ(T) increases with lowering T . At low temperatures, T≪T0 , the temperature-dependent part of the Hartree correction assumes a logarithmic form with a coefficient of order unity, δσH∝ln(1/T) . As a result, the negative exchange contribution δσex∝-lngln(1/T) becomes dominant, which yields localization in the limit of T→0 . We further discuss dephasing at strong coupling and show that the dephasing rates are of the order of T , owing to the interplay of inelastic scattering and renormalization. On the other hand, the dephasing length is anomalously short, Lφ≪LT , where LT is the thermal length. For the case of composite fermions with long-range Coulomb interaction, the gauge-field propagator is less singular. The resulting Hartree correction has the usual sign and temperature dependence, δσH∝lngln(1/T) , and for realistic g is overcompensated by the negative exchange contribution due to the gauge-boson and scalar parts of the interaction. In this case, the dephasing length Lφ is of the order of LT for not too low temperatures and exceeds LT for T≲gT0 .

The resolution of identity and chain of spheres approximations for the LPNO-CCSD singles Fock term

NASA Astrophysics Data System (ADS)

Izsák, Róbert; Hansen, Andreas; Neese, Frank

2012-10-01

In the present work, the RIJCOSX approximation, developed earlier for accelerating the SCF procedure, is applied to one of the limiting factors of LPNO-CCSD calculations: the evaluation of the singles Fock term. It turns out that the introduction of RIJCOSX in the evaluation of the closed shell LPNO-CCSD singles Fock term causes errors below the microhartree limit. If the proposed procedure is also combined with RIJCOSX in SCF, then a somewhat larger error occurs, but reaction energy errors will still remain negligible. The speedup for the singles Fock term only is about 9-10 fold for the largest basis set applied. For the case of Penicillin using the def2-QZVPP basis set, a single point energy evaluation takes 2 day 16 h on a single processor leading to a total speedup of 2.6 as compared to a fully analytic calculation. Using eight processors, the same calculation takes only 14 h.

Final Scientific/Technical Report: Breakthrough Design and Implementation of Many-Body Theories for Electron Correlation

DOE Office of Scientific and Technical Information (OSTI.GOV)

So Hirata

2012-01-03

This report discusses the following highlights of the project: (1) grid-based Hartree-Fock equation solver; (2) explicitly correlated coupled-cluster and perturbation methods; (3) anharmonic vibrational frequencies and vibrationally averaged NMR and structural parameters of FHF; (4) anharmonic vibrational frequencies and vibrationally averaged structures of hydrocarbon combustion species; (5) anharmonic vibrational analysis of the guanine-cytosine base pair; (6) the nature of the Born-Oppenheimer approximation; (7) Polymers and solids Brillouin-zone downsampling - the modulo MP2 method; (8) explicitly correlated MP2 for extended systems; (9) fast correlated method for molecular crystals - solid formic acid; and (10) fast correlated method for molecular crystals -more » solid hydrogen fluoride.« less

Heat capacity of the neutron star inner crust within an extended nuclear statistical equilibrium model

NASA Astrophysics Data System (ADS)

Burrello, S.; Gulminelli, F.; Aymard, F.; Colonna, M.; Raduta, Ad. R.

2015-11-01

Background: Superfluidity in the crust is a key ingredient for the cooling properties of proto-neutron stars. Present theoretical calculations employ the quasiparticle mean-field Hartree-Fock-Bogoliubov theory with temperature-dependent occupation numbers for the quasiparticle states. Purpose: Finite temperature stellar matter is characterized by a whole distribution of different nuclear species. We want to assess the importance of this distribution on the calculation of heat capacity in the inner crust. Method: Following a recent work, the Wigner-Seitz cell is mapped into a model with cluster degrees of freedom. The finite temperature distribution is then given by a statistical collection of Wigner-Seitz cells. We additionally introduce pairing correlations in the local density BCS approximation both in the homogeneous unbound neutron component, and in the interface region between clusters and neutrons. Results: The heat capacity is calculated in the different baryonic density conditions corresponding to the inner crust, and in a temperature range varying from 100 KeV to 2 MeV. We show that accounting for the cluster distribution has a small effect at intermediate densities, but it considerably affects the heat capacity both close to the outer crust and close to the core. We additionally show that it is very important to consider the temperature evolution of the proton fraction for a quantitatively reliable estimation of the heat capacity. Conclusions: We present the first modelization of stellar matter containing at the same time a statistical distribution of clusters at finite temperature, and pairing correlations in the unbound neutron component. The effect of the nuclear distribution on the superfluid properties can be easily added in future calculations of the neutron star cooling curves. A strong influence of resonance population on the heat capacity at high temperature is observed, which deserves to be further studied within more microscopic calculations.

Double Photoionization of helium atom using Screening Potential Approach

NASA Astrophysics Data System (ADS)

Saha, Haripada

2014-05-01

The triple differential cross section for double Photoionization of helium atom will be investigated using our recently extended MCHF method. It is well known that electron correlation effects in both the initial and the final states are very important. To incorporate these effects we will use the multi-configuration Hartree-Fock method to account for electron correlation in the initial state. The electron correlation in the final state will be taken into account using the angle-dependent screening potential approximation. The triple differential cross section (TDCS) will be calculated for 20 eV photon energy, which has experimental results. Our results will be compared with available experimental and the theoretical observations.

A reformulation of the coupled perturbed self-consistent field equations entirely within a local atomic orbital density matrix-based scheme

NASA Astrophysics Data System (ADS)

Ochsenfeld, Christian; Head-Gordon, Martin

1997-05-01

To exploit the exponential decay found in numerical studies for the density matrix and its derivative with respect to nuclear displacements, we reformulate the coupled perturbed self-consistent field (CPSCF) equations and a quadratically convergent SCF (QCSCF) method for Hartree-Fock and density functional theory within a local density matrix-based scheme. Our D-CPSCF (density matrix-based CPSCF) and D-QCSCF schemes open the way for exploiting sparsity and to achieve asymptotically linear scaling of computational complexity with molecular size ( M), in case of D-CPSCF for all O( M) derivative densities. Furthermore, these methods are even for small molecules strongly competitive to conventional algorithms.

Restoring the Pauli principle in the random phase approximation ground state

NASA Astrophysics Data System (ADS)

Kosov, D. S.

2017-12-01

Random phase approximation ground state contains electronic configurations where two (and more) identical electrons can occupy the same molecular spin-orbital violating the Pauli exclusion principle. This overcounting of electronic configurations happens due to quasiboson approximation in the treatment of electron-hole pair operators. We describe the method to restore the Pauli principle in the RPA wavefunction. The proposed theory is illustrated by the calculations of molecular dipole moments and electronic kinetic energies. The Hartree-Fock based RPA, which is corrected for the Pauli principle, gives the results of comparable accuracy with Møller-Plesset second order perturbation theory and coupled-cluster singles and doubles method.

Sharp threshold of blow-up and scattering for the fractional Hartree equation

NASA Astrophysics Data System (ADS)

Guo, Qing; Zhu, Shihui

2018-02-01

We consider the fractional Hartree equation in the L2-supercritical case, and find a sharp threshold of the scattering versus blow-up dichotomy for radial data: If M[u0 ]s -sc/sc E [u0 ] < M[ Q ]s -sc/sc E [ Q ] and M[u0 ]s -sc/sc ‖u0‖ H˙s 2 < M[ Q ]s -sc/sc ‖Q‖ H˙s 2 , then the solution u (t) is globally well-posed and scatters; if M[u0 ]s -sc/sc E [u0 ] < M[ Q ]s -sc/sc E [ Q ] and M[u0 ]s -sc/sc ‖u0‖ H˙s 2 > M[ Q ]s -sc/sc ‖Q‖ H˙s 2 , the solution u (t) blows up in finite time. This condition is sharp in the sense that the solitary wave solution eit Q (x) is global but not scattering, which satisfies the equality in the above conditions. Here, Q is the ground-state solution for the fractional Hartree equation.

Application of 2D graphic representation of protein sequence based on Huffman tree method.

PubMed

Qi, Zhao-Hui; Feng, Jun; Qi, Xiao-Qin; Li, Ling

2012-05-01

Based on Huffman tree method, we propose a new 2D graphic representation of protein sequence. This representation can completely avoid loss of information in the transfer of data from a protein sequence to its graphic representation. The method consists of two parts. One is about the 0-1 codes of 20 amino acids by Huffman tree with amino acid frequency. The amino acid frequency is defined as the statistical number of an amino acid in the analyzed protein sequences. The other is about the 2D graphic representation of protein sequence based on the 0-1 codes. Then the applications of the method on ten ND5 genes and seven Escherichia coli strains are presented in detail. The results show that the proposed model may provide us with some new sights to understand the evolution patterns determined from protein sequences and complete genomes. Copyright © 2012 Elsevier Ltd. All rights reserved.

Hartree-Fock and density functional theory study of alpha-cyclodextrin conformers.

PubMed

Jiménez, Verónica; Alderete, Joel B

2008-01-31

Herein, we report the geometry optimization of four conformers of alpha-cyclodextrin (alpha-CD) by means of PM3, HF/STO-3G, HF/3-21G, HF/6-31G(d), B3LYP/6-31G(d), and X3LYP/6-31G(d) calculations. The analysis of several geometrical parameters indicates that all conformers possess bond lengths, angles, and dihedrals that agree fairly well with the crystalline structure of alpha-CD. However, only three of them (1-3) resemble the polar character of CDs and show intramolecular hydrogen-bonding patterns that agree with experimental NMR data. Among them, conformer 3 appears to be the most stable species both in the gas phase and in solution; therefore, it is expected to be the most suitable representative structure for alpha-CD conformation. The purpose of selecting such a species is to identify an appropriate structure to be employed as a starting point for reliable computational studies on complexation phenomena. Our results indicate that the choice of a particular alpha-CD conformer should affect the results of ab initio computational studies on the inclusion complexation with this cyclodextrin since both the direction and the magnitude of the dipole moment depend strongly on the conformation of alpha-CD.

Model's sparse representation based on reduced mixed GMsFE basis methods

NASA Astrophysics Data System (ADS)

Jiang, Lijian; Li, Qiuqi

2017-06-01

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. A typical application for the elliptic PDEs is the flow in heterogeneous random porous media. Mixed generalized multiscale finite element method (GMsFEM) is one of the accurate and efficient approaches to solve the flow problem in a coarse grid and obtain the velocity with local mass conservation. When the inputs of the PDEs are parameterized by the random variables, the GMsFE basis functions usually depend on the random parameters. This leads to a large number degree of freedoms for the mixed GMsFEM and substantially impacts on the computation efficiency. In order to overcome the difficulty, we develop reduced mixed GMsFE basis methods such that the multiscale basis functions are independent of the random parameters and span a low-dimensional space. To this end, a greedy algorithm is used to find a set of optimal samples from a training set scattered in the parameter space. Reduced mixed GMsFE basis functions are constructed based on the optimal samples using two optimal sampling strategies: basis-oriented cross-validation and proper orthogonal decomposition. Although the dimension of the space spanned by the reduced mixed GMsFE basis functions is much smaller than the dimension of the original full order model, the online computation still depends on the number of coarse degree of freedoms. To significantly improve the online computation, we integrate the reduced mixed GMsFE basis methods with sparse tensor approximation and obtain a sparse representation for the model's outputs. The sparse representation is very efficient for evaluating the model's outputs for many instances of parameters. To illustrate the efficacy of the proposed methods, we present a few numerical examples for elliptic PDEs with multiscale and random inputs. In particular, a two-phase flow model in random porous

Model's sparse representation based on reduced mixed GMsFE basis methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Lijian, E-mail: ljjiang@hnu.edu.cn; Li, Qiuqi, E-mail: qiuqili@hnu.edu.cn

2017-06-01

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. A typical application for the elliptic PDEs is the flow in heterogeneous random porous media. Mixed generalized multiscale finite element method (GMsFEM) is one of the accurate and efficient approaches to solve the flow problem in a coarse grid and obtain the velocity with local mass conservation. When the inputs of the PDEs are parameterized by the random variables, the GMsFE basis functions usually depend on the random parameters. This leads to a largemore » number degree of freedoms for the mixed GMsFEM and substantially impacts on the computation efficiency. In order to overcome the difficulty, we develop reduced mixed GMsFE basis methods such that the multiscale basis functions are independent of the random parameters and span a low-dimensional space. To this end, a greedy algorithm is used to find a set of optimal samples from a training set scattered in the parameter space. Reduced mixed GMsFE basis functions are constructed based on the optimal samples using two optimal sampling strategies: basis-oriented cross-validation and proper orthogonal decomposition. Although the dimension of the space spanned by the reduced mixed GMsFE basis functions is much smaller than the dimension of the original full order model, the online computation still depends on the number of coarse degree of freedoms. To significantly improve the online computation, we integrate the reduced mixed GMsFE basis methods with sparse tensor approximation and obtain a sparse representation for the model's outputs. The sparse representation is very efficient for evaluating the model's outputs for many instances of parameters. To illustrate the efficacy of the proposed methods, we present a few numerical examples for elliptic PDEs with multiscale and random inputs. In particular, a two-phase flow model in random

Approximating the Shifted Hartree-Exchange-Correlation Potential in Direct Energy Kohn-Sham Theory.

PubMed

Sharpe, Daniel J; Levy, Mel; Tozer, David J

2018-02-13

Levy and Zahariev [Phys. Rev. Lett. 113 113002 (2014)] have proposed a new approach for performing density functional theory calculations, termed direct energy Kohn-Sham (DEKS) theory. In this approach, the electronic energy equals the sum of orbital energies, obtained from Kohn-Sham-like orbital equations involving a shifted Hartree-exchange-correlation potential, which must be approximated. In the present study, density scaling homogeneity considerations are used to facilitate DEKS calculations on a series of atoms and molecules, leading to three nonlocal approximations to the shifted potential. The first two rely on preliminary Kohn-Sham calculations using a standard generalized gradient approximation (GGA) exchange-correlation functional and the results illustrate the benefit of describing the dominant Hartree component of the shift exactly. A uniform electron gas analysis is used to eliminate the need for these preliminary Kohn-Sham calculations, leading to a potential with an unconventional form that yields encouraging results, providing strong motivation for further research in DEKS theory.

Cross Sections for Electron Impact Excitation of Astrophysically Abundant Atoms and Ions

NASA Technical Reports Server (NTRS)

Tayal, S. S.

2006-01-01

Electron collisional excitation rates and transition probabilities are important for computing electron temperatures and densities, ionization equilibria, and for deriving elemental abundances from emission lines formed in the collisional and photoionized astrophysical plasmas. Accurate representation of target wave functions that properly account for the important correlation and relaxation effects and inclusion of coupling effects including coupling to the continuum are essential components of a reliable collision calculation. Non-orthogonal orbitals technique in multiconfiguration Hartree-Fock approach is used to calculate oscillator strengths and transition probabilities. The effect of coupling to the continuum spectrum is included through the use of pseudostates which are chosen to account for most of the dipole polarizabilities of target states. The B-spline basis is used in the R-matrix approach to calculate electron excitation collision strengths and rates. Results for oscillator strengths and electron excitation collision strengths for transitions in N I, O I, O II, O IV, S X and Fe XIV have been produced

A multiple distributed representation method based on neural network for biomedical event extraction.

PubMed

Wang, Anran; Wang, Jian; Lin, Hongfei; Zhang, Jianhai; Yang, Zhihao; Xu, Kan

2017-12-20

Biomedical event extraction is one of the most frontier domains in biomedical research. The two main subtasks of biomedical event extraction are trigger identification and arguments detection which can both be considered as classification problems. However, traditional state-of-the-art methods are based on support vector machine (SVM) with massive manually designed one-hot represented features, which require enormous work but lack semantic relation among words. In this paper, we propose a multiple distributed representation method for biomedical event extraction. The method combines context consisting of dependency-based word embedding, and task-based features represented in a distributed way as the input of deep learning models to train deep learning models. Finally, we used softmax classifier to label the example candidates. The experimental results on Multi-Level Event Extraction (MLEE) corpus show higher F-scores of 77.97% in trigger identification and 58.31% in overall compared to the state-of-the-art SVM method. Our distributed representation method for biomedical event extraction avoids the problems of semantic gap and dimension disaster from traditional one-hot representation methods. The promising results demonstrate that our proposed method is effective for biomedical event extraction.

Interaction of the NO 3pπ (C {sup 2}Π) Rydberg state with RG (RG = Ne, Kr, and Xe): Potential energy surfaces and spectroscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ershova, Olga V.; Besley, Nicholas A., E-mail: Nick.Besley@nottingham.ac.uk; Wright, Timothy G., E-mail: Tim.Wright@nottingham.ac.uk

2015-01-21

We present new potential energy surfaces for the interaction of NO(C {sup 2}Π) with each of Ne, Kr, and Xe. The potential energy surfaces have been calculated using second order Møller-Plesset perturbation theory, exploiting a procedure to converge the reference Hartree-Fock wavefunction for the excited states: the maximum overlap method. The bound rovibrational states obtained from the surfaces are used to simulate the electronic spectra and their appearance is in good agreement with available (2+1) REMPI spectra. We discuss the assignment and appearance of these spectra, comparing to that of NO-Ar.

Medium-heavy nuclei from nucleon-nucleon interactions in lattice QCD

NASA Astrophysics Data System (ADS)

Inoue, Takashi; Aoki, Sinya; Charron, Bruno; Doi, Takumi; Hatsuda, Tetsuo; Ikeda, Yoichi; Ishii, Noriyoshi; Murano, Keiko; Nemura, Hidekatsu; Sasaki, Kenji; HAL QCD Collaboration

2015-01-01

On the basis of the Brueckner-Hartree-Fock method with the nucleon-nucleon forces obtained from lattice QCD simulations, the properties of the medium-heavy doubly magic nuclei such as 16O and 40Ca are investigated. We found that those nuclei are bound for the pseudoscalar meson mass MPS≃470 MeV. The mass number dependence of the binding energies, single-particle spectra, and density distributions are qualitatively consistent with those expected from empirical data at the physical point, although these hypothetical nuclei at heavy quark mass have smaller binding energies than the real nuclei.

Experimental and theoretical debate on efficient second harmonic generation in Bis (Cinnamic acid): Hexamine cocrystal

NASA Astrophysics Data System (ADS)

Vijayalakshmi, S.; Kalyanaraman, S.; Ravindran, T. R.

2014-02-01

Second harmonic generation (SHG) in Bis (Cinnamic acid): Hexamine cocrystal was extensively analyzed through charge transfer (CT). The CT interactions through hydrogen bonding were well established with the aid of vibrational analysis and Natural Bond Orbital (NBO) analysis. The retentivity of coplanar nature of the cinnamic acid in the cocrystal was confirmed through UV-Visible spectroscopy and supported by Raman studies. Structural analysis indicated the quinoidal character of the given material presenting a high SHG efficiency. The first order hyperpolarizability value was calculated theoretically by density functional theory (DFT) and Hartree-Fock (HF) methods in support for the large value of SHG.

Delocalization of frontier orbitals induced red emission for heptazine based thermally activated delayed fluorescence molecule: First-principles study

NASA Astrophysics Data System (ADS)

Kang, Yongxiang; Zhao, Liyun; Leng, Jiancai

2018-04-01

Design of red organic emitting molecules with characteristic of thermally activated delayed fluorescence (TADF) remains a great challenge. Here, electronic and optical properties of a series of multi-branched TADF molecules have been investigated based on the newly-proposed optimal Hartree-Fock percentage method. Results show that, though enlarging the delocalization of HOMO and LUMO, the emission wavelength is redshift. The designed red TADF molecule possesses smaller reorganization energy than these for reported molecules. This indicates the non-radiative energy consumption of excited state is small and effective luminescence can be expected. Thus, a promising red thermally activated delayed fluorescence molecule is proposed.

Unified equation of state for neutron stars on a microscopic basis

NASA Astrophysics Data System (ADS)

Sharma, B. K.; Centelles, M.; Viñas, X.; Baldo, M.; Burgio, G. F.

2015-12-01

We derive a new equation of state (EoS) for neutron stars (NS) from the outer crust to the core based on modern microscopic calculations using the Argonne v18 potential plus three-body forces computed with the Urbana model. To deal with the inhomogeneous structures of matter in the NS crust, we use a recent nuclear energy density functional that is directly based on the same microscopic calculations, and which is able to reproduce the ground-state properties of nuclei along the periodic table. The EoS of the outer crust requires the masses of neutron-rich nuclei, which are obtained through Hartree-Fock-Bogoliubov calculations with the new functional when they are unknown experimentally. To compute the inner crust, Thomas-Fermi calculations in Wigner-Seitz cells are performed with the same functional. Existence of nuclear pasta is predicted in a range of average baryon densities between ≃0.067 fm-3 and ≃0.0825 fm-3, where the transition to the core takes place. The NS core is computed from the new nuclear EoS assuming non-exotic constituents (core of npeμ matter). In each region of the star, we discuss the comparison of the new EoS with previous EoSs for the complete NS structure, widely used in astrophysical calculations. The new microscopically derived EoS fulfills at the same time a NS maximum mass of 2 M⊙ with a radius of 10 km, and a 1.5 M⊙ NS with a radius of 11.6 km.

Ab initio molecular orbital studies of the positive muon and muonium in 4-arylmethyleneamino-TEMPO derivatives

NASA Astrophysics Data System (ADS)

Briere, T. M.; Jeong, J.; Das, T. P.; Ohira, S.; Nagamine, K.

2000-08-01

The muon and muonium bonding sites of the 4-arylmethyleneamino-2,2,6,6-tetramethylpiperidin-1-yloxyl radical crystals with aryl groups consisting of biphenyl and 4-pyridyl were studied via ab initio Hartree-Fock theory. The hyperfine fields, including both intramolecular and intermolecular interactions, were calculated at the sites of interest and compared to zero field μSR results.

Weak interactions in Graphane/BN systems under static electric fields—A periodic ab-initio study.

PubMed

Steinkasserer, Lukas Eugen Marsoner; Gaston, Nicola; Paulus, Beate

2015-04-21

Ab-initio calculations via periodic Hartree-Fock (HF) and local second-order Møller-Plesset perturbation theory (LMP2) are used to investigate the adsorption properties of combined Graphane/boron nitride systems and their response to static electric fields. It is shown how the latter can be used to alter both structural as well as electronic properties of these systems.

Unitary Transformations in the Quantum Model for Conceptual Conjunctions and Its Application to Data Representation

PubMed Central

Veloz, Tomas; Desjardins, Sylvie

2015-01-01

Quantum models of concept combinations have been successful in representing various experimental situations that cannot be accommodated by traditional models based on classical probability or fuzzy set theory. In many cases, the focus has been on producing a representation that fits experimental results to validate quantum models. However, these representations are not always consistent with the cognitive modeling principles. Moreover, some important issues related to the representation of concepts such as the dimensionality of the realization space, the uniqueness of solutions, and the compatibility of measurements, have been overlooked. In this paper, we provide a dimensional analysis of the realization space for the two-sector Fock space model for conjunction of concepts focusing on the first and second sectors separately. We then introduce various representation of concepts that arise from the use of unitary operators in the realization space. In these concrete representations, a pair of concepts and their combination are modeled by a single conceptual state, and by a collection of exemplar-dependent operators. Therefore, they are consistent with cognitive modeling principles. This framework not only provides a uniform approach to model an entire data set, but, because all measurement operators are expressed in the same basis, allows us to address the question of compatibility of measurements. In particular, we present evidence that it may be possible to predict non-commutative effects from partial measurements of conceptual combinations. PMID:26617556

Unitary Transformations in the Quantum Model for Conceptual Conjunctions and Its Application to Data Representation.

PubMed

Veloz, Tomas; Desjardins, Sylvie

2015-01-01

Quantum models of concept combinations have been successful in representing various experimental situations that cannot be accommodated by traditional models based on classical probability or fuzzy set theory. In many cases, the focus has been on producing a representation that fits experimental results to validate quantum models. However, these representations are not always consistent with the cognitive modeling principles. Moreover, some important issues related to the representation of concepts such as the dimensionality of the realization space, the uniqueness of solutions, and the compatibility of measurements, have been overlooked. In this paper, we provide a dimensional analysis of the realization space for the two-sector Fock space model for conjunction of concepts focusing on the first and second sectors separately. We then introduce various representation of concepts that arise from the use of unitary operators in the realization space. In these concrete representations, a pair of concepts and their combination are modeled by a single conceptual state, and by a collection of exemplar-dependent operators. Therefore, they are consistent with cognitive modeling principles. This framework not only provides a uniform approach to model an entire data set, but, because all measurement operators are expressed in the same basis, allows us to address the question of compatibility of measurements. In particular, we present evidence that it may be possible to predict non-commutative effects from partial measurements of conceptual combinations.

A coherent discrete variable representation method on a sphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Hua -Gen

Here, the coherent discrete variable representation (ZDVR) has been extended for construct- ing a multidimensional potential-optimized DVR basis on a sphere. In order to deal with the non-constant Jacobian in spherical angles, two direct product primitive basis methods are proposed so that the original ZDVR technique can be properly implemented. The method has been demonstrated by computing the lowest states of a two dimensional (2D) vibrational model. Results show that the extended ZDVR method gives accurate eigenval- ues and exponential convergence with increasing ZDVR basis size.

A coherent discrete variable representation method on a sphere

DOE PAGES

Yu, Hua -Gen

2017-09-05

Here, the coherent discrete variable representation (ZDVR) has been extended for construct- ing a multidimensional potential-optimized DVR basis on a sphere. In order to deal with the non-constant Jacobian in spherical angles, two direct product primitive basis methods are proposed so that the original ZDVR technique can be properly implemented. The method has been demonstrated by computing the lowest states of a two dimensional (2D) vibrational model. Results show that the extended ZDVR method gives accurate eigenval- ues and exponential convergence with increasing ZDVR basis size.

Importance of dispersion and electron correlation in ab initio protein folding.

PubMed

He, Xiao; Fusti-Molnar, Laszlo; Cui, Guanglei; Merz, Kenneth M

2009-04-16

Dispersion is well-known to be important in biological systems, but the effect of electron correlation in such systems remains unclear. In order to assess the relationship between the structure of a protein and its electron correlation energy, we employed both full system Hartree-Fock (HF) and second-order Møller-Plesset perturbation (MP2) calculations in conjunction with the Polarizable Continuum Model (PCM) on the native structures of two proteins and their corresponding computer-generated decoy sets. Because of the expense of the MP2 calculation, we have utilized the fragment molecular orbital method (FMO) in this study. We show that the sum of the Hartree-Fock (HF) energy and force field (LJ6)-derived dispersion energy (HF + LJ6) is well correlated with the energies obtained using second-order Møller-Plesset perturbation (MP2) theory. In one of the two examples studied, the correlation energy as well as the empirical dispersive energy term was able to discriminate between native and decoy structures. On the other hand, for the second protein we studied, neither the correlation energy nor dispersion energy showed discrimination capabilities; however, the ab initio MP2 energy and the HF+LJ6 both ranked the native structure correctly. Furthermore, when we randomly scrambled the Lennard-Jones parameters, the correlation between the MP2 energy and the sum of the HF energy and dispersive energy (HF+LJ6) significantly drops, which indicates that the choice of Lennard-Jones parameters is important.

Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakata, Hiroya, E-mail: nakata.h.ab@m.titech.ac.jp; RIKEN, Research Cluster for Innovation, Nakamura Lab, 2-1 Hirosawa, Wako, Saitama 351-0198; Japan Society for the Promotion of Science, Kojimachi Business Center Building, 5-3-1 Kojimachi, Chiyoda-ku, Tokyo 102-0083

2015-03-28

Analytic second derivatives of the energy with respect to nuclear coordinates have been developed for spin restricted density functional theory (DFT) based on the fragment molecular orbital method (FMO). The derivations were carried out for the three-body expansion (FMO3), and the two-body expressions can be obtained by neglecting the three-body corrections. Also, the restricted Hartree-Fock (RHF) Hessian for FMO3 can be obtained by neglecting the density-functional related terms. In both the FMO-RHF and FMO-DFT Hessians, certain terms with small magnitudes are neglected for computational efficiency. The accuracy of the FMO-DFT Hessian in terms of the Gibbs free energy is evaluatedmore » for a set of polypeptides and water clusters and found to be within 1 kcal/mol of the corresponding full (non-fragmented) ab initio calculation. The FMO-DFT method is also applied to transition states in S{sub N}2 reactions and for the computation of the IR and Raman spectra of a small Trp-cage protein (PDB: 1L2Y). Some computational timing analysis is also presented.« less

A second-order unconstrained optimization method for canonical-ensemble density-functional methods

NASA Astrophysics Data System (ADS)

Nygaard, Cecilie R.; Olsen, Jeppe

2013-03-01

A second order converging method of ensemble optimization (SOEO) in the framework of Kohn-Sham Density-Functional Theory is presented, where the energy is minimized with respect to an ensemble density matrix. It is general in the sense that the number of fractionally occupied orbitals is not predefined, but rather it is optimized by the algorithm. SOEO is a second order Newton-Raphson method of optimization, where both the form of the orbitals and the occupation numbers are optimized simultaneously. To keep the occupation numbers between zero and two, a set of occupation angles is defined, from which the occupation numbers are expressed as trigonometric functions. The total number of electrons is controlled by a built-in second order restriction of the Newton-Raphson equations, which can be deactivated in the case of a grand-canonical ensemble (where the total number of electrons is allowed to change). To test the optimization method, dissociation curves for diatomic carbon are produced using different functionals for the exchange-correlation energy. These curves show that SOEO favors symmetry broken pure-state solutions when using functionals with exact exchange such as Hartree-Fock and Becke three-parameter Lee-Yang-Parr. This is explained by an unphysical contribution to the exact exchange energy from interactions between fractional occupations. For functionals without exact exchange, such as local density approximation or Becke Lee-Yang-Parr, ensemble solutions are favored at interatomic distances larger than the equilibrium distance. Calculations on the chromium dimer are also discussed. They show that SOEO is able to converge to ensemble solutions for systems that are more complicated than diatomic carbon.

β -decay scheme of 140Te to I 140 : Suppression of Gamow-Teller transitions between the neutron h9 /2 and proton h11 /2 partner orbitals

NASA Astrophysics Data System (ADS)

Moon, B.; Moon, C.-B.; Odahara, A.; Lozeva, R.; Söderström, P.-A.; Browne, F.; Yuan, C.; Yagi, A.; Hong, B.; Jung, H. S.; Lee, P.; Lee, C. S.; Nishimura, S.; Doornenbal, P.; Lorusso, G.; Sumikama, T.; Watanabe, H.; Kojouharov, I.; Isobe, T.; Baba, H.; Sakurai, H.; Daido, R.; Fang, Y.; Nishibata, H.; Patel, Z.; Rice, S.; Sinclair, L.; Wu, J.; Xu, Z. Y.; Yokoyama, R.; Kubo, T.; Inabe, N.; Suzuki, H.; Fukuda, N.; Kameda, D.; Takeda, H.; Ahn, D. S.; Shimizu, Y.; Murai, D.; Bello Garrote, F. L.; Daugas, J. M.; Didierjean, F.; Ideguchi, E.; Ishigaki, T.; Morimoto, S.; Niikura, M.; Nishizuka, I.; Komatsubara, T.; Kwon, Y. K.; Tshoo, K.

2017-07-01

We report for the first time the β -decay scheme of 140Te (Z =52 ) to 140I (Z =53 ), with a specific focus on the Gamow-Teller strength along N =87 isotones. These results were obtained in an experiment performed at the Radioactive Ion Beam Factory (RIBF), RIKEN, where the parent nuclide, 140Te, was produced through the in-flight fission of a 238U beam at 345 MeV per nucleon impinging on a 9Be target. Based on data from the high-efficiency γ -ray spectrometer, EUROBALL-RIKEN Cluster Array (EURICA), we constructed a decay scheme of 140I. The half-life of 140Te has been determined to be 350(5) ms. A level at 926 keV has been assigned as a (1+) state based on the logf t value of 4.89(6). This (1+) state, commonly observed in odd-odd nuclei, can be interpreted in terms of the π h11 /2ν h9 /2 configuration formed by the Gamow-Teller transition between a neutron in the h9 /2 orbital and a proton in the h11 /2 orbital. We observe a sharp contrast to this type of β -decay branching to the lower-lying 1+ states between 140I and 136I, where we see a large reduction as the number of neutrons increases. This is in contrast to the prediction by large-scale shell model calculations. To investigate this type of the suppression, results of the Nilsson model calculations will be discussed. Along the isotones with N =87 , we discuss a characteristic feature of the Gamow-Teller distributions at 1+ states with respect to the isospin difference.

σ-SCF: A direct energy-targeting method to mean-field excited states

NASA Astrophysics Data System (ADS)

Ye, Hong-Zhou; Welborn, Matthew; Ricke, Nathan D.; Van Voorhis, Troy

2017-12-01

The mean-field solutions of electronic excited states are much less accessible than ground state (e.g., Hartree-Fock) solutions. Energy-based optimization methods for excited states, like Δ-SCF (self-consistent field), tend to fall into the lowest solution consistent with a given symmetry—a problem known as "variational collapse." In this work, we combine the ideas of direct energy-targeting and variance-based optimization in order to describe excited states at the mean-field level. The resulting method, σ-SCF, has several advantages. First, it allows one to target any desired excited state by specifying a single parameter: a guess of the energy of that state. It can therefore, in principle, find all excited states. Second, it avoids variational collapse by using a variance-based, unconstrained local minimization. As a consequence, all states—ground or excited—are treated on an equal footing. Third, it provides an alternate approach to locate Δ-SCF solutions that are otherwise hardly accessible by the usual non-aufbau configuration initial guess. We present results for this new method for small atoms (He, Be) and molecules (H2, HF). We find that σ-SCF is very effective at locating excited states, including individual, high energy excitations within a dense manifold of excited states. Like all single determinant methods, σ-SCF shows prominent spin-symmetry breaking for open shell states and our results suggest that this method could be further improved with spin projection.

σ-SCF: A direct energy-targeting method to mean-field excited states.

PubMed

Ye, Hong-Zhou; Welborn, Matthew; Ricke, Nathan D; Van Voorhis, Troy

2017-12-07

The mean-field solutions of electronic excited states are much less accessible than ground state (e.g., Hartree-Fock) solutions. Energy-based optimization methods for excited states, like Δ-SCF (self-consistent field), tend to fall into the lowest solution consistent with a given symmetry-a problem known as "variational collapse." In this work, we combine the ideas of direct energy-targeting and variance-based optimization in order to describe excited states at the mean-field level. The resulting method, σ-SCF, has several advantages. First, it allows one to target any desired excited state by specifying a single parameter: a guess of the energy of that state. It can therefore, in principle, find all excited states. Second, it avoids variational collapse by using a variance-based, unconstrained local minimization. As a consequence, all states-ground or excited-are treated on an equal footing. Third, it provides an alternate approach to locate Δ-SCF solutions that are otherwise hardly accessible by the usual non-aufbau configuration initial guess. We present results for this new method for small atoms (He, Be) and molecules (H 2 , HF). We find that σ-SCF is very effective at locating excited states, including individual, high energy excitations within a dense manifold of excited states. Like all single determinant methods, σ-SCF shows prominent spin-symmetry breaking for open shell states and our results suggest that this method could be further improved with spin projection.

Communication: Relativistic Fock-space coupled cluster study of small building blocks of larger uranium complexes.

PubMed

Tecmer, Paweł; Gomes, André Severo Pereira; Knecht, Stefan; Visscher, Lucas

2014-07-28

We present a study of the electronic structure of the [UO2](+), [UO2](2 +), [UO2](3 +), NUO, [NUO](+), [NUO](2 +), [NUN](-), NUN, and [NUN](+) molecules with the intermediate Hamiltonian Fock-space coupled cluster method. The accuracy of mean-field approaches based on the eXact-2-Component Hamiltonian to incorporate spin-orbit coupling and Gaunt interactions are compared to results obtained with the Dirac-Coulomb Hamiltonian. Furthermore, we assess the reliability of calculations employing approximate density functionals in describing electronic spectra and quantities useful in rationalizing Uranium (VI) species reactivity (hardness, electronegativity, and electrophilicity).

Communication: Relativistic Fock-space coupled cluster study of small building blocks of larger uranium complexes

NASA Astrophysics Data System (ADS)

Tecmer, Paweł; Severo Pereira Gomes, André; Knecht, Stefan; Visscher, Lucas

2014-07-01

We present a study of the electronic structure of the [UO2]+, [UO2]2 +, [UO2]3 +, NUO, [NUO]+, [NUO]2 +, [NUN]-, NUN, and [NUN]+ molecules with the intermediate Hamiltonian Fock-space coupled cluster method. The accuracy of mean-field approaches based on the eXact-2-Component Hamiltonian to incorporate spin-orbit coupling and Gaunt interactions are compared to results obtained with the Dirac-Coulomb Hamiltonian. Furthermore, we assess the reliability of calculations employing approximate density functionals in describing electronic spectra and quantities useful in rationalizing Uranium (VI) species reactivity (hardness, electronegativity, and electrophilicity).

Two-photon excitation cross section in light and intermediate atoms in frozen-core LS-coupling approximation

NASA Technical Reports Server (NTRS)

Omidvar, K.

1980-01-01

Using the method of explicit summation over the intermediate states two-photon absorption cross sections in light and intermediate atoms based on the simplistic frozen-core approximation and LS coupling have been formulated. Formulas for the cross section in terms of integrals over radial wave functions are given. Two selection rules, one exact and one approximate, valid within the stated approximations are derived. The formulas are applied to two-photon absorptions in nitrogen, oxygen, and chlorine. In evaluating the radial integrals, for low-lying levels, the Hartree-Fock wave functions, and for high-lying levels, hydrogenic wave functions obtained by the quantum-defect method have been used. A relationship between the cross section and the oscillator strengths is derived.

Natural chemical shielding analysis of nuclear magnetic resonance shielding tensors from gauge-including atomic orbital calculations

NASA Astrophysics Data System (ADS)

Bohmann, Jonathan A.; Weinhold, Frank; Farrar, Thomas C.

1997-07-01

Nuclear magnetic shielding tensors computed by the gauge including atomic orbital (GIAO) method in the Hartree-Fock self-consistent-field (HF-SCF) framework are partitioned into magnetic contributions from chemical bonds and lone pairs by means of natural chemical shielding (NCS) analysis, an extension of natural bond orbital (NBO) analysis. NCS analysis complements the description provided by alternative localized orbital methods by directly calculating chemical shieldings due to delocalized features in the electronic structure, such as bond conjugation and hyperconjugation. Examples of NCS tensor decomposition are reported for CH4, CO, and H2CO, for which a graphical mnemonic due to Cornwell is used to illustrate the effect of hyperconjugative delocalization on the carbon shielding.

Accelerating molecular property calculations with nonorthonormal Krylov space methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Furche, Filipp; Krull, Brandon T.; Nguyen, Brian D.

Here, we formulate Krylov space methods for large eigenvalue problems and linear equation systems that take advantage of decreasing residual norms to reduce the cost of matrix-vector multiplication. The residuals are used as subspace basis without prior orthonormalization, which leads to generalized eigenvalue problems or linear equation systems on the Krylov space. These nonorthonormal Krylov space (nKs) algorithms are favorable for large matrices with irregular sparsity patterns whose elements are computed on the fly, because fewer operations are necessary as the residual norm decreases as compared to the conventional method, while errors in the desired eigenpairs and solution vectors remainmore » small. We consider real symmetric and symplectic eigenvalue problems as well as linear equation systems and Sylvester equations as they appear in configuration interaction and response theory. The nKs method can be implemented in existing electronic structure codes with minor modifications and yields speed-ups of 1.2-1.8 in typical time-dependent Hartree-Fock and density functional applications without accuracy loss. The algorithm can compute entire linear subspaces simultaneously which benefits electronic spectra and force constant calculations requiring many eigenpairs or solution vectors. The nKs approach is related to difference density methods in electronic ground state calculations, and particularly efficient for integral direct computations of exchange-type contractions. By combination with resolution-of-the-identity methods for Coulomb contractions, three- to fivefold speed-ups of hybrid time-dependent density functional excited state and response calculations are achieved.« less

Accelerating molecular property calculations with nonorthonormal Krylov space methods

DOE PAGES

Furche, Filipp; Krull, Brandon T.; Nguyen, Brian D.; ...

2016-05-03

Here, we formulate Krylov space methods for large eigenvalue problems and linear equation systems that take advantage of decreasing residual norms to reduce the cost of matrix-vector multiplication. The residuals are used as subspace basis without prior orthonormalization, which leads to generalized eigenvalue problems or linear equation systems on the Krylov space. These nonorthonormal Krylov space (nKs) algorithms are favorable for large matrices with irregular sparsity patterns whose elements are computed on the fly, because fewer operations are necessary as the residual norm decreases as compared to the conventional method, while errors in the desired eigenpairs and solution vectors remainmore » small. We consider real symmetric and symplectic eigenvalue problems as well as linear equation systems and Sylvester equations as they appear in configuration interaction and response theory. The nKs method can be implemented in existing electronic structure codes with minor modifications and yields speed-ups of 1.2-1.8 in typical time-dependent Hartree-Fock and density functional applications without accuracy loss. The algorithm can compute entire linear subspaces simultaneously which benefits electronic spectra and force constant calculations requiring many eigenpairs or solution vectors. The nKs approach is related to difference density methods in electronic ground state calculations, and particularly efficient for integral direct computations of exchange-type contractions. By combination with resolution-of-the-identity methods for Coulomb contractions, three- to fivefold speed-ups of hybrid time-dependent density functional excited state and response calculations are achieved.« less

Vibrational spectrum and assignments of 2-(4-methoxyphenyl)-1 H-benzo[ d]imidazole by ab initio Hartree-Fock and density functional methods

NASA Astrophysics Data System (ADS)

Arslan, Hakan; Algül, Öztekin

2008-06-01

The room temperature attenuated total reflection Fourier transform infrared spectrum of the 2-(4-methoxyphenyl)-1 H-benzo[ d]imidazole has been recorded with diamond/ZnSe prism. The conformational behaviour, structural stability of optimized geometry, frequency and intensity of the vibrational bands of the title compound were investigated by utilizing ab initio calculations with 6-311G** basis set at HF, B3LYP, BLYP, B3PW91 and mPW1PW91 levels. The harmonic vibrational frequencies were calculated and scaled values have been compared with experimental IR spectrum. The observed and the calculated frequencies are found to be in good agreement. The theoretical vibrational spectra of the title compound were interpreted by means of potential energy distributions using VEDA 4 program. Furthermore, the optimal uniform scaling factors calculated for the title compound are 0.9120, 0.9596, 0.9660, 0.9699, and 0.9993 for HF, mPW1PW91, B3PW91, B3LYP and BLYP methods, respectively.

Standard model of knowledge representation

NASA Astrophysics Data System (ADS)

Yin, Wensheng

2016-09-01

Knowledge representation is the core of artificial intelligence research. Knowledge representation methods include predicate logic, semantic network, computer programming language, database, mathematical model, graphics language, natural language, etc. To establish the intrinsic link between various knowledge representation methods, a unified knowledge representation model is necessary. According to ontology, system theory, and control theory, a standard model of knowledge representation that reflects the change of the objective world is proposed. The model is composed of input, processing, and output. This knowledge representation method is not a contradiction to the traditional knowledge representation method. It can express knowledge in terms of multivariate and multidimensional. It can also express process knowledge, and at the same time, it has a strong ability to solve problems. In addition, the standard model of knowledge representation provides a way to solve problems of non-precision and inconsistent knowledge.

Isoscalar neutron-proton pairing and SU(4)-symmetry breaking in Gamow-Teller transitions

NASA Astrophysics Data System (ADS)

Kaneko, K.; Sun, Y.; Mizusaki, T.

2018-05-01

The isoscalar neutron-proton pairing is thought to be important for nuclei with equal number of protons and neutrons but its manifestation in structure properties remains to be understood. We investigate the Gamow-Teller (GT) transitions for the f7 /2-shell nuclei in large-scale shell-model calculations with the realistic Hamiltonian. We show that the isoscalar T =0 ,Jπ=1+ neutron-proton pairing interaction plays a decisive role for the concentration of GT strengths at the first-excited 11+ state in 42Sc, and that the suppression of these strengths in 46V, 50Mn, and 54Co is mainly caused by the spin-orbit force supplemented by the quadrupole-quadrupole interaction. Based on the good reproduction of the charge-exchange reaction data, we further analyze the interplay between the isoscalar and isovector pairing correlations. We conclude that even for the most promising A =42 nuclei where the SU(4) isoscalar-isovector-pairing symmetry is less broken, the probability of forming an isoscalar neutron-proton pairing condensation is less than 60% as compared to the expectation at the SU(4)-symmetry limit.

Dynamical description of the fission process using the TD-BCS theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scamps, Guillaume, E-mail: scamps@nucl.phys.tohoku.ac.jp; Simenel, Cédric; Lacroix, Denis

2015-10-15

The description of fission remains a challenge for nuclear microscopic theories. The time-dependent Hartree-Fock approach with BCS pairing is applied to study the last stage of the fission process. A good agreement is found for the one-body observables: the total kinetic energy and the average mass asymmetry. The non-physical dependence of two-body observables with the initial shape is discussed.

The energy gap in a-Si 1 - xC g: H alloys

NASA Astrophysics Data System (ADS)

Valladares, Ariel A.; Valladares, Alexander; Enrique Sansores, L.; Nelis, Mary Ann Me

1997-02-01

The electronic structure of amorphous tetrahedral clusters of the type a-Si 1 - xC g: H are studied using the pseudopotential SCF Hartree-Fock approximation. The reduced energy gap isgiven by Egr( x) - 1 + 0.84 x for x ⩽ 0.5, whereas experimentally Egr( x) = 1 + 0.96 x. For x ⩾ 0.5 the dip in the gap value reported experimentally is verified.

Orthogonal polynomials, Laguerre Fock space, and quasi-classical asymptotics

NASA Astrophysics Data System (ADS)

Engliš, Miroslav; Ali, S. Twareque

2015-07-01

Continuing our earlier investigation of the Hermite case [S. T. Ali and M. Engliš, J. Math. Phys. 55, 042102 (2014)], we study an unorthodox variant of the Berezin-Toeplitz quantization scheme associated with Laguerre polynomials. In particular, we describe a "Laguerre analogue" of the classical Fock (Segal-Bargmann) space and the relevant semi-classical asymptotics of its Toeplitz operators; the former actually turns out to coincide with the Hilbert space appearing in the construction of the well-known Barut-Girardello coherent states. Further extension to the case of Legendre polynomials is likewise discussed.

The nature of excess electrons in anatase and rutile from hybrid DFT and RPA.

PubMed

Spreafico, Clelia; VandeVondele, Joost

2014-12-21

The behavior of excess electrons in undoped and defect free bulk anatase and rutile TiO2 has been investigated by state-of-the-art electronic structure methods including hybrid density functional theory (DFT) and the random phase approximation (RPA). Consistent with experiment, charge trapping and polaron formation is observed in both anatase and rutile. The difference in the anisotropic shape of the polarons is characterized, confirming for anatase the large polaron picture. For anatase, where polaron formation energies are small, charge trapping is observed also with standard hybrid functionals, provided the simulation cell is sufficiently large (864 atoms) to accommodate the lattice relaxation. Even though hybrid orbitals are required as a starting point for RPA in this system, the obtained polaron formation energies are relatively insensitive to the amount of Hartree-Fock exchange employed. The difference in trapping energy between rutile and anatase can be obtained accurately with both hybrid functionals and RPA. Computed activation energies for polaron hopping and delocalization clearly show that anatase and rutile might have different charge transport mechanisms. In rutile, only hopping is likely, whereas in anatase hopping and delocalization are competing. Delocalization will result in conduction-band-like and thus enhanced transport. Anisotropic conduction, in agreement with experimental data, is observed, and results from the tendency to delocalize in the [001] direction in rutile and the (001) plane in anatase. For future work, our calculations serve as a benchmark and suggest RPA on top on hybrid orbitals (PBE0 with 30% Hartree-Fock exchange), as a suitable method to study the rich chemistry and physics of TiO2.

A Comparison of Quantum and Molecular Mechanical Methods to Estimate Strain Energy in Druglike Fragments.

PubMed

Sellers, Benjamin D; James, Natalie C; Gobbi, Alberto

2017-06-26

Reducing internal strain energy in small molecules is critical for designing potent drugs. Quantum mechanical (QM) and molecular mechanical (MM) methods are often used to estimate these energies. In an effort to determine which methods offer an optimal balance in accuracy and performance, we have carried out torsion scan analyses on 62 fragments. We compared nine QM and four MM methods to reference energies calculated at a higher level of theory: CCSD(T)/CBS single point energies (coupled cluster with single, double, and perturbative triple excitations at the complete basis set limit) calculated on optimized geometries using MP2/6-311+G**. The results show that both the more recent MP2.X perturbation method as well as MP2/CBS perform quite well. In addition, combining a Hartree-Fock geometry optimization with a MP2/CBS single point energy calculation offers a fast and accurate compromise when dispersion is not a key energy component. Among MM methods, the OPLS3 force field accurately reproduces CCSD(T)/CBS torsion energies on more test cases than the MMFF94s or Amber12:EHT force fields, which struggle with aryl-amide and aryl-aryl torsions. Using experimental conformations from the Cambridge Structural Database, we highlight three example structures for which OPLS3 significantly overestimates the strain. The energies and conformations presented should enable scientists to estimate the expected error for the methods described and we hope will spur further research into QM and MM methods.

An ab-initio study of the relative stability of the ggg and the gtg conformer in hexane

NASA Astrophysics Data System (ADS)

Koglin, Eckhard; Meier, Robert J.

1999-10-01

Earlier ab-initio work suggested, on the basis of MP2 level calculations, that the hexane ggg conformer is more stable than the gtg conformer. Because this is unexpected and if true might have a significant impact on force field parametrisations, we have applied Hartree-Fock and post-HF methods to evaluate the relative stability of these conformers. We find that at levels higher than MP2 the gtg conformer is more stable than the ggg conformer, in agreement with the conventional idea that each additional gauche bond causes a further decrease in stability of the conformer. DFT methods were also applied, but although DFT methods including gradient corrections show correct qualitative behaviour, quantitatively the relative energies are far off compared to the post-HF results.

Explicit polarization (X-Pol) potential using ab initio molecular orbital theory and density functional theory.

PubMed

Song, Lingchun; Han, Jaebeom; Lin, Yen-lin; Xie, Wangshen; Gao, Jiali

2009-10-29

The explicit polarization (X-Pol) method has been examined using ab initio molecular orbital theory and density functional theory. The X-Pol potential was designed to provide a novel theoretical framework for developing next-generation force fields for biomolecular simulations. Importantly, the X-Pol potential is a general method, which can be employed with any level of electronic structure theory. The present study illustrates the implementation of the X-Pol method using ab initio Hartree-Fock theory and hybrid density functional theory. The computational results are illustrated by considering a set of bimolecular complexes of small organic molecules and ions with water. The computed interaction energies and hydrogen bond geometries are in good accord with CCSD(T) calculations and B3LYP/aug-cc-pVDZ optimizations.

A new scheme for perturbative triples correction to (0,1) sector of Fock space multi-reference coupled cluster method: theory, implementation, and examples.

PubMed

Dutta, Achintya Kumar; Vaval, Nayana; Pal, Sourav

2015-01-28

We propose a new elegant strategy to implement third order triples correction in the light of many-body perturbation theory to the Fock space multi-reference coupled cluster method for the ionization problem. The computational scaling as well as the storage requirement is of key concerns in any many-body calculations. Our proposed approach scales as N(6) does not require the storage of triples amplitudes and gives superior agreement over all the previous attempts made. This approach is capable of calculating multiple roots in a single calculation in contrast to the inclusion of perturbative triples in the equation of motion variant of the coupled cluster theory, where each root needs to be computed in a state-specific way and requires both the left and right state vectors together. The performance of the newly implemented scheme is tested by applying to methylene, boron nitride (B2N) anion, nitrogen, water, carbon monoxide, acetylene, formaldehyde, and thymine monomer, a DNA base.

Landau levels from neutral Bogoliubov particles in two-dimensional nodal superconductors under strain and doping gradients

NASA Astrophysics Data System (ADS)

Nica, Emilian M.; Franz, Marcel

2018-02-01

Motivated by recent work on strain-induced pseudomagnetic fields in Dirac and Weyl semimetals, we analyze the possibility of analogous fields in two-dimensional nodal superconductors. We consider the prototypical case of a d -wave superconductor, a representative of the cuprate family, and find that the presence of weak, spatially varying strain leads to pseudomagnetic fields and Landau quantization of Bogoliubov quasiparticles in the low-energy sector. A similar effect is induced by the presence of generic, weak doping gradients. In contrast to genuine magnetic fields in superconductors, the strain- and doping-gradient-induced pseudomagnetic fields couple in a way that preserves time-reversal symmetry and is not subject to the screening associated with the Meissner effect. These effects can be probed by tuning weak applied supercurrents which lead to shifts in the energies of the Landau levels and hence to quantum oscillations in thermodynamic and transport quantities.

Limit behavior of mass critical Hartree minimization problems with steep potential wells

NASA Astrophysics Data System (ADS)

Guo, Yujin; Luo, Yong; Wang, Zhi-Qiang

2018-06-01

We consider minimizers of the following mass critical Hartree minimization problem: eλ(N ) ≔inf {u ∈H1(Rd ) , ‖u‖2 2=N } Eλ(u ) , where d ≥ 3, λ > 0, and the Hartree energy functional Eλ(u) is defined by Eλ(u ) ≔∫Rd|∇u (x ) |2d x +λ ∫Rdg (x ) u2(x ) d x -1/2 ∫Rd∫Rdu/2(x ) u2(y ) |x -y |2 d x d y . Here the steep potential g(x) satisfies 0 =g (0 ) =infRdg (x ) ≤g (x ) ≤1 and 1 -g (x ) ∈Ld/2(Rd ) . We prove that there exists a constant N* > 0, independent of λg(x), such that if N ≥ N*, then eλ(N) does not admit minimizers for any λ > 0; if 0 < N < N*, then there exists a constant λ*(N) > 0 such that eλ(N) admits minimizers for any λ > λ*(N) and eλ(N) does not admit minimizers for 0 < λ < λ*(N). For any given 0 < N < N*, the limit behavior of positive minimizers for eλ(N) is also studied as λ → ∞, where the mass concentrates at the bottom of g(x).

Ab initio quantum chemical study of electron transfer in carboranes

NASA Astrophysics Data System (ADS)

Pati, Ranjit; Pineda, Andrew C.; Pandey, Ravindra; Karna, Shashi P.

2005-05-01

The electron transfer (ET) properties of 10- and 12-vertex carboranes are investigated by the ab initio Hartree-Fock method within the Marcus-Hush (MH) two-state model and the Koopman theorem (KT) approach. The calculated value of the ET coupling matrix element, VAB, is consistently higher in the KT approach than in the MH two-state model. For the carborane molecules functionalized by -CH 2 groups at C-vertices, VAB strongly depends on the relative orientation of the planes containing the terminal -CH 2 groups. The predicted conformation dependence of VAB offers a molecular mechanism to control ET between two active centers in molecular systems.

Non-expanded dispersion and induction energies, and damping functions, for molecular interactions with application to HF-He

NASA Astrophysics Data System (ADS)

Knowles, Peter J.; Meath, William J.

The evaluation of second order non-expanded dispersion and induction energies, and the associated damping functions, for interactions involving molecules is discussed with emphasis placed on using the time-dependent coupled Hartree-Fock method. Results are given for the HF-He interaction for all individual partial wave non-expanded dispersion and induction energies varying asymptotically for large R through O(R-8) and O(R-10) respectively and for most of the individual dispersion energies varying as R-9 and R-10. They are used to illustrate various features of charge overlap effects and the damping functions for molecular interactions, which are considerably more complicated than for atom-atom interactions.

The self-trapping transition in the non-half-filled strongly correlated extended Holstein-Hubbard model in two-dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sankar, I. V., E-mail: ivshankar27@gmail.com; Chatterjee, Ashok, E-mail: ivshankar27@gmail.com

2014-04-24

The two-dimensional extended Holstein-Hubbard model (EHH) has been considered at strong correlation regime in the non-half-filled band case to understand the self-trapping transition of electrons in strongly correlated electron system. We have used the method of optimized canonical transformations to transform an EHH model into an effective extended Hubbard (EEH) model. In the strong on-site correlation limit an EH model can be transformed into a t-J model which is finally solved using Hartree-Fock approximation (HFA). We found that, for non-half-filled band case, the transition is abrupt in the adiabatic region whereas it is continuous in the anti-adiabatic region.

Imidazole derivatives as angiotensin II AT1 receptor blockers: Benchmarks, drug-like calculations and quantitative structure-activity relationships modeling

NASA Astrophysics Data System (ADS)

Alloui, Mebarka; Belaidi, Salah; Othmani, Hasna; Jaidane, Nejm-Eddine; Hochlaf, Majdi

2018-03-01

We performed benchmark studies on the molecular geometry, electron properties and vibrational analysis of imidazole using semi-empirical, density functional theory and post Hartree-Fock methods. These studies validated the use of AM1 for the treatment of larger systems. Then, we treated the structural, physical and chemical relationships for a series of imidazole derivatives acting as angiotensin II AT1 receptor blockers using AM1. QSAR studies were done for these imidazole derivatives using a combination of various physicochemical descriptors. A multiple linear regression procedure was used to design the relationships between molecular descriptor and the activity of imidazole derivatives. Results validate the derived QSAR model.

Equation of state for nucleonic matter and its quark mass dependence from the nuclear force in lattice QCD.

PubMed

Inoue, Takashi; Aoki, Sinya; Doi, Takumi; Hatsuda, Tetsuo; Ikeda, Yoichi; Ishii, Noriyoshi; Murano, Keiko; Nemura, Hidekatsu; Sasaki, Kenji

2013-09-13

Quark mass dependence of the equation of state (EOS) for nucleonic matter is investigated, on the basis of the Brueckner-Hartree-Fock method with the nucleon-nucleon interaction extracted from lattice QCD simulations. We observe saturation of nuclear matter at the lightest available quark mass corresponding to the pseudoscalar meson mass ≃469  MeV. Mass-radius relation of the neutron stars is also studied with the EOS for neutron-star matter from the same nuclear force in lattice QCD. We observe that the EOS becomes stiffer and thus the maximum mass of neutron star increases as the quark mass decreases toward the physical point.

Calculation of (P,T) -odd electric dipole moments for the diamagnetic atoms X129e , Y171b , H199g , R211n , and R225a

NASA Astrophysics Data System (ADS)

Dzuba, V. A.; Flambaum, V. V.; Porsev, S. G.

2009-09-01

Electric dipole moments of diamagnetic atoms of experimental interest are calculated using the relativistic Hartree-Fock and random-phase approximation methods, the many-body perturbation theory, and the configuration-interaction technique. We consider (P,T) -odd interactions, which give rise to atomic electric dipole moment in the second order of the perturbation theory. These include nuclear Schiff moment, (P,T) -odd electron-nucleon interaction, and electron electric dipole moment. Interpretation of an experimental constraint of a permanent electric dipole moment of H199g [W. C. Griffith, M. D. Swallows, T. H. Loftus, M. V. Romalis, B. R. Heckel, and E. N. Fortson, Phys. Rev. Lett. 102, 101601 (2009)] is discussed.

Theoretical studies of large water clusters: (H2O)28, (H2O)29, (H2O)30, and (H2O)31 hexakaidecahedral structures

NASA Astrophysics Data System (ADS)

Khan, Arshad

1997-04-01

The 28, 29, 30, and 31 mer hexakaidecahedral water clusters were studied by applying the intermediate neglect of differential overlap self-consistent field restricted Hartree-Fock method (INDO SCF RHF) after parametrization for H and O atoms. The most stable 29 and 30 mer clusters have one and two water molecules, respectively within the cavity of the distorted hexakaidecahedral cage with stabilization energy/monomer values of around 10.9 and 11.0 kcal, respectively. The 31 mer cluster with three water molecules within the cavity is less stable than the isomer with two molecules within the cavity and the third one bonded outside of the cage by around 3 kcal/mol.

Structure and Electronic Properties of Nano-complex CCl4…Cr(AcacCl)3 on Evidence Derived from Vibrational Spectroscopy

NASA Astrophysics Data System (ADS)

Slabzhennikov, S. N.; Kuarton, L. A.; Ryabchenko, O. B.

In order to specify influence of intermolecular interaction on IR spectrum of interacting species, an investigation of a process CCl4 + Cr(AcacCl)3 → CCl4…Cr(AcacCl)3 has been performed by means of Hartree-Fock-Roothaan method in MIDI basis set with p- and d- polarization functions. An estimation of intermolecular interaction in geometrical parameters, electron density function both between interacting particles and inside themselves, frequencies and intensities of normal modes has been carried out. Chemical bonds with the most significant shifts of characteristics under formation of nano-complex CCl4…Cr(AcacCl)3 have been noted.

Microwave spectrum and structure of bicyclo /1.1.1/ pentanone and comparison with several theoretical structures

NASA Technical Reports Server (NTRS)

Mcrae, Glenn A.; Cohen, Edward A.; Sponsler, Michael B.; Dougherty, Dennis A.

1986-01-01

The microwave spectra of five isotopic species of bicyclo (1.1.1) pentanone have been investigated. The rotational constants along with various centrifugal distortion constants for each species have been determined. From the rotational constants, a complete r(s) structure has been determined for the heavy atoms. Analysis of Stark effect measurements has shown the dipole moment to be along the a principal inertial axis with a magnitude of 3.164 (5) D. These results are compared with those obtained by four current theoretical methods: molecular mechanics (MM2), MNDO, and Hartree-Fock ab initio theory with STO-3G and 3-21G basis sets.

Extent of Fock-exchange mixing for a hybrid van der Waals density functional?

NASA Astrophysics Data System (ADS)

Jiao, Yang; Schröder, Elsebeth; Hyldgaard, Per

2018-05-01

The vdW-DF-cx0 exchange-correlation hybrid design [K. Berland et al., J. Chem. Phys. 146, 234106 (2017)] has a truly nonlocal correlation component and aims to facilitate concurrent descriptions of both covalent and non-covalent molecular interactions. The vdW-DF-cx0 design mixes a fixed ratio, a, of the Fock exchange into the consistent-exchange van der Waals density functional, vdW-DF-cx [K. Berland and P. Hyldgaard, Phys. Rev. B 89, 035412 (2014)]. The mixing value a is sometimes taken as a semi-empirical parameter in hybrid formulations. Here, instead, we assert a plausible optimum average a value for the vdW-DF-cx0 design from a formal analysis; A new, independent determination of the mixing a is necessary since the Becke fit [A. D. Becke, J. Chem. Phys. 98, 5648 (1993)], yielding a' = 0.2, is restricted to semilocal correlation and does not reflect non-covalent interactions. To proceed, we adapt the so-called two-legged hybrid construction [K. Burke et al., Chem. Phys. Lett. 265, 115 (1997)] to a starting point in the vdW-DF-cx functional. For our approach, termed vdW-DF-tlh, we estimate the properties of the adiabatic-connection specification of the exact exchange-correlation functional, by combining calculations of the Fock exchange and of the coupling-constant variation in vdW-DF-cx. We find that such vdW-DF-tlh hybrid constructions yield accurate characterizations of molecular interactions (even if they lack self-consistency). The accuracy motivates trust in the vdW-DF-tlh determination of system-specific values of the Fock-exchange mixing. We find that an average value a' = 0.2 best characterizes the vdW-DF-tlh description of covalent and non-covalent interactions, although there exists some scatter. This finding suggests that the original Becke value, a' = 0.2, also represents an optimal average Fock-exchange mixing for the new, truly nonlocal-correlation hybrids. To enable self-consistent calculations, we furthermore define and test a zero

Computational Investigation of the Geometrical and Electronic Structures of VGen-/0 (n = 1-4) Clusters by Density Functional Theory and Multiconfigurational CASSCF/CASPT2 Method.

PubMed

Tran, Van Tan; Nguyen, Minh Thao; Tran, Quoc Tri

2017-10-12

Density functional theory and the multiconfigurational CASSCF/CASPT2 method have been employed to study the low-lying states of VGe n -/0 (n = 1-4) clusters. For VGe -/0 and VGe 2 -/0 clusters, the relative energies and geometrical structures of the low-lying states are reported at the CASSCF/CASPT2 level. For the VGe 3 -/0 and VGe 4 -/0 clusters, the computational results show that due to the large contribution of the Hartree-Fock exact exchange, the hybrid B3LYP, B3PW91, and PBE0 functionals overestimate the energies of the high-spin states as compared to the pure GGA BP86 and PBE functionals and the CASPT2 method. On the basis of the pure GGA BP86 and PBE functionals and the CASSCF/CASPT2 results, the ground states of anionic and neutral clusters are defined, the relative energies of the excited states are computed, and the electron detachment energies of the anionic clusters are evaluated. The computational results are employed to give new assignments for all features in the photoelectron spectra of VGe 3 - and VGe 4 - clusters.

High dimensional model representation method for fuzzy structural dynamics

NASA Astrophysics Data System (ADS)

Adhikari, S.; Chowdhury, R.; Friswell, M. I.

2011-03-01

Uncertainty propagation in multi-parameter complex structures possess significant computational challenges. This paper investigates the possibility of using the High Dimensional Model Representation (HDMR) approach when uncertain system parameters are modeled using fuzzy variables. In particular, the application of HDMR is proposed for fuzzy finite element analysis of linear dynamical systems. The HDMR expansion is an efficient formulation for high-dimensional mapping in complex systems if the higher order variable correlations are weak, thereby permitting the input-output relationship behavior to be captured by the terms of low-order. The computational effort to determine the expansion functions using the α-cut method scales polynomically with the number of variables rather than exponentially. This logic is based on the fundamental assumption underlying the HDMR representation that only low-order correlations among the input variables are likely to have significant impacts upon the outputs for most high-dimensional complex systems. The proposed method is first illustrated for multi-parameter nonlinear mathematical test functions with fuzzy variables. The method is then integrated with a commercial finite element software (ADINA). Modal analysis of a simplified aircraft wing with fuzzy parameters has been used to illustrate the generality of the proposed approach. In the numerical examples, triangular membership functions have been used and the results have been validated against direct Monte Carlo simulations. It is shown that using the proposed HDMR approach, the number of finite element function calls can be reduced without significantly compromising the accuracy.

A calculation for radial expectation values of helium like actinide ions (Z=89-93)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ürer, G., E-mail: gurer@sakarya.edu.tr; Arslan, M., E-mail: murat.arslan4@ogr.sakarya.edu.tr; Balkaya, E., E-mail: eda.balkaya@ogr.sakarya.edu.tr

2016-03-25

Radial expectation values, , for helium like actinides (Z{sub Ac}=89, Z{sub Th}=90, Z{sub Pa}=91, Z{sub U}=92, and Z{sub Np}=93) are reported using the Multiconfiguration Hartree-Fock (MCHF) within the framework Breit-Pauli corrections. Atomic data as energy levels, wavelengths, weighted oscillator strengths, and transition probabilities for allowed and forbidden transitions need these calculations. The obtained results are compared available works.

Testing the single-state dominance hypothesis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Álvarez-Rodríguez, R.; Moreno, O.; Moya de Guerra, E.

2013-12-30

We present a theoretical analysis of the single-state dominance hypothesis for the two-neutrino double-beta decay process. The theoretical framework is a proton-neutron QRPA based on a deformed Hartree-Fock mean field with BCS pairing correlations. We focus on the decays of {sup 100}Mo, {sup 116}Cd and {sup 128}Te. We do not find clear evidences for single-state dominance within the present approach.

Theoretical description of the 2A/double prime/ and 2A/prime/ states of the peroxyformyl radical. [for air pollution and Mars atmospheric studies

NASA Technical Reports Server (NTRS)

Winter, N. W.; Goddard, W. A., III; Bender, C. F.

1975-01-01

Simple orbital ideas are used to describe the lowest two states of the peroxyformyl radical, and ab initio Hartree-Fock calculations in these states are reported. It is found that both states may be formed exothermically by association of O2 and HCO in their ground states; however, the excited state may decompose readily to OH and CO2. The possible role of such processes in oxidation of aldelydes is discussed.

Toroidal high-spin isomers in light nuclei with N ≠ Z

NASA Astrophysics Data System (ADS)

Staszczak, A.; Wong, Cheuk-Yin

2015-11-01

The combined considerations of both the bulk liquid-drop-type behavior and the quantized aligned rotation with cranked Skyrme-Hartree-Fock approach revealed previously (Staszczak and Wong 2014 Phys. Lett. B 738 401) that even-even, N = Z, toroidal high-spin isomeric states have general occurrences for light nuclei with 28≤slant A≤slant 52. We find that in this mass region there are in addition N\

Unified method of knowledge representation in the evolutionary artificial intelligence systems

NASA Astrophysics Data System (ADS)

Bykov, Nickolay M.; Bykova, Katherina N.

2003-03-01

The evolution of artificial intelligence systems called by complicating of their operation topics and science perfecting has resulted in a diversification of the methods both the algorithms of knowledge representation and usage in these systems. Often by this reason it is very difficult to design the effective methods of knowledge discovering and operation for such systems. In the given activity the authors offer a method of unitized representation of the systems knowledge about objects of an external world by rank transformation of their descriptions, made in the different features spaces: deterministic, probabilistic, fuzzy and other. The proof of a sufficiency of the information about the rank configuration of the object states in the features space for decision making is presented. It is shown that the geometrical and combinatorial model of the rank configurations set introduce their by group of some system of incidence, that allows to store the information on them in a convolute kind. The method of the rank configuration description by the DRP - code (distance rank preserving code) is offered. The problems of its completeness, information capacity, noise immunity and privacy are reviewed. It is shown, that the capacity of a transmission channel for such submission of the information is more than unit, as the code words contain the information both about the object states, and about the distance ranks between them. The effective algorithm of the data clustering for the object states identification, founded on the given code usage, is described. The knowledge representation with the help of the rank configurations allows to unitize and to simplify algorithms of the decision making by fulfillment of logic operations above the DRP - code words. Examples of the proposed clustering techniques operation on the given samples set, the rank configuration of resulted clusters and its DRP-codes are presented.

Electron-electron interaction and spin-orbit coupling in InAs/AlSb heterostructures with a two-dimensional electron gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gavrilenko, V. I.; Krishtopenko, S. S., E-mail: ds_a-teens@mail.ru; Goiran, M.

2011-01-15

The effect of electron-electron interaction on the spectrum of two-dimensional electron states in InAs/AlSb (001) heterostructures with a GaSb cap layer with one filled size-quantization subband. The energy spectrum of two-dimensional electrons is calculated in the Hartree and Hartree-Fock approximations. It is shown that the exchange interaction decreasing the electron energy in subbands increases the energy gap between subbands and the spin-orbit splitting of the spectrum in the entire region of electron concentrations, at which only the lower size-quantization band is filled. The nonlinear dependence of the Rashba splitting constant at the Fermi wave vector on the concentration of two-dimensionalmore » electrons is demonstrated.« less

A ganglion-cell-based primary image representation method and its contribution to object recognition

NASA Astrophysics Data System (ADS)

Wei, Hui; Dai, Zhi-Long; Zuo, Qing-Song

2016-10-01

A visual stimulus is represented by the biological visual system at several levels: in the order from low to high levels, they are: photoreceptor cells, ganglion cells (GCs), lateral geniculate nucleus cells and visual cortical neurons. Retinal GCs at the early level need to represent raw data only once, but meet a wide number of diverse requests from different vision-based tasks. This means the information representation at this level is general and not task-specific. Neurobiological findings have attributed this universal adaptation to GCs' receptive field (RF) mechanisms. For the purposes of developing a highly efficient image representation method that can facilitate information processing and interpretation at later stages, here we design a computational model to simulate the GC's non-classical RF. This new image presentation method can extract major structural features from raw data, and is consistent with other statistical measures of the image. Based on the new representation, the performances of other state-of-the-art algorithms in contour detection and segmentation can be upgraded remarkably. This work concludes that applying sophisticated representation schema at early state is an efficient and promising strategy in visual information processing.

A project based on multi-configuration Dirac-Fock calculations for plasma spectroscopy

NASA Astrophysics Data System (ADS)

Comet, M.; Pain, J.-C.; Gilleron, F.; Piron, R.

2017-09-01

We present a project dedicated to hot plasma spectroscopy based on a Multi-Configuration Dirac-Fock (MCDF) code, initially developed by J. Bruneau. The code is briefly described and the use of the transition state method for plasma spectroscopy is detailed. Then an opacity code for local-thermodynamic-equilibrium plasmas using MCDF data, named OPAMCDF, is presented. Transition arrays for which the number of lines is too large to be handled in a Detailed Line Accounting (DLA) calculation can be modeled within the Partially Resolved Transition Array method or using the Unresolved Transition Arrays formalism in jj-coupling. An improvement of the original Partially Resolved Transition Array method is presented which gives a better agreement with DLA computations. Comparisons with some absorption and emission experimental spectra are shown. Finally, the capability of the MCDF code to compute atomic data required for collisional-radiative modeling of plasma at non local thermodynamic equilibrium is illustrated. In addition to photoexcitation, this code can be used to calculate photoionization, electron impact excitation and ionization cross-sections as well as autoionization rates in the Distorted-Wave or Close Coupling approximations. Comparisons with cross-sections and rates available in the literature are discussed.

On extending Kohn-Sham density functionals to systems with fractional number of electrons.

PubMed

Li, Chen; Lu, Jianfeng; Yang, Weitao

2017-06-07

We analyze four ways of formulating the Kohn-Sham (KS) density functionals with a fractional number of electrons, through extending the constrained search space from the Kohn-Sham and the generalized Kohn-Sham (GKS) non-interacting v-representable density domain for integer systems to four different sets of densities for fractional systems. In particular, these density sets are (I) ensemble interacting N-representable densities, (II) ensemble non-interacting N-representable densities, (III) non-interacting densities by the Janak construction, and (IV) non-interacting densities whose composing orbitals satisfy the Aufbau occupation principle. By proving the equivalence of the underlying first order reduced density matrices associated with these densities, we show that sets (I), (II), and (III) are equivalent, and all reduce to the Janak construction. Moreover, for functionals with the ensemble v-representable assumption at the minimizer, (III) reduces to (IV) and thus justifies the previous use of the Aufbau protocol within the (G)KS framework in the study of the ground state of fractional electron systems, as defined in the grand canonical ensemble at zero temperature. By further analyzing the Aufbau solution for different density functional approximations (DFAs) in the (G)KS scheme, we rigorously prove that there can be one and only one fractional occupation for the Hartree Fock functional, while there can be multiple fractional occupations for general DFAs in the presence of degeneracy. This has been confirmed by numerical calculations using the local density approximation as a representative of general DFAs. This work thus clarifies important issues on density functional theory calculations for fractional electron systems.

Wavelets in electronic structure calculations

NASA Astrophysics Data System (ADS)

Modisette, Jason Perry

1997-09-01

Ab initio calculations of the electronic structure of bulk materials and large clusters are not possible on today's computers using current techniques. The storage and diagonalization of the Hamiltonian matrix are the limiting factors in both memory and execution time. The scaling of both quantities with problem size can be reduced by using approximate diagonalization or direct minimization of the total energy with respect to the density matrix in conjunction with a localized basis. Wavelet basis members are much more localized than conventional bases such as Gaussians or numerical atomic orbitals. This localization leads to sparse matrices of the operators that arise in SCF multi-electron calculations. We have investigated the construction of the one-electron Hamiltonian, and also the effective one- electron Hamiltonians that appear in density-functional and Hartree-Fock theories. We develop efficient methods for the generation of the kinetic energy and potential matrices, the Hartree and exchange potentials, and the local exchange-correlation potential of the LDA. Test calculations are performed on one-electron problems with a variety of potentials in one and three dimensions.

Thermal Pairing in Nuclei

NASA Astrophysics Data System (ADS)

Dang, Nguyen Dinh

2008-04-01

The modified Hartree-Fock-Bogoliubov (MHFB) theory at finite temperature is derived for finite nuclei.1 In the limit of constant pairing parameter, the MHFB theory yields the modified BCS (MBCS) theory.2 These are the microscopic theories that can describe the crossover region at temperature T around the critical value Tc of the BCS superfluid-normal (SN) phase transition. By requiring the unitarity conservation of the particle-density matrix, the derivation of these theories is achieved by constructing a modified quasiparticle density matrix, where the fluctuation of the quasiparticle number is microscopically built in. This matrix can be directly obtained from the usual quasiparticle-density matrix by applying the secondary Bogoliubov transformation, which includes the quasiparticle occupation number. The calculations of the thermal pairing gap, total energy, heat capacity, quasiparticle and pairing correlation functions were carried out within MBCS theory for the Richardson model3 as well as realistic single-particle spectra. The Richardson model under consideration has varying Ω equidistant levels and N particles with a level distant equal to 1 MeV. It is shown that the limitation of the configuration space sets a limiting temperature TM up to which the MBCS theory can be applied. Enlarging the space in the half-filled case (Ω = N) by one valence level (Ω = N + 1) extends TM to a much higher temperature so that the predictions by the MBCS theory can be compared directly with the exact results up to T ~ 4 - 5 MeV even for small N. The MBCS gap does not collapse, but decreases monotonously with increasing T. The total energy and heat capacity predicted by the MBCS theory are closer to the exact results than those predicted by the BCS theory, especially in the region of the SN phase transition predicted within the BCS theory. The discontinuity in the BCS heat capacity at the critical temperature Tc is smoothed out within the MBCS theory, especially for small N

A combined representation method for use in band structure calculations. 1: Method

NASA Technical Reports Server (NTRS)

Friedli, C.; Ashcroft, N. W.

1975-01-01

A representation was described whose basis levels combine the important physical aspects of a finite set of plane waves with those of a set of Bloch tight-binding levels. The chosen combination has a particularly simple dependence on the wave vector within the Brillouin Zone, and its use in reducing the standard one-electron band structure problem to the usual secular equation has the advantage that the lattice sums involved in the calculation of the matrix elements are actually independent of the wave vector. For systems with complicated crystal structures, for which the Korringa-Kohn-Rostoker (KKR), Augmented-Plane Wave (APW) and Orthogonalized-Plane Wave (OPW) methods are difficult to apply, the present method leads to results with satisfactory accuracy and convergence.

Two-photon excitation cross-section in light and intermediate atoms

NASA Technical Reports Server (NTRS)

Omidvar, K.

1980-01-01

The method of explicit summation over the intermediate states is used along with LS coupling to derive an expression for two-photon absorption cross section in light and intermediate atoms in terms of integrals over radial wave functions. Two selection rules, one exact and one approximate, are also derived. In evaluating the radial integrals, for low-lying levels, the Hartree-Fock wave functions, and for high-lying levels, hydrogenic wave functions obtained by the quantum defect method are used. A relationship between the cross section and the oscillator strengths is derived. Cross sections due to selected transitions in nitrogen, oxygen, and chlorine are given. The expression for the cross section is useful in calculating the two-photon absorption in light and intermediate atoms.

Static electric dipole polarizabilities of tri- and tetravalent U, Np, and Pu ions.

PubMed

Parmar, Payal; Peterson, Kirk A; Clark, Aurora E

2013-11-21

High-quality static electric dipole polarizabilities have been determined for the ground states of the hard-sphere cations of U, Np, and Pu in the III and IV oxidation states. The polarizabilities have been calculated using the numerical finite field technique in a four-component relativistic framework. Methods including Fock-space coupled cluster (FSCC) and Kramers-restricted configuration interaction (KRCI) have been performed in order to account for electron correlation effects. Comparisons between polarizabilities calculated using Dirac-Hartree-Fock (DHF), FSCC, and KRCI methods have been made using both triple- and quadruple-ζ basis sets for U(4+). In addition to the ground state, this study also reports the polarizability data for the first two excited states of U(3+/4+), Np(3+/4+), and Pu(3+/4+) ions at different levels of theory. The values reported in this work are the most accurate to date calculations for the dipole polarizabilities of the hard-sphere tri- and tetravalent actinide ions and may serve as reference values, aiding in the calculation of various electronic and response properties (for example, intermolecular forces, optical properties, etc.) relevant to the nuclear fuel cycle and material science applications.

The effect of basis set and exchange-correlation functional on time-dependent density functional theory calculations within the Tamm-Dancoff approximation of the x-ray emission spectroscopy of transition metal complexes.

PubMed

Roper, Ian P E; Besley, Nicholas A

2016-03-21

The simulation of X-ray emission spectra of transition metal complexes with time-dependent density functional theory (TDDFT) is investigated. X-ray emission spectra can be computed within TDDFT in conjunction with the Tamm-Dancoff approximation by using a reference determinant with a vacancy in the relevant core orbital, and these calculations can be performed using the frozen orbital approximation or with the relaxation of the orbitals of the intermediate core-ionised state included. Both standard exchange-correlation functionals and functionals specifically designed for X-ray emission spectroscopy are studied, and it is shown that the computed spectral band profiles are sensitive to the exchange-correlation functional used. The computed intensities of the spectral bands can be rationalised by considering the metal p orbital character of the valence molecular orbitals. To compute X-ray emission spectra with the correct energy scale allowing a direct comparison with experiment requires the relaxation of the core-ionised state to be included and the use of specifically designed functionals with increased amounts of Hartree-Fock exchange in conjunction with high quality basis sets. A range-corrected functional with increased Hartree-Fock exchange in the short range provides transition energies close to experiment and spectral band profiles that have a similar accuracy to those from standard functionals.

Analytic model of a multi-electron atom

NASA Astrophysics Data System (ADS)

Skoromnik, O. D.; Feranchuk, I. D.; Leonau, A. U.; Keitel, C. H.

2017-12-01

A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis completeness allows us to employ the secondary-quantized representation for the construction of regular perturbation theory, which includes in a natural way correlation effects, converges fast and enables an effective calculation of the subsequent corrections. The hydrogen-like basis set provides a possibility to perform all summations over intermediate states in closed form, including both the discrete and continuous spectra. This is achieved with the help of the decomposition of the multi-particle Green function in a convolution of single-electronic Coulomb Green functions. We demonstrate that our fully analytical zeroth-order approximation describes the whole spectrum of the system, provides accuracy, which is independent of the number of electrons and is important for applications where the Thomas-Fermi model is still utilized. In addition already in second-order perturbation theory our results become comparable with those via a multi-configuration Hartree-Fock approach.

Projector Augmented Wave formulation of orbital-dependent exchange-correlation functionals

NASA Astrophysics Data System (ADS)

Xu, Xiao; Holzwarth, N. A. W.

2012-02-01

The use of orbital-dependent exchange-correlation functionals within electronic structure calculations has recently received renewed attention for improving the accuracy of the calculations, especially correcting self-interaction errors. Since the Projector Augmented Wave (PAW) methodootnotetext P. Bl"ochl, Phys. Rev. B 50, 17953 (1994). is an efficient pseudopotential-like scheme which ensures accurate evaluation of all multipole moments of direct and exchange Coulomb integrals, it is a natural choice for implementing orbital-dependent formalisms. Using Fock exchange as an example of an orbital-dependent functional, we developed the formulation and numerical implementation of the approximate optimized effective potential formalism of Kreiger, Li, and Iafrate (KLI)ootnotetext J. B. Krieger, Y. Li, and G. J. Iafrate Phys. Rev. A 45, 101 (1992). within the PAW method, comparing results with the analogous Hartree-Fock treatment.ootnotetext Xiao Xu and N. A. W. Holzwarth, Phys. Rev. B 81, 245105 (2010); 84, 155113 (2011). Test results are presented for ground state properties of two well-known materials -- diamond and LiF. This formalism can be extended to treat orbital-dependent functionals more generally.

A Sparse Self-Consistent Field Algorithm and Its Parallel Implementation: Application to Density-Functional-Based Tight Binding.

PubMed

Scemama, Anthony; Renon, Nicolas; Rapacioli, Mathias

2014-06-10

We present an algorithm and its parallel implementation for solving a self-consistent problem as encountered in Hartree-Fock or density functional theory. The algorithm takes advantage of the sparsity of matrices through the use of local molecular orbitals. The implementation allows one to exploit efficiently modern symmetric multiprocessing (SMP) computer architectures. As a first application, the algorithm is used within the density-functional-based tight binding method, for which most of the computational time is spent in the linear algebra routines (diagonalization of the Fock/Kohn-Sham matrix). We show that with this algorithm (i) single point calculations on very large systems (millions of atoms) can be performed on large SMP machines, (ii) calculations involving intermediate size systems (1000-100 000 atoms) are also strongly accelerated and can run efficiently on standard servers, and (iii) the error on the total energy due to the use of a cutoff in the molecular orbital coefficients can be controlled such that it remains smaller than the SCF convergence criterion.

Static electric dipole polarizabilities of An(5+/6+) and AnO2 (+/2+) (An = U, Np, and Pu) ions.

PubMed

Parmar, Payal; Peterson, Kirk A; Clark, Aurora E

2014-12-21

The parallel components of static electric dipole polarizabilities have been calculated for the lowest lying spin-orbit states of the penta- and hexavalent oxidation states of the actinides (An) U, Np, and Pu, in both their atomic and molecular diyl ion forms (An(5+/6+) and AnO2 (+/2+)) using the numerical finite-field technique within a four-component relativistic framework. The four-component Dirac-Hartree-Fock method formed the reference for MP2 and CCSD(T) calculations, while multireference Fock space coupled-cluster (FSCC), intermediate Hamiltonian Fock space coupled-cluster (IH-FSCC) and Kramers restricted configuration interaction (KRCI) methods were used to incorporate additional electron correlation. It is observed that electron correlation has significant (∼5 a.u.(3)) impact upon the parallel component of the polarizabilities of the diyls. To the best of our knowledge, these quantities have not been previously reported and they can serve as reference values in the determination of various electronic and response properties (for example intermolecular forces, optical properties, etc.) relevant to the nuclear fuel cycle and material science applications. The highest quality numbers for the parallel components (αzz) of the polarizability for the lowest Ω levels corresponding to the ground electronic states are (in a.u.(3)) 44.15 and 41.17 for UO2 (+) and UO2 (2+), respectively, 45.64 and 41.42 for NpO2 (+) and NpO2 (2+), respectively, and 47.15 for the PuO2 (+) ion.

Quantified Gamow shell model interaction for p s d -shell nuclei

NASA Astrophysics Data System (ADS)

Jaganathen, Y.; Betan, R. M. Id; Michel, N.; Nazarewicz, W.; Płoszajczak, M.

2017-11-01

Background: The structure of weakly bound and unbound nuclei close to particle drip lines is one of the major science drivers of nuclear physics. A comprehensive understanding of these systems goes beyond the traditional configuration interaction approach formulated in the Hilbert space of localized states (nuclear shell model) and requires an open quantum system description. The complex-energy Gamow shell model (GSM) provides such a framework as it is capable of describing resonant and nonresonant many-body states on equal footing. Purpose: To make reliable predictions, quality input is needed that allows for the full uncertainty quantification of theoretical results. In this study, we carry out the optimization of an effective GSM (one-body and two-body) interaction in the p s d f -shell-model space. The resulting interaction is expected to describe nuclei with 5 ≤A ≲12 at the p -s d -shell interface. Method: The one-body potential of the 4He core is modeled by a Woods-Saxon + spin-orbit + Coulomb potential, and the finite-range nucleon-nucleon interaction between the valence nucleons consists of central, spin-orbit, tensor, and Coulomb terms. The GSM is used to compute key fit observables. The χ2 optimization is performed using the Gauss-Newton algorithm augmented by the singular value decomposition technique. The resulting covariance matrix enables quantification of statistical errors within the linear regression approach. Results: The optimized one-body potential reproduces nucleon-4He scattering phase shifts up to an excitation energy of 20 MeV. The two-body interaction built on top of the optimized one-body field is adjusted to the bound and unbound ground-state binding energies and selected excited states of the helium, lithium, and beryllium isotopes up to A =9 . A very good agreement with experimental results was obtained for binding energies. First applications of the optimized interaction include predictions for two-nucleon correlation densities

Quantified Gamow shell model interaction for p s d -shell nuclei

DOE PAGES

Jaganathen, Y.; Betan, R. M. Id; Michel, N.; ...

2017-11-20

Background: The structure of weakly bound and unbound nuclei close to particle drip lines is one of the major science drivers of nuclear physics. A comprehensive understanding of these systems goes beyond the traditional configuration interaction approach formulated in the Hilbert space of localized states (nuclear shell model) and requires an open quantum system description. The complex-energy Gamow shell model (GSM) provides such a framework as it is capable of describing resonant and nonresonant many-body states on equal footing. Purpose: To make reliable predictions, quality input is needed that allows for the full uncertainty quantification of theoretical results. In thismore » study, we carry out the optimization of an effective GSM (one-body and two-body) interaction in the psdf-shell-model space. The resulting interaction is expected to describe nuclei with 5 ≤ A ≲ 12 at the p-sd-shell interface. Method: The one-body potential of the 4He core is modeled by a Woods-Saxon + spin-orbit + Coulomb potential, and the finite-range nucleon-nucleon interaction between the valence nucleons consists of central, spin-orbit, tensor, and Coulomb terms. The GSM is used to compute key fit observables. The χ 2 optimization is performed using the Gauss-Newton algorithm augmented by the singular value decomposition technique. The resulting covariance matrix enables quantification of statistical errors within the linear regression approach. Results: The optimized one-body potential reproduces nucleon- 4He scattering phase shifts up to an excitation energy of 20 MeV. The two-body interaction built on top of the optimized one-body field is adjusted to the bound and unbound ground-state binding energies and selected excited states of the helium, lithium, and beryllium isotopes up to A = 9 . A very good agreement with experimental results was obtained for binding energies. First applications of the optimized interaction include predictions for two-nucleon correlation

Transformation between scientific and social representations of conception: the method of serial reproduction.

PubMed

Bangerter, A

2000-12-01

The social representation (SR) of conception was investigated using an adapted version of Bartlett's (1932) method of serial reproduction. A sample of 75 participants reproduced a text describing the conception process in 20 segregated chains of four reproductive generations. Changes in sentence structure and content were analysed. Results indicated that when the scientific representation of conception is apprehended by laypersons, two different processes take place. First, the abstract biological description of the process is progressively transformed into an anthropomorphic description centred on the sperm and ovum (personification). Second, stereotypical sex-role attributes are projected onto the sperm and ovum. Limitations of the method of serial reproduction are discussed, as well as its potential for modelling processes of cultural diffusion of knowledge.

Covariant density functional theory: predictive power and first attempts of a microscopic derivation

NASA Astrophysics Data System (ADS)

Ring, Peter

2018-05-01

We discuss systematic global investigations with modern covariant density functionals. The number of their phenomenological parameters can be reduced considerable by using microscopic input from ab-initio calculations in nuclear matter. The size of the tensor force is still an open problem. Therefore we use the first full relativistic Brueckner-Hartree-Fock calculations in finite nuclear systems in order to study properties of such functionals, which cannot be obtained from nuclear matter calculations.