... 11. Observations and Folklore 80 ... Observations and Folklore A key to the accurate functioning of neural networks based on Gaussian radial basis ...
DTIC Science & Technology
The authors have applied the generator coordinate Hartree-Fock method to generate adapted Gaussian basis sets for the atoms from H through Xe. The Griffin-Hill-Wheeler-Hartree-Fock equations are integrated numerically generating accurate basis sets for these atoms. The atomic wave functions are an improvement over ...
Energy Citations Database
Energy-optimized, near Hartree-Fock (NHF) quality Gaussian type orbital (GTO) basis sets are reported for the second-row (Li to Ne) and fourth-row (K to Kr) atoms. The most accurate basis sets reported for the second row are (18s 13p) sets which are with ...
National Technical Information Service (NTIS)
A prescription is presented and implemented for Sc through Cu that leads to practical-sized Gaussian d basis sets capable of accurate descriptions of the s/sup m/d/sup n-m/ states of the atom. Optimized Gaussian basis sets containing four, five, and six primitives are given along with ...
A powerful, flexible system of computer programs was developed for the computation of self-consistent-field wavefunctions for small polyatomic molecules in a gaussian basis. Accurate wavefunctions were computed for water, formaldehyde, and ethylene. A pre...
Accurate self-consistent-field functions were computed for several small polyatomic molecules, including benzene, in a basis of Gaussian functions. All multicenter molecular integrals were calculated and the core electrons explicitly included. This work r...
Ab initio calculations of the electronic structure of Hn- and Hn+ clusters have been carried out using accurate Gaussian basis sets and with levels of theory up to fourth-order perturbation theory (MP4) and single and double excitation configuration inter...
An accurate description of a radially polarized fundamental Gaussian beam is presented on the basis of complex-source-point spherical waves (CSPSWs). In contrast to other descriptions based on the perturbative Lax series, the expressions for the electromagnetic field components of this description have explicit and simple mathematical ...
A basis set contraction scheme is described for carrying out reactive scattering calculations within the S-matrix version of the Kohn variational principle. The new basis functions are distributed Gaussians for the radial (translational) degrees of freedom, as used before, but with quasi-adiabatic internal eigenfunctions for the ...
The expansion coefficients of a multi-Gaussian ultrasonic beam model are obtained by a new approach that applies Prony s method in a K-space domain. This method allows the fitting of the Gaussian beam directly at the face of the transducer with very high computational efficiency. It is demonstrated that the K-space Prony's method can be used to ...
PubMed
Within the framework of the complex basis function method, the photoionization cross sections of H(2)(+) and H(2) were calculated based on the variational principle for the frequency-dependent polarizabilities. In these calculations, complex orbital exponents of Gaussian-type basis functions for the final state continuum wavefunctions ...
Calculations of the hyperpolarizability are typically much more difficult to converge with basis set size than the linear polarizability. In order to understand these convergence issues and hence obtain accurate ab initio values, we compare calculations of the static hyperpolarizability of the gas-phase chloroform molecule (CHCl3) using three different ...
NASA Astrophysics Data System (ADS)
An accurate potential surface of 68 grid points for the H/sub 3//sup +/ system is given. The surface was calculated at the level of a full configuration expansion using a large basis set of 63 contracted Gaussian functions. This surface should be suitable for extremely accurate predictions of the ...
The behavior of the two exponential parameters in an even-tempered gaussian basis set is investigated as the set optimally approaches an integral transform representation of the radial portion of atomic and molecular orbitals. This approach permits a highly accurate assessment of the Hartree-Fock limit for atoms and molecules.
The principle of augmentation, used to introduce inner-atom core structure into slowly varying basis functions, is applied to Gaussian orbitals to define a new basis set for highly accurate total-energy calculations for atomic clusters within the density-functional formalism. Diffuse ...
Distributions of binding energies of a water molecule in the water liquid-vapor interface are obtained on the basis of molecular simulation with the SPC/E model of water. These binding energies together with the observed interfacial density profile are used to test a minimally conditioned Gaussian quasi-chemical statistical thermodynamic theory. Binding ...
DOE Information Bridge
The numerical accuracy of the plane-wave-Gaussian (PWG) mixed-basis method of calculating crystalline energy bands is displayed for Nb. Atomic studies involving the Gaussian basis and crystalline studies involving the PWG mixed basis are systematically de...
We describe a method for calculating the matrix elements of the Coulomb operator for Gaussian basis sets using an intermediate discrete Fourier transform of the density. Our goals are the same as those of the Gaussian and augmented-plane-wave method of Parrinello and co-workers [M. Krack and M. Parrinello, Phys. Chem. Chem. Phys. 2, ...
Efficient optimization of the basis set is key to achieving a very high accuracy in variational calculations of molecular systems employing basis functions that are explicitly dependent on the interelectron distances. In this work we present a method for a systematic enlargement of basis sets of explicitly correlated functions based on ...
Standard sets of supplementary diffuse s and p functions, multiple polarization functions (double and triple sets of d functions), and higher angular momentum polarization functions (f functions) are defined for use with the 6-31G and 6-311G basis sets. Preliminary applications of the modified basis sets to the calculation of the bond energy and ...
An efficient method for obtaining molecular vibrational eigenstates using a basis set made up of semiclassical eigenstates is presented. The semiclassical basis functions are constructed from a set of Gaussian functions distributed uniformly on the invariant N-torus defined by a single quasiperiodic classical trajectory. A uniform ...
We present a sub-0.3 K accuracy, ground-state one-dimensional potential energy curve of the metastable linear configuration of the (H2)2 cluster calculated exclusively with explicitly correlated Gaussian functions with shifted centers. The H2 internuclear distance is kept at the isolated H2 vibrational ground-state average value of 1.448 736 bohr and the intermonomer ...
We present a sub-0.3 K accuracy, ground-state one-dimensional potential energy curve of the metastable linear configuration of the (H(2))(2) cluster calculated exclusively with explicitly correlated Gaussian functions with shifted centers. The H(2) internuclear distance is kept at the isolated H(2) vibrational ground-state average value of 1.448 736 bohr and the intermonomer ...
... The basis functions are usually local that they respond ... f(x) function is a transfer function that x ... are weight parameters, and h(x) is Gaussian function. ...
We present a method for efficient calculation of exchange correlation in a density-functional theory calculation with Gaussian basis functions. It seamlessly combines the treatments of smooth (low-energy cutoff) and nonsmooth parts of the electron density such that computational performance can be maximized without approximation. Benchmark calculations ...
A recently framed quantum/semiclassical treatment for the internal nuclear dynamics of a small molecule and the induced small-amplitude coherent motion of a low-temperature host medium (Chapman, C. T.; Cina, J. A. J. Chem. Phys.2007,127, 114502) is further analyzed and subjected to initial tests of its numerical implementation. In the illustrative context of a 1D system interacting with a 1D ...
Peak wavelength and full-width-half-maximum (FWHM) are the two important parameters to characterize the spectra of monochromatic LED lights. In this work, a low-cost miniature filter-array spectrum sensor for accurate LED measurement is proposed. For mapping the data from the outputs of the filter-array spectrum sensor to the measurement parameters of peak wavelength and FWHM, ...
Recent advances in explicitly correlated electronic structure methods, namely MP2-F12 and CCSD(T)-F12, have demonstrated significant improvements in accuracy and efficiency due to the much improved convergence with respect to the one-particle basis set. Recent work in our group involving the heavy post-d main group elements will be presented, including new F12-optimized ...
Large expansions in basis sets of explicitly correlated Gaussian functions and the variation-perturbation technique were used to calculate the static dipole polarizability of the helium dimer at 16 different internuclear separations from 1.0 to 9.0 bohrs. The convergence towards the complete basis set limit was analyzed in order to ...
A method for accurate numerical integration is proposed and illustrated by a variety of examples. The method depends on an ability to efficiently evaluate the weights and abscissas of Gaussian quadrature formulas, and software to achieve this purpose is a...
Gaussian Quadrature can only be applied if integration is performed over the interval from ... accurately using only a 4-point Gaussian integration scheme. ...
NASA Website
This paper reports an approach to the analysis of the local anharmonic states of motion and tunnelling of hydrogen illustrated with the molecule malonaldehyde. A potential energy function is used accurately to fit the local potential energy surface. The basis fitting functions in the potential resemble the Morse basis function, , but ...
... A. Probability and Random Processes for Electrical ... TERMS Interpolation, Gaussian Process, Image Processing, Enhancement, Maximum ...
The variational nodal transport method is generalized for the treatment of heterogeneous nodes while maintaining nodal balances. Adapting variational methods to heterogeneous nodes requires the ability to integrate over a node with discontinuous cross sections. Integrals are evaluated using composite Gaussian quadrature rules, which permit accurate ...
A procedure is presented to fit gridded molecular properties to auxiliary basis sets (ABSs) of Hermite Gaussians, analogous to the density fitting (DF) method (Dunlap; et al. J. Chem. Phys. 1979, 71, 4993). In this procedure, the ab initio calculated properties (density, electrostatic potential, and/or electric field) are fitted via a linear- or ...
PubMed Central
The calculation of the diffraction field radiated from the ultrasonic transducer can be simplified by using the Gaussian beam expansion technique. The key problem of this technique is how to determine the coefficients of Gaussian functions. We present a simple and accurate optimization method to calculate the ...
We investigate two methods for obtaining optimal basis sets for deep-level Green's-function calculations. In the first method, the eigenstates of the potential provide the basis set. In the second we define a ``Pauling-band'' projector onto perfect-crystal eigenstates within 10 eV of the valence-band edge. The basis states in this case ...
... at each point as a Gaussian distribution and use this model to interpolate the computed focus measures to obtain more accurate depth estimates. ...
correlation-consistent valence basis sets were developed for the third-row main block elements (K, Ca, Ga-Kr) for use with relativistic effective core potentials. These basis sets are somewhat larger than double-zeta in size, with polarization functions, and are balanced for use in both Hartree-Fock and correlation calculations. Spin-orbit splittings for ...
The problem addressed in the work supported was to develop a method for accurate all electron self consistent calculations of the electronic structure of small clusters of transition metal atoms on the basis of both local spin density functional theory and of symmetrized combinations of Gaussian orbitals. Our intention was to use the ...
Relativistic basis sets for first-row atoms have been constructed by using the near-Hartree-Fock (nonrelativistic) eigenvectors calculated by Partridge. These bases generate results of near-Dirac-Hartree-Fock quality. Relativistic total and orbital energies, relativistic corrections to the total energy, and magnetic interaction energies for the first-row atoms have been ...
Variational calculations of ground and excited bound states on atomic and molecular systems performed with basis functions that explicitly depend on the interparticle distances can generate very accurate results provided that the basis function parameters are thoroughly optimized by the minimization of the energy. In this work we have ...
Gaussian mixture model is a popular method to model dynamic scenes viewed by a fixed camera. However, we found that it is not a trivial problem for each component of Gaussian mixture to learn the accurate parameters for complex pixels. Furthermore, traditional method of Gaussian mixture has to make a tradeoff ...
We report on the development and testing of large polarized basis sets (LPolX, where X is the element symbol) for accurate calculations of linear and nonlinear electric properties of molecules. The method used to generate LPolX sets is based on our studies of the analytic dependence of Gaussian functions on external time-independent ...
Hartree-Fock calculations are reported on the atoms gallium through krypton using (13s9p5d) and (14s11p5d) Gaussian basis sets. (AIP(
The asymptotic expression may be used to calculate matrix elements of the Gaussian potential between the basis functions of three-dimensional harmonic oscillator , starting with some values of quantum...
The variational nodal transport method is reduced to its diffusion form and generalized for the treatment of heterogeneous nodes while maintaining nodal balances. Adapting variational methods to heterogeneous nodes requires the ability to integrate over a node with discontinuous cross sections. In this work, integrals are evaluated using composite gaussian quadrature rules, ...
NASA technical memorandum contains tables of estimated Hartree-Fock wave functions for atoms lithium
NASA Technical Reports Server (NTRS)
... by three spatial wavenumbers corresponding to the three space coordinates, and by ... B. Gaussian beams as basis elements for radiation from large ...
... on the basis of noisy samples, with applications to machine learning, S. Yakowitz ... in a cone for a class of vector Gaussian processes, S. Berman ...
... For environmental uncertainties which are distributed according to a Gaussian pdf, the appropriate basis are the modified Hermite polynomials � [6 ...
... DEPT OF ELECTRICAL-ELECTRONICS ENGINEERING. ... sequence of protein determines the ... Descriptors : *PROTEINS, *MAPPING, NEURAL NETS ...
Highly accurate relativistic Gaussian basis sets are developed for the 103 elements from H(Z=1) to Lr (Z=103). Orbital exponents are optimized by minimizing the atomic self-consistent field (SCF) energy with the scalar relativistic third-order Douglas-Kroll approximation. The basis sets are designed to have equal ...
Gaussian-2 (G2) theory for third-row non-transition elements is used to calculate accurate electron affinities of germanium clusters, Ge{sub n} (n=2-5). The results for n=2-4 are in agreement with experiment while there is some disagreement for Ge{sub 5}. The electron affinities are also calculated using G2 theory modified by adding a diffuse function to ...
This paper reports on numerical experiments on the `independent component analysis' (ICA) of some nonGaussian stochastic processes. It is found that the orthonormal basis discovered by ICA are strikingly close to wavelet basis.
E-print Network
A modified regional self-interaction correction (mRSIC) method is proposed for obtaining accurate core-excitation energies in time-dependent density functional theory (TDDFT) calculations. The mRSIC method is an improvement of the RSIC method (Tsuneda et al. J Comput Chem 2003, 24, 1592). It takes into account the energy contributions from 2s and higher atomic orbitals that ...
Efficient and safe operation of a laser requires precise alignment of the resonator. This paper describes a method for aligning an unstable resonator very accurately with off-axis injection of the alignment beam ultilizing multiple reflections of the Gaussian beam inside the resonator.
We consider the mean on-axis far-field (or focal-plane) irradiance of a Gaussian Beam truncated by a circular aperture in the presence of atmospheric turbulence. In the absence of turbulence, we present an accurate analytic approximation for the irradianc...
A method for the calculation of abscissas and weight factors using Gaussian integration for integrands with a logarithmic singularity is presented. The method shows good convergent properties and allows for the accurate estimation of the error. A program ...
Some dynamic environments are characterized by time histories that are not Gaussian. A more accurate simulation of these environments can be generated if a realization of a non Gaussian time history can be reproduced which has a specified auto spectral de...
A common problem in particle simulations is effective field interpolation. Field interpolation is any method for creating an accurate representation of a given continuous field by a linear combination of overlapping basis functions. This paper presents two techniques for field interpolation, based on a radial basis function (RBF) ...
Radial basis function (RBF) interpolants have become popular in computer graphics, neural networks and for solving partial differential equations in many fields of science and engineering. In this article, we compare five different species of RBFs: Gaussians, hyperbolic secant (sech�s), inverse quadratics, multiquadrics and inverse multiquadrics. We show ...
In most Information Retrieval (IR) applications, Euclidean distance is used for similarity measurement. It is adequate in many cases but this distance metric is not very accurate when there exist some different local data distributions in the database. We propose a Gaussian mixture distance for performing accurate nearest-neighbor ...
We establish the accuracy of the spectrum that is estimated with an inexpensive fluorescence spectral microscope utilizing a small set of spectral filters [Soriano et al, Opt. Exp. 10, 1458 1464 (2002)]. The spectrum at an arbitrary image location of the fluorescent sample is estimated as a linear superposition of basis spectra that are derived by singular value decomposition ...
An augmented valence triple-zeta basis set, referred to as G3Large, is reported for the first-row transition metal elements Sc through Zn. The basis set is constructed in a manner similar to the G3Large basis set developed previously for other elements (H-Ar, K, Ca, Ga-Kr) and used as a key component in Gaussian-3 ...
Firstly, the analytical expression for the M2 factor of the off-axial Hermite-cosh-Gaussian beams is derived based on the second-order moments definition. Secondly, the analytical propagation expression for the kurtosis parameter of the off-axial Hermite-cosh-Gaussian beams is also derived on the basis of the analytical propagation ...
On the basis of the vectorial Rayleigh-Sommerfeld formulas and by means of the relation between Hermite and Laguerre polynomials, the analytical expressions for the propagation of the Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) beams beyond the paraxial approximation are derived, with the corresponding far-field propagation ...
We propose a new approach to the analysis of stochastic processes (such as fluctuating laser fields) with super-Gaussian statistics: the expansion of stochastic processes in terms of first and higher powers of Gaussian components, which are used like a basis set. This approach is applied to treat the super-Gaussian ...
We propose a new approach to the analysis of stochastic processes (such as fluctuating laser fields) with non-Gaussian statistics: the expansion of stochastic processes in terms of first and higher power of Gaussian components, which are used like a basis set. This approach is applied to treat the non-Gaussian ...
Contracted Gaussian-type function sets are developed for correlating functions of the ten main group elements from Cs to Ra. A segmented contraction scheme is used for its compactness and efficiency. Contraction coefficients and exponents are determined by minimizing the deviation from accurate natural orbitals or K-orbitals, incorporating the relativistic ...
An analytical form of expansion coefficients of a diffracted field for an arbitrary Hermite-Gaussian beam in an alien Hermite-Gaussian basis is obtained. A possible physical interpretation of the well-known Young phenomenological diffraction principle and experiments on diffraction of Hermite-Gaussian beams of the ...
An analysis is presented that shows how floating spherical Gaussian orbital (FSGO) basis sets can be related to atomic Gaussian orbital basis sets. In addition, through the development of the concept of local rotational invariance, it is shown how FSGO basis sets can, in a systematic and ...
This paper compares harmonic and anharmonic zero-point energies and thermodynamic functions for a number of molecules of small and medium size. Anharmonic corrections cannot be neglected for quantitative studies, but can be obtained quite effectively by a perturbative treatment including cubic force constants to the second order and semidiagonal quartic constants to the first order. Simple finite ...
A new class of 32n2 boron cages which are made closed by six squares is proposed and a procedure to build such cages using an ?-boron sheet is described. Each member from this infinite set of boron cages has a structure that is compatible with the most stable ?-boron sheet that maintains an optimal balance of the two-center and three-center bonds. Accurate density functional ...
Highly accurate ground-state nonrelativistic variational calculations of Ps{sub 2}, {sup 1}HPs, and {sup {infinity}}HPs are reported. The calculations have been performed using 5000 explicitly correlated Gaussian basis functions and yielded the lowest variational energy upper bounds for these systems to date. The relative accuracies of ...
Very accurate calculations of the pure vibrational spectrum of the HeH(+) ion are reported. The method used does not assume the Born-Oppenheimer approximation, and the motion of both the electrons and the nuclei are treated on equal footing. In such an approach the vibrational motion cannot be decoupled from the motion of electrons, and thus the pure vibrational states are ...
The ?3(L) statistic of random matrix theory is defined as the average of a set of random numbers {?}, derived from a spectrum. The distribution p(?) of these random numbers is used as the basis of a maximum likelihood method to gauge the fraction x of levels missed in an experimental spectrum. The method is tested on an ensemble of depleted spectra from the ...
We consider exponential time integration schemes for fast numerical pricing of European, American, barrier and butterfly options when the stock price follows a dynamics described by a jump-diffusion process. The resulting pricing equation which is in the form of a partial integro-differential equation is approximated in space using finite elements. Our methods require the computation of a single ...
Calculations of leptonic and hadronic annihilation rates in the hydrogen-antihydrogen molecule are presented. Both the leptonic potential and leptonic wave function are evaluated within the Born-Oppenheimer approximation employing the Ritz variational principle. Nonadiabatic corrections to the leptonic potential are also obtained. Explicitly correlated Gaussians are employed ...
Gaussian-2 (G2) theory for third-row non-transition elements is used to calculate energies of germanium clusters, Ge{sub n} (n = 2-5). The G2 energies are used to derive accurate binding energies for the clusters. The results for Ge{sub 2} and Ge{sub 3} are in agreement with experiment while there is some disagreement for Ge{sub 4} and Ge{sub 5}. The ...
A refined version of the ''shape consistent'' effective potential procedure of Christiansen, Lee, and Pitzer was used to compute averaged relativistic effective potentials (AREP) and spin--orbit operators for the elements Rb through Xe. Particular attention was given to the partitioning of the core and valence space and, where appropriate, more than one set of ...
We present results of first-principles atomic and electronic structure calculations for a number of silver halides. For a most accurate treatment of the halides we employ our self-interaction and relaxation-corrected pseudopotentials together with Gaussian-orbital basis sets. Our results for the rocksalt-structure crystals AgCl and ...
We report on the Gaussian file search system designed as part of the ChemXSeer digital library. Gaussian files are produced by the Gaussian software [4], a software package used for calculating molecular electronic structure and properties. The output files are semi-structured, allowing relatively easy access to the ...
Expanding single-particle wave functions in a local basis set using Gaussian-type orbitals (GTO) is well established. All-electron GTO basis sets of so-called multi-? quality are available for a large number of elements. However, the application of GTOs in ab-initio calculations for periodic systems is not straightforward. Diffuse i.e. ...
The Gaussian, exponential and Laguerre basis functions are examined in a variational calculation of energies and wavefunctions. The Laguerre basis set is already orthonormal and complete, but the Gaussian and exponential basis sets are not orthonormal. We used the linear and Coulomb potentials ...
We apply the variational method to the ground-state and first-excited-state energies of a Gaussian well and show that the expansion of the approximate energy when the potential strength approaches zero does not agree with the exact result. We argue that a recent semiclassical approach to tunneling through a Gaussian barrier does not agree with an ...
This paper proposes a radial basis function neural network (RBFNN), called the q-Gaussian RBFNN, that reproduces different radial basis functions (RBFs) by means of a real parameter q. The architecture, weights and node topology are learnt through a hybrid algorithm (HA). In order to test the overall performance, an experimental study ...
Based on reproducing kernel Hilbert space theory and radial basis approximation theory, a grid method is developed for numerically solving the N-dimensional bound-state Schrodinger equation. Central to the method is the construction of an appropriate bounded reproducing kernel (RK) Lambda(alpha)( ||r ||) from the linear operator -nabla(2)(r)+lambda(2) where nabla(2)(r) is the ...
The influence of changes in the contracted Gaussian basis set used for ab initio calculations of nuclear magnetic resonance (NMR) phosphorous chemical shift anisotropy (CSA) tensors was investigated. The isotropic chemical shift and chemical shift anisotropy were found to converge with increasing complexity of the basis set at the ...
The globally uniform semiclassical wave function expresses the solution to the time independent Schroedinger equation in terms of fixed width Gaussian wave packets traveling along a set of trajectories. There is a globally uniform wave function (GUWF) for each value of the Gaussian width parameter {gamma}. Numerical data show that a small ...
We report on the construction of an all-electron Gaussian-basis DFT code for systems periodic in one, two, and three dimensions. This is in part a reimplementation of algorithms in the serial code, GTOFF, which has been successfully applied to the study of crystalline solids, surfaces, and ultra-thin films. The current development is being carried out in an object-oriented ...
The Gaussian plume atmospheric dispersion model is one of the most widely used models for assessing the impact of radionuclides released to the atmosphere. This model is a statistical solution to the basic atmospheric diffusion equation. As a result, the Gaussian model should give more accurate results when used to calculate average ...
Configuration-interaction studies are reported for the Rydberg states of the helium atom using mixed
wave functions; only the eight valence electrons were correlated in the latter. All of the contraction schemes investigated were based on the (1 3s 8p) ...
The square of a narrowband Gaussian process is used to simulate sunspot cycles at computer speeds. The method is appealing because: (1) the model is extremely simple yet its physical basis, a simple resonance, is a widely occurring natural phenomenon, and (2) the model recreates practically all of the features of the observed sunspot record. In particular, ...
Gaussian 76 is a general-purpose computer program for ab initio Hartree-Fock molecular orbital calculations. It can handle basis sets involving s, p and d-type gaussian functions. Certain standard sets (STO-3G, 4-31G, 6-31G*, etc.) are stored internally f...
Formulas are developed for calculation of infrared absorption spectra with the help of Gaussian variational wave packets. The excitation is viewed as occurring to a linear combination of basis states corresponding to a Gaussian multiplied by Hermite polynomials of coordinates. Application of the formulas is examplified on HDO isolated ...
Gaussianity is the very basis for derivation of the cosmological parameters from the cosmic microwave background (CMB) angular power spectrum. Non-Gaussian signal, whether originated from experimental error or primordial source, could mimic extra power in the power spectrum, thereby leading to a wrong set of parameters. In this paper ...
Starting from the quantum Fokker-Planck equation, a viable quantum Gaussian channel is constructed in a quantum information network. It is shown that the solution of this equation satisfies a Gaussian distribution channel. Transforming the solution of the Fokker-Planck equation and substituting it into the information formula, a quantum dynamical mutual ...
We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has a power spectral density varying as 1/f{sup g}amma. We present an accurate and fast [O(N)] algorithm for parameter ...
... treatments; (3) completion of a study of the ... the theoretical basis for accurate measurement of small ... of a first exploratory interlaboratory evaluation of ...
A superposition of propagating Bessel beams was recently numerically demonstrated to approximate a Gaussian beam and was used to evaluate the scattering by a sphere centered on the focal point of the beam. An analytical beam synthesis used in optics by Agrawal and Pattanayak [J. Opt. Soc. Am. 69, 575-578 (1979)] is found here to be recovered as the weak focusing limit of the ...
We comprehensively study the least-squares Gaussian approximations of the diffraction-limited 2D-3D paraxial-nonparaxial point-spread functions (PSFs) of the wide field fluorescence microscope (WFFM), the laser scanning confocal microscope (LSCM), and the disk scanning confocal microscope (DSCM). The PSFs are expressed using the Debye integral. Under an L(infinity) constraint ...
Large basis sets of explicitly correlated Gaussian (ECG) functions with carefully optimized nonlinear parameters have been used to calculate the binding energies of H2 and He2 at their equilibrium internuclear distances R. In the case of the helium dimer, the wave function includes a product of two helium atom functions, which accounts for the main part of ...
describe here the application of a type of artificial neural network, the Gaussian radial basis function (RBF) network, in the identification of a large number of phytoplankton strains from their 11-dimensional flow cytometric characteristics measured by the European Optical Plankton Analyser instrument. The effect of network parameters on optimization is ...
The use of real-valued stabilization graphs for calculation of resonance energies and widths is considered in connection with the lowest Feshbach resonance state of H/sup -/, nominally (Phi/sub 2//sub s/)/sup 2/. One problem that arises is the difficulty of generating stabilization graphs with well defined avoided crossings between the resonance state of interest and nearby interacting continuum ...
The 110+, 11(?1)+ and 11(?2)+ states of the helium atom in the magnetic field regime between 0 and 100 a.u. are studied using a full configuration-interaction (CI) approach. The total energies, derivatives of the total energy with respect to the magnetic field and ionisation energies are calculated with Hylleraas-like functions in spherical coordinates in low to intermediate fields and ...
A computational approach is presented for efficient solution of two-dimensional few-body problems, such as quantum dots or excitonic complexes, using the stochastic variational method. The computer program can be used to calculate the energies and wave functions of various two-dimensional systems. Catalogue identifier: AEBE_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBE_v1_0.html ...
A new autopilot design for bank-to-turn (BTT) missiles is presented. In the design of autopilot, a ridge Gaussian neural network with local learning capability and fewer tuning parameters than Gaussian neural networks is proposed to model the controlled nonlinear systems. We prove that the proposed ridge Gaussian neural network, which ...
A new set of basis functions based on truncated Gaussian wavelets is proposed for optical waveguide analysis using the well-known Galerkin method. A spatially limited Gaussian wavelet train is formed by judiciously truncating the tails of Gaussian functions. The proposed set of basis functions ...
The behavior of the two exponential parameters in an even-tempered gaussian basis set is investigated as the set optimally approaches an integral transform representation of the radial portion of atomic and molecular orbitals. This approach permits a high...
Total intermolecular interaction energies are determined with a first version of the Gaussian electrostatic model (GEM-0), a force field based on a density fitting approach using s-type Gaussian functions. The total interaction energy is computed in the spirit of the sum of interacting fragment ab initio (SIBFA) force field by separately evaluating each ...
Aims: The dust emission spectrum and the brightness profile of passively heated condensed cores is analyzed in relation to their astrophysical environment. The model is used to study systematically the radiative transfer effects on essential parameters such as the dust emissivity, dust temperature, and luminosity of the cores and to derive uncertainties in typical estimates of the IR flux and ...
We report methodological and computational details of our Kohn-Sham density-functional method with Gaussian orbitals for systems with periodic boundary conditions. Our approach for the Coulomb problem is based on the direct space fast multipole method, which achieves not only linear scaling of computational time with system size but also very high accuracy in all infinite ...
Gaussian-type basis sets for the 3d Rydberg orbitals and 3d correlation orbitals are developed for the first and second-row main group elements. The numbers of the Gaussian-type functions (GTFs) used for the 3d orbitals are 1-3 for the former elements and 1-4 for the latter elements. The 3d Rydberg orbitals for the firrst-row main ...
A computational framework to obtain an accurate quantification of the Gaussian and non-Gaussian component of water molecules' diffusion through brain tissues with diffusion kurtosis imaging, is presented. The diffusion kurtosis imaging model quantifies the kurtosis, the degree of non-Gaussianity, on a direction ...
This article reports studies by Fukushima and coworkers since 1980 concerning their highly accurate numerical integral method using Gaussian quadratures to evaluate the total energy in electronic state calculations. Gauss-Legendre and Gauss-Laguerre quadratures were used for integrals in the finite and infinite regions, respectively. Our previous article ...
Results of extensive LCAO-MO-SCF calculations on BeH2 utilizing Gaussian basis functions are presented. It is established that BeH2 is linear in its ground state, and the equilibrium bond distance has been determined. Force constants and normal frequencie...
We establish the functional equivalence of a generalized class of Gaussian radial basis function (RBFs) networks and the full Takagi-Sugeno model (1983) of fuzzy inference. This generalizes an existing result which applies to the standard Gaussian RBF network and a restricted form of the Takagi-Sugeno fuzzy system. The more general ...
Explicitly correlated, n-electron, one-center s Gaussian (ECG) functions that depend on the interelectron distances in the exponent are combined with s ECGs which also depend on the interelectron separations through pre-exponential rij2 multipliers. The pre-exponentially rij2-dependent ECGs are included in the basis to better describe the interelectron ...
Expressions for integrals involving general Gaussian (s, p, d, ...) basis Bloch functions are presented. Applying the Poisson transformation and the Ewald-type partitioning scheme, all lattice sums appearing in these expressions lead to fast convergence in both direct and Fourier spaces. Numerical results produced for selected test cases show that a ...
An atomic Dirac-Fock-Roothaan program is described for generalized average energy of configurations using Gaussian-type basis functions. It can treat three kinds of atomic nuclear models of point charge, uniformly charged sphere, and Gaussian proton-charge distribution. It runs within first memories or uses disk file for intermediate ...
The anomalous spectral behaviors of a chirped Gaussian pulsed beam diffracted by an annular aperture in the turbulent atmosphere are studied. On the basis of the extended Huygens-Fresnel principle and by introducing a hard aperture function into a finite sum of complex Gaussian functions, the approximate analytical expression for the ...
Mutual expansion formulas are developed for three types of Gaussian orbitals; Hermite Gaussians, Cartesian Gaussians, and spherical Gaussians. Overlap, kinetic energy and Coulomb energy matrix elements are presented for generalized spherical basis functions proportional to ...
The local statistical properties of photographic images, when represented in a multi-scale basis, have been described using Gaussian scale mixtures. Here, we use this local description as a substrate for constructing a global field of Gaussian scale mixtures (FoGSMs). Specifically, we model multi-scale subbands as a product of an ...
Standard and augmented correlation consistent sextuple zeta (cc-pV6Z and aug-cc-pV6Z) basis sets have been determined for the second-row atoms aluminum through argon. Using these sets, dissociation energies and spectroscopic constants for the ground states of HCl, PN, and P{sub 2} have been calculated using several theoretical methods, including Moeller-Plesset perturbation ...
The influence of changes in the contracted Gaussian basis set used for ab initio calculations of nuclear magnetic resonance (NMR) phosphorous chemical shift anisotropy (CSA) tensors was investigated. The isotropic chemical shitl and chemical shift anisotropy were found to converge with increasing complexity of the basis set at the ...
The efficiency, accuracy, and stability of two different pseudo-spectral methods using scaled Hermite basis and weight functions, applied to the nonlinear Vlasov-Poisson equations in one dimension (1d-1v), are explored and compared. A variable velocity scale U is introduced into the Hermite basis and is shown to yield orders of magnitude reduction in ...
The observed abundance of high-redshift galaxies and clusters contains precious information about the properties of the initial perturbations. We present a method to compute analytically the number density of objects as a function of mass and redshift for a range of physically motivated non-Gaussian models. In these models the non-Gaussianity can be dialed ...
A new induced dipole polarization model based on interacting Gaussian charge densities is presented. In contrast to the original induced point dipole model, the Gaussian polarization model is capable of finite interactions at short distances. Aspects of convergence related to the Gaussian model will be explored. The ...
A quantum dynamics approach, called Gaussian molecular dynamics, is introduced. As in the centroid molecular dynamics, the N-body quantum system is mapped to an N-body classical system with an effective Hamiltonian arising within the variational Gaussian wave-packet approximation. The approach is exact for the harmonic oscillator and for the ...
This work presents an analytic description of the coherent excitation of a two-state quantum system by an external field with a Gaussian temporal shape and a constant frequency. A very accurate analytic approximation to the transition probability is derived by using the Dykhne-Davis-Pechukas approach. This approximation provides analytic expressions for ...
Using the H2(+) ion as an example, it is shown that the algebraic approximation to the Dirac equation in momentum space is capable of giving accurate relativistic energies for molecular systems. A small number of Gaussians are sufficient for such calculat...
The method of the penumbra, that of the reconstruction of the gaussian profile and that of the background are used to determine the in-air spatial spread of clinical electron beams. The method of the background appears to be the most accurate. Besides, the failures of the Fermi-Eyges theory in describing the beam transport are shown.
A new data-treatment procedure allows for more accurate determination of electron temperatures and electron concentrations in analytical plasmas. A Thomson scattering spectrum, useful for these determinations, is often not purely Gaussian in shape, even w...
The Navstar Global Positioning System (GPS) is a highly accurate space based navigation system providing all weather, 24 hour a day service to both military and civilian users. The system provides a Gaussian position solution with four satellites, each pr...
A method is described which provides a dc voltage corresponding to the average pulse height of input pulses with a Gaussian pulse height distribution and thereby permits accurate and successive measurements of pulse height variations by the use of a digital voltmeter and associated equipment.
The objective of this work was to implement and evaluate a method, derived by D.L. Ermak, for generating skewed random numbers using a combination of uniform random numbers. This method is shown to provide accurate approximations to a Gaussian probability...
The relationship of the concentration of air pollutants to wind direction has been determined by nonparametric regression using a Gaussian kernel. The results are smooth curves with error bars that allow for the accurate determination of the wind direction where the concentrat...
EPA Science Inventory
Reliable derivatives of digital images have always been hard to obtain, especially (but not only) at high orders. We present new filters that give more accurate derivatives than the traditional Gaussian ones. We show that the traditional filters give inco...
The authors study the problem of computing the optimal value function for a Markov Decision Process (MDP) with positive costs. Computing this function quickly and accurately is a basic step in many schemes for deciding how to act in stochastic environment...
Analyses of the statistical properties of electromagnetic scattering from random rough surfaces for finite clutter cells have assumed that the rough surface can be modeled by a Gaussian correlation function. However, some real surfaces are more accurately...
The Gaussian effective potential (GEP) is an approximation to quantum mechanics that semiquantitatively estimates quantum effects such as zero-point fluctuations and tunneling. We show how to use the GEP to compute semiclassical eigenvalues. It is well known that the GEP provides very accurate variational approximations to the ground-state energy of simple ...
The large-scale clustering of galaxies can serve as a probe of primordial non-Gaussianity in the Universe competitive with the anisotropies of the cosmic microwave background. Here, we present improved theoretical predictions which include an important, previously overlooked correction to the bias. We demonstrate that the new predictions are able to reproduce the results of ...
We review recent theoretical and computational advances in the full relativistic four-component Dirac-Kohn-Sham (DKS) approach and its application to the calculation of the electronic structure of chemical systems containing many heavy atoms. We describe our implementation of an all-electron DKS approach based on the use of G-spinor basis sets, Hermite ...
Electric field gradients at the nuclei of halogen atoms are calculated using a finite field approach. The four-component Dirac-Coulomb Hamiltonian serves as the framework, all electrons are correlated by the relativistic Fock-space coupled cluster method with single and double excitations, and the Gaunt term, the main part of the Breit interaction, is included. Large basis ...
Preoperative diagnosis of neoplasms in the parotid gland is essential for successful surgical treatment. The purpose of this study is to apply Raman spectroscopy in order to distinguish the spectral differences between pleomorphic adenoma and Warthin tumor from that of normal parotid gland tissues. Furthermore we establish the diagnostic model of the Raman spectra of neoplasms in parotid gland by ...
The problem of estimating and tracking the signal parameters of a nonstationary stochastic Morse communication signal was investigated. The signal parameters are the characteristic element durations of the Morse message. A two dimensional estimation space is assumed containing six modes for the composite mark-space signal. Each mode is assumed to be an independent Gaussian ...
As a new mode of molecular imaging, bioluminescence tomography (BLT) will have significant effect on revealing the molecular and cellular information in vivo at the whole-body small animal level because of its high sensitive detection and facile operation. However, BLT is an ill-posed problem, it is necessary to incorporate a priori knowledge into the tomographic algorithm. In this paper, a novel ...
We describe a new method to generate a smooth algebraic spline (AS) approximation of the molecular surface (MS) based on an initial coarse linear triangulation derived from the atomic coordinate information of biomolecules, present in the PDB (Protein Data Bank). Our method first constructs a triangular prism scaffold covering the MS triangulation, and then generates a piecewise polynomial ...
The authors report computational applications for the newly developed distributed approximating function (DAF) approach to real time quantal wavepacket propagation for several one-dimensional model problems. The DAF is constructed to fit all wavepackets accurately which can be represented, to the same accuracy, by a polynomial of degree M, or less, within the envelope of the ...
An ab initio method is developed for variational grand-canonical molecular electronic structure of open systems based on the Gibbs-Peierls-Boguliobov inequality. We describe the theory and a practical method for performing the calculations within standard quantum chemistry codes using Gaussian basis sets. The computational effort scales similarly to the ...
Linear models have already been proved accurate enough to recover spectral functions. We have resorted to such linear models to recover spectral daylight with the response of no more than a few real sensors. We performed an exhaustive search to obtain the best set of Gaussian sensors with a combination of optimum spectral position and bandwidth. We also ...
We present an accurate and efficient technique for calculating thermal X-ray absorption fine structure (XAFS) Debye-Waller factors (DWFs) applicable to crystalline materials. Using Density Functional Theory on a 3�3�3 supercell pattern of MnO structure, under the nonlocal hybrid B3LYP functional paired with Gaussian local basis ...
The ground states of the positronic complexes LiPs, NaPs, e+Be, e+Mg, and of the parent ordinary-matter systems have been simulated by means of the all-electron fixed-node diffusion Monte Carlo (DMC) method. Positron affinities and positronium binding energies are computed by direct difference between the DMC energy results. LiPs was recomputed in order to test the possibility of approximating the ...
We compare different nonlinear approximations to gravitational clustering in the weakly nonlinear regime, using as a comparative statistic the evolution of non-Gaussianity which can characterized by a set of numbers Sp describing connected moments of the density field at the lowest order in (the mean value of (delta squared)):(the mean value of deltanc approximately = Sn(the ...
This paper presents a novel numerical method, the moving least square Ritz method (MLS-Ritz), for free vibration analysis of classical thin plates. The proposed method utilizes the strength of the moving least square approach to define the Ritz trial function for the transverse displacement of the plates. A set of points is pre-selected on the calculation domain of a plate that forms the ...
The ITER transmission line system will transport 20 MW of power from 24 1-MW gyrotrons at 170GHz using overmoded metallic cylindrical waveguides that are 63.5 mm in diameter with quarter wavelength corrugations. Each line must have less than 83% loss, requiring precise loss measurements of waveguide components. An accurate measurement of the loss in these waveguide components ...
We accurately analyze the {sup 6}He+{sup 209}Bi scattering at 19 and 22.5 MeV near the Coulomb barrier energy, using the continuum-discretized coupled-channels (CDCC) method based on the n+n+ {sup 4}He+{sup 209}Bi four-body model. The three-body breakup continuum of {sup 6}He is discretized by diagonalizing the internal Hamiltonian of {sup 6}He in a space spanned by the ...
Intuitively population based algorithms such as genetic programming provide a natural environment for supporting solutions that learn to decompose the overall task between multiple individuals, or a team. This work presents a framework for evolving teams without recourse to prespecifying the number of cooperating individuals. To do so, each individual evolves a mapping to a distribution of ...
This research combined open path FTIR (OP-FTIR) technique and computed tomography (CT) to reconstruct air contaminant concentration distribution in a two-dimensional plane. Remote sensing FTIR instrument was used to scan radial beam geometry and obtain path integrated concentration (PIC) data of acetone gas in the measuring plane. Smooth basis function minimization (SBFM) ...
The results of Doppler spectroscopy of hydrogen Balmer lines from a stainless steel (SS) and copper (Cu) hollow cathode (HC) glow discharge in ammonia and argon-ammonia mixture are reported. The experimental profiles in ammonia discharge are fitted well by superposing three Gaussian profiles. The half widths, in energy units, of narrow and medium Gaussians ...
Eigenvectors have been calculated for the A=18, 19, 20, 21, and 26 nuclei in an sd shell basis. The decomposition of these states into their shell model components shows, in agreement with other recent work, that this distribution is not a single Gaussian. We find that the largest amplitudes are distributed approximately in a Gaussian ...
On the basis of the fact that a hard-edged elliptical aperture can be expanded approximately as a finite sum of complex Gaussian functions in tensor form, an analytical propagation expression for an elliptical Gaussian beam (EGB) through a misaligned optical system with an elliptical aperture is derived by use of vector integration. ...
We introduce a Gaussian quantum operator representation, using the most general possible multimode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems and also includes generalized squeezed-state and thermal bases. It enables ...
Gaussian 76 is a general-purpose computer program for ab initio Hartree-Fock molecular orbital calculations. It can handle basis sets involving s, p and d-type gaussian functions. Certain standard sets (STO-3G, 4-31G, 6-31G*, etc.) are stored internally for easy use. Closed shell (RHF) or unrestricted open shell (UHF) wave functions ...
A method for the Gaussian basis set generation for molecular relativistic Dirac-Fock calculations is proposed. The basis set exponents are obtained in the process of stochastic optimization (a hybrid of simplex and simulated annealing optimization techniques has been employed) of a functional defined as the sum of squares of ...
This paper reports on numerical experiments on the `independent component analysis' (ICA) of some nonGaussian stochastic processes. It is found that the orthonormal basis discovered by ICA are strikingly close to wavelet basis. 1 Introduction: ICA and CHA Independent component analysis (ICA) consists in finding a linear decomposition ...
Methods based on an exact exchange operator (EX) are increasingly popular, but are still restricted to analytical basis functions (e.,. Gaussians) for medium system sizes. We here introduce a localized resolution-of-identity approach for the two-electron Coulomb operator, based on expanding single-particle basis function products ...
This paper proposes a joint maximum likelihood and Bayesian methodology for estimating Gaussian mixture models. In Bayesian inference, the distributions of parameters are modeled, characterized by hyperparameters. In the case of Gaussian mixtures, the distributions of parameters are considered as Gaussian for the mean, Wishart for the ...
The phase characteristics of Gaussian beams in negative refractive index (NRI) slabs have been quantitatively investigated via the finite-difference time-domain (FDTD) method. The phase and magnitude distributions for both the normal and oblique incidences of continuous wave Gaussian beams are presented. For the normal incidence, all three contributions of ...
Some dynamic environments are characterized by time histories that are not Gaussian. A more accurate simulation of these environments can be generated if a realization of a non Gaussian time history can be reproduced which has a specified auto spectral density (also called power spectral density) and a specified skewness and kurtosis ...
The authors propose a new linear-scaling method for the fast evaluation of Coulomb integrals with Gaussian basis functions called the Gaussian and finite-element Coulomb (GFC) method. In this method, the Coulomb potential is expanded in a basis of mixed Gaussian and finite-element auxiliary ...
The assumed joint probability density function (PDF) between vertical velocity and conserved temperature and total water scalars has been suggested to be a relatively computationally inexpensive and unified subgrid-scale (SGS) parameterization for boundary layer clouds and turbulent moments. This paper analyzes the performance of five families of PDFs using large-eddy simulations of deep ...
This paper proposes non-Gaussian models for parametric spectral estimation with application to event-related desynchronization (ERD) estimation of nonstationary EEG. Existing approaches for time-varying spectral estimation use time-varying autoregressive (TVAR) state-space models with Gaussian state noise. The parameter estimation is solved by a ...
... kinds of rewards for accurate probability esti- mation do improve performance over ... No Case Basis for Posterior Odds Bayesian calculation ...
... basis for making more accurate fuel requirements estimates. ... pect to the mission and type of employment; to the speed at which ...
... there does not exist an adequate means by ... Interest were, "How accurately can progress in management be ... interviewed on a yearly basis to keep in ...
The properties of a pair of vortices embedded in a Gaussian beam focused by a high numerical-aperture are studied on the basis of vector Debye integral. The vortices move and rotate in the vicinity of the focal plane for a pair of vortices with equal topological charges. For incident beam with a pair of vortices with opposite topological charges, the ...
The coupled-cluster wave function factorizes to a very good approximation into a product of an intrinsic wave function and a Gaussian for the center-of-mass coordinate. The width of the Gaussian is in general not identical to the oscillator length of the underlying single-particle basis. The quality of the separation can be verified by ...
We have theoretically studied the pulsed regime of electromagnetically induced transparency. In particular, simulations of propagation of Gaussian and 0? copropagating laser pulses in a medium consisting of three-level ? atoms have been performed. It has been found that even at the two-photon resonance, the length of propagation for the 0? pulses is much smaller than the one ...
We demonstrate how very precise (virtually exact) solutions of various quantum mechanical problems can be obtained using the variational method with explicitly correlated Gaussian basis functions (ECGFs). As examples we consider several benchmark systems, such as few-electron atoms and molecules, as well as Coulomb systems containing exotic particles. We ...
-Fock (HF) with localized Gaussian basis sets LANL2dz using the Gaussian 03 software package.40 As expected://pubs.acs.org|doi:10.1021/ja9005749 #12;incorporated to the VASP code.37 The generalized gradient ap- proximation (GGA) facets (right) calculated using GGA (VASP) methodology. (b) The GGA optimized geometries of passivated Cd
Reconstructed meteorological data are often used in some form of long-term wind trajectory models for estimating the historical impacts of atmospheric emissions. Meteorological data for the straight-line Gaussian plume model are put into a joint frequency distribution, a three-dimensional array describing atmospheric wind direction, speed, and stability. Methods using the ...
Microwave background temperature and polarization observations are a powerful way to constrain cosmological parameters if the likelihood function can be calculated accurately. The temperature and polarization fields are correlated, partial-sky coverage correlates power spectrum estimators at different l, and the likelihood function for a theory spectrum given a set of observed ...
Representative surface reconstruction algorithms taking a gradient field as input enforce the integrability constraint in a discrete manner. While enforcing integrability allows the subsequent integration to produce surface heights, existing algorithms have one or more of the following disadvantages: They can only handle dense per-pixel gradient fields, smooth out sharp features in a partially ...
Automatic multi-modal image registration is central to numerous tasks in medical imaging today and has a vast range of applications e.g., image guidance, atlas construction, etc. In this paper, we present a novel multi-modal 3D non-rigid registration algorithm where in 3D images to be registered are represented by their corresponding local frequency maps efficiently computed using the Riesz ...
Alpha rhythm is a major component of spontaneous electroencephalographic (EEG) data. We develop a novel method that can be used to estimate the instantaneous phases and amplitudes of the alpha rhythm with high accuracy by modeling the alpha rhythm phase and amplitude as Markov random field (MRF) models. By using a belief propagation technique, we construct an exact-inference algorithm that can be ...
Implicit solvent models approximate the effects of solvent through a potential of mean force and therefore make solvated simulations computationally efficient. Yet despite their computational efficiency, the inherent approximations made by implicit solvent models can sometimes lead to inaccurate results. To test the accuracy of a number of popular implicit solvent models, we determined whether ...
The variational Gaussian wave-packet method for computation of equilibrium density matrices of quantum many-body systems is further developed. The density matrix is expressed in terms of Gaussian resolution, in which each Gaussian is propagated independently in imaginary time beta=(k(B)T)(-1) starting at the classical limit beta=0. For ...
Vibrational spacings for H/sup +//sub 3/ are calculated for two different fits to the potential energy surface of Dykstra and Swope. We use a variational calculation with a distributed Gaussian basis (DGB); the calculation is shown to be simple and efficient.
Relativistic many-body perturbation theory calculations have been performed on the ground state of Ne atom. The reference state of the single configuration Dirac-Fock wave function was computed using an expansion of Gaussian basis functions. Second- and t...
Formulas are derived for the density matrices belonging to an n-particle wave function built on the basis of single-center explicitly correlated Gaussian basis functions. An explicit formula for the first-order density matrix, P(r{sub 1}, r{sub 1}{prime}), is obtained for computing the probability distribution P(r{sub 1}, r{sub 1}). ...
We computed the infrared vibrational modes and frequencies of a group of four primary amines, four secondary amines, and three tertiary amines. The computations make use of the Gaussian 86 Program Package with the 3-21G basis set and the Hartree-Fock opti...
We have computed infrared vibrational spectra of a group of halogen-substituted alcohols, mercaptans, and sulfides. The computations are based on the use of the Gaussian 82 Program Package, using Hartree-Fock procedures with the 3-21 G basis set. The ulti...
recovering the correlation energy of valence electrons. Size increases by adding shells (or sets) of fns for periodic materials; In metals, for ex, it is appropriate to treat valence electrons as free electrons An "orbital" is a one-electron function AOs represented by atom-centered Gaussians in most quantum chemistry
