Coupled cluster Green function: Model involving single and double excitations
NASA Astrophysics Data System (ADS)
Bhaskaran-Nair, Kiran; Kowalski, Karol; Shelton, William A.
2016-04-01
In this paper, we report on the development of a parallel implementation of the coupled-cluster (CC) Green function formulation (GFCC) employing single and double excitations in the cluster operator (GFCCSD). A key aspect of this work is the determination of the frequency dependent self-energy, Σ(ω). The detailed description of the underlying algorithm is provided, including approximations used that preserve the pole structure of the full GFCCSD method, thereby reducing the computational costs while maintaining an accurate character of methodology. Furthermore, for systems with strong local correlation, our formulation reveals a diagonally dominate block structure where as the non-local correlation increases, the block size increases proportionally. To demonstrate the accuracy of our approach, several examples including calculations of ionization potentials for benchmark systems are presented and compared against experiment.
Coupled cluster Green function: Model involving single and double excitations.
Bhaskaran-Nair, Kiran; Kowalski, Karol; Shelton, William A
2016-04-14
In this paper, we report on the development of a parallel implementation of the coupled-cluster (CC) Green function formulation (GFCC) employing single and double excitations in the cluster operator (GFCCSD). A key aspect of this work is the determination of the frequency dependent self-energy, Σ(ω). The detailed description of the underlying algorithm is provided, including approximations used that preserve the pole structure of the full GFCCSD method, thereby reducing the computational costs while maintaining an accurate character of methodology. Furthermore, for systems with strong local correlation, our formulation reveals a diagonally dominate block structure where as the non-local correlation increases, the block size increases proportionally. To demonstrate the accuracy of our approach, several examples including calculations of ionization potentials for benchmark systems are presented and compared against experiment. PMID:27083702
Locally Renormalized Coupled-Cluster Equations for Singly and Doubly Excited Clusters
Kowalski, Karol
2006-07-10
The Numerator-Denominator Connected (NDC) Expansion for the Coupled-Cluster (CC) method [K. Kowalski, P. Piecuch, J. Chem. Phys. 122 (2005) 074107], is used to construct a new set of stationary conditions for approximate coupled-cluster approaches. Several CC approximations based on models involving singles and doubles (CCSD) as well as singles, doubles, and triples (CCSDT) are developed and discussed in the context of ground-state applications. The resulting locally-renormalized CCSD (LR-CCSD) and CCSDT (LR-CCSDT) equations are shown to regularize the expressions for the cluster amplitudes in the challenging situations that occur when the orbital energy differences approach zero. Affordable schemes for handling the local denominators (all-holes-Jn coupling), that naturally appear in locally renormalized formalisms, are also discussed.
NASA Astrophysics Data System (ADS)
Evangelista, Francesco A.
2011-06-01
We report a general implementation of alternative formulations of single-reference coupled cluster theory (extended, unitary, and variational) with arbitrary-order truncation of the cluster operator. These methods are applied to compute the energy of Ne and the equilibrium properties of HF and C2. Potential energy curves for the dissociation of HF and the BeH2 model computed with the extended, variational, and unitary coupled cluster approaches are compared to those obtained from the multireference coupled cluster approach of Mukherjee et al. [J. Chem. Phys. 110, 6171 (1999)] and the internally contracted multireference coupled cluster approach [F. A. Evangelista and J. Gauss, J. Chem. Phys. 134, 114102 (2011), 10.1063/1.3559149]. In the case of Ne, HF, and C2, the alternative coupled cluster approaches yield almost identical bond length, harmonic vibrational frequency, and anharmonic constant, which are more accurate than those from traditional coupled cluster theory. For potential energy curves, the alternative coupled cluster methods are found to be more accurate than traditional coupled cluster theory, but are three to ten times less accurate than multireference coupled cluster approaches. The most challenging benchmark, the BeH2 model, highlights the strong dependence of the alternative coupled cluster theories on the choice of the Fermi vacuum. When evaluated by the accuracy to cost ratio, the alternative coupled cluster methods are not competitive with respect to traditional CC theory, in other words, the simplest theory is found to be the most effective one.
Full coupled cluster singles, doubles and triples model for the description of electron correlation
Hoffmann, M.R.
1984-10-01
Equations for the determination of the cluster coefficients in a full coupled cluster theory involving single, double and triple cluster operators with respect to an independent particle reference, expressible as a single determinant of spin-orbitals, are derived. The resulting wave operator is full, or untruncated, consistant with the choice of cluster operator truncation and the requirements of the connected cluster theorem. A time-independent diagrammatic approach, based on second quantization and the Wick theorem, is employed. Final equations are presented that avoid the construction of rank three intermediary tensors. The model is seen to be a computationally viable, size-extensive, high-level description of electron correlation in small polyatomic molecules.
NASA Astrophysics Data System (ADS)
Luo, Qing; Li, Dongxu; Jiang, Jianping
2014-01-01
Control moment gyros (CMGs) are widely used as actuators for attitude control in spacecraft. However, micro-vibrations produced by CMGs will degrade the pointing performance of high-sensitivity instruments on-board the spacecraft. This paper addresses dynamic modelling and performs an analysis on the micro-vibration isolation for a single gimbal CMG (SGCMG) cluster. First, an analytical model was developed to describe both the coupled SGCMG cluster and the multi-axis isolation system that can express the dynamic outputs. This analytical model accurately reflects the mass and inertia properties, the gyroscopic effects and flexible modes of the coupled system, which can be generalized for isolation applications of SGCMG clusters. Second, the analytical model was validated using MSC.NASTRAN software based on the finite element technique. The dynamic characteristics of the coupled system are affected by the mass distribution and the gyroscopic effects of the SGCMGs. The gyroscopic effects produced by the rotary flywheel will stiffen or soften several of the structural modes of the coupled system. In addition, the gyroscopic effect of each SGCMG can interact with or counteract that of others, which induce vibration modes coupled together. Finally, the performance of the passive isolation was analysed. It was demonstrated that the gyroscopic effects should be considered in isolation studies on SGCMG clusters; otherwise, the isolation performance will be underestimated if they are ignored.
Jankowski, K.; Kowalski, K.; Jankowski, P.
1995-03-05
Single-reference coupled-cluster (SR-CC) methods parametrized with respect to four alternative reference-state configurations and orbital sets are applied to the simple H4 model system in which the degree of quasi-degeneracy of the electronic states can be varied in a wide range. Both the ground state and 10 excited states are considered with the aim of numerically studying the attainability and properties of multiple solutions of the system of nonlinear equations for the cluster amplitudes. Comparisons of up to four alternative descriptions of a given state in terms of various solutions of the SR-CC equations are made. It is found that for some excited states different parametrizations yield very close results and that the classification of the solutions into standard and nonstandard ones may not be straightforward. 15 refs., 12 tabs.
Density-fitted singles and doubles coupled cluster on graphics processing units
Sherrill, David; Sumpter, Bobby G; DePrince, III, A. Eugene
2014-01-01
We adapt an algorithm for singles and doubles coupled cluster (CCSD) that uses density fitting (DF) or Cholesky decomposition (CD) in the construction and contraction of all electron repulsion integrals (ERI s) for use on heterogeneous compute nodes consisting of a multicore CPU and at least one graphics processing unit (GPU). The use of approximate 3-index ERI s ameliorates two of the major difficulties in designing scientific algorithms for GPU s: (i) the extremely limited global memory on the devices and (ii) the overhead associated with data motion across the PCI bus. For the benzene trimer described by an aug-cc-pVDZ basis set, the use of a single NVIDIA Tesla C2070 (Fermi) GPU accelerates a CD-CCSD computation by a factor of 2.1, relative to the multicore CPU-only algorithm that uses 6 highly efficient Intel core i7-3930K CPU cores. The use of two Fermis provides an acceleration of 2.89, which is comparable to that observed when using a single NVIDIA Kepler K20c GPU (2.73).
Noga, Jozef; Šimunek, Ján
2010-09-14
We propose an alternative new approach to obtain the Slater determinant ground state solution within an independent-particle approximation using the exponential ansatz for the wave function (Thouless theorem) and exact treatment in terms of variational coupled cluster singles. Although the resulting nonlinear equations formally represent nonterminating expansions, these can be reformulated to finite expansions in terms of the density matrix correction. The latter can be exactly calculated using a very simple recurrence relation within the occupied-occupied block, while the complementary occupied-virtual and virtual-virtual blocks are related and trivially obtained by subsequent matrix multiplications involving the amplitudes of the single-excitation operator. The density matrix is naturally idempotent in any step of the iterative procedure. Blocks of the density matrix are without any further change, apart from the sign, used in the orbital transformation matrix. The latter is not a unitary one, hence leading to nonorthogonal and unnormalized molecular orbitals. These are, however, biorthogonal and can be easily orthonormalized per blocks, if needed in the post-SCF calculations. Formulation is diagonalization free, and the implementation can be easily parallelized. Finally, the formulation provides a challenging way to the solution with "a priori" localized orbitals, a way toward a linear scaling algorithm. PMID:26616071
NASA Technical Reports Server (NTRS)
Lee, Timothy J.; Langhoff, Stephen R. (Technical Monitor)
1997-01-01
Recent work on the development of single-reference perturbation theories for the study of excited electronic states will be discussed. The utility of these methods will be demonstrated by comparison to linear-response coupled-cluster excitation energies. Results for some halogen molecules of interest in stratospheric chemistry will be presented.
A hierarchy of local coupled cluster singles and doubles response methods for ionization potentials
NASA Astrophysics Data System (ADS)
Wälz, Gero; Usvyat, Denis; Korona, Tatiana; Schütz, Martin
2016-02-01
We present a hierarchy of local coupled cluster (CC) linear response (LR) methods to calculate ionization potentials (IPs), i.e., excited states with one electron annihilated relative to a ground state reference. The time-dependent perturbation operator V(t), as well as the operators related to the first-order (with respect to V(t)) amplitudes and multipliers, thus are not number conserving and have half-integer particle rank m. Apart from calculating IPs of neutral molecules, the method offers also the possibility to study ground and excited states of neutral radicals as ionized states of closed-shell anions. It turns out that for comparable accuracy IPs require a higher-order treatment than excitation energies; an IP-CC LR method corresponding to CC2 LR or the algebraic diagrammatic construction scheme through second order performs rather poorly. We therefore systematically extended the order with respect to the fluctuation potential of the IP-CC2 LR Jacobian up to IP-CCSD LR, keeping the excitation space of the first-order (with respect to V(t)) cluster operator restricted to the m = /1 2 ⊕ /3 2 subspace and the accuracy of the zero-order (ground-state) amplitudes at the level of CC2 or MP2. For the more expensive diagrams beyond the IP-CC2 LR Jacobian, we employ local approximations. The implemented methods are capable of treating large molecular systems with hundred atoms or more.
Rigamonti, Luca; Cornia, Andrea; Nava, Andrea; Perfetti, Mauro; Boulon, Marie-Emmanuelle; Barra, Anne-Laure; Zhong, Xiaoliang; Park, Kyungwha; Sessoli, Roberta
2014-08-28
Single-crystal torque magnetometry performed on weakly-coupled polynuclear systems provides access to a complete description of single-site anisotropy tensors. Variable-temperature, variable-field torque magnetometry was used to investigate triiron(III) complex [Fe3La(tea)2(dpm)6] (Fe3La), a lanthanum(III)-centred variant of tetrairon(III) single molecule magnets (Fe4) (H3tea = triethanolamine, Hdpm = dipivaloylmethane). Due to the presence of the diamagnetic lanthanoid, magnetic interactions among iron(III) ions (si = 5/2) are very weak (<0.1 cm(−1)) and the magnetic response of Fe3La is predominantly determined by single-site anisotropies. The local anisotropy tensors were found to have Di > 0 and to be quasi-axial with |Ei/Di| ~ 0.05. Their hard axes form an angle of approximately 70° with the threefold molecular axis, which therefore corresponds to an easy magnetic direction for the molecule. The resulting picture was supported by a High Frequency EPR investigation and by DFT calculations. Our study confirms that the array of peripheral iron(III) centres provides substantially noncollinear anisotropy contributions to the ground state of Fe4 complexes, which are of current interest in molecular magnetism and spintronics. PMID:25014192
Parrish, Robert M.; Sherrill, C. David; Hohenstein, Edward G.; Kokkila, Sara I. L.; Martínez, Todd J.
2014-05-14
We apply orbital-weighted least-squares tensor hypercontraction decomposition of the electron repulsion integrals to accelerate the coupled cluster singles and doubles (CCSD) method. Using accurate and flexible low-rank factorizations of the electron repulsion integral tensor, we are able to reduce the scaling of the most vexing particle-particle ladder term in CCSD from O(N{sup 6}) to O(N{sup 5}), with remarkably low error. Combined with a T{sub 1}-transformed Hamiltonian, this leads to substantial practical accelerations against an optimized density-fitted CCSD implementation.
Kowalski, Karol; Hammond, Jeffrey R.; De Jong, Wibe A.
2007-10-28
This paper discusses practical scheme of correcting the linear response coupled cluster with singles and doubles (LR-CCSD) equations by shifting their poles, corresponding to the equation-of-motion CCSD (EOMCCSD) excitation energies, through adding the no-iterative corrections due to triples to the EOMCCSD excitation energies. A simple criterion is derived for the excited states to be corrected in the spectral resolution of similarity transformed Hamiltonian on the CCSD level. Benchmark calculations were performed to compare the accuracies of static and dynamic polarizabilities obtained in the way with the CC3 and CCSDT counterparts.
Bozkaya, Uğur
2016-04-14
An efficient implementation of the asymmetric triples correction for the coupled-cluster singles and doubles [ΛCCSD(T)] method [S. A. Kucharski and R. J. Bartlett, J. Chem. Phys. 108, 5243 (1998); T. D. Crawford and J. F. Stanton, Int. J. Quantum Chem. 70, 601 (1998)] with the density-fitting [DF-ΛCCSD(T)] approach is presented. The computational time for the DF-ΛCCSD(T) method is compared with that of ΛCCSD(T). Our results demonstrate that the DF-ΛCCSD(T) method provide substantially lower computational costs than ΛCCSD(T). Further application results show that the ΛCCSD(T) and DF-ΛCCSD(T) methods are very beneficial for the study of single bond breaking problems as well as noncovalent interactions and transition states. We conclude that ΛCCSD(T) and DF-ΛCCSD(T) are very promising for the study of challenging chemical systems, where the coupled-cluster singles and doubles with perturbative triples method fails. PMID:27083709
NASA Astrophysics Data System (ADS)
Bozkaya, Uǧur
2016-04-01
An efficient implementation of the asymmetric triples correction for the coupled-cluster singles and doubles [ΛCCSD(T)] method [S. A. Kucharski and R. J. Bartlett, J. Chem. Phys. 108, 5243 (1998); T. D. Crawford and J. F. Stanton, Int. J. Quantum Chem. 70, 601 (1998)] with the density-fitting [DF-ΛCCSD(T)] approach is presented. The computational time for the DF-ΛCCSD(T) method is compared with that of ΛCCSD(T). Our results demonstrate that the DF-ΛCCSD(T) method provide substantially lower computational costs than ΛCCSD(T). Further application results show that the ΛCCSD(T) and DF-ΛCCSD(T) methods are very beneficial for the study of single bond breaking problems as well as noncovalent interactions and transition states. We conclude that ΛCCSD(T) and DF-ΛCCSD(T) are very promising for the study of challenging chemical systems, where the coupled-cluster singles and doubles with perturbative triples method fails.
NASA Astrophysics Data System (ADS)
Cullen, John M.; Zerner, Michael C.
1982-10-01
From the diagrammatic construction of the full coupled-cluster theory of all single and double excitations, a linearized theory, a direct configuration interaction theory (CISD), a CEPA-like theory, and a linked singles and doubles (LSD) theory are separated. These theories are then compared with one another, with the results from full fourth-order perturbation theory, and with exact results when available. The LSD model, corresponding to the removal of unlinked terms of the CISD, and its spin adapted version, appear most accurate in Pariser-Parr-Pople studies where the exact numbers are known. Examples within the localized bond model are given indicating that this model is also the most successful of those examined in generating not only the basis set correlation, but the necessary delocalization and polarization required to correct for the zeroth-order local description.
Minati, Ludovico E-mail: ludovico.minati@unitn.it
2014-12-01
In this paper, experimental evidence of multiple synchronization phenomena in a large (n = 30) ring of chaotic oscillators is presented. Each node consists of an elementary circuit, generating spikes of irregular amplitude and comprising one bipolar junction transistor, one capacitor, two inductors, and one biasing resistor. The nodes are mutually coupled to their neighbours via additional variable resistors. As coupling resistance is decreased, phase synchronization followed by complete synchronization is observed, and onset of synchronization is associated with partial synchronization, i.e., emergence of communities (clusters). While component tolerances affect community structure, the general synchronization properties are maintained across three prototypes and in numerical simulations. The clusters are destroyed by adding long distance connections with distant notes, but are otherwise relatively stable with respect to structural connectivity changes. The study provides evidence that several fundamental synchronization phenomena can be reliably observed in a network of elementary single-transistor oscillators, demonstrating their generative potential and opening way to potential applications of this undemanding setup in experimental modelling of the relationship between network structure, synchronization, and dynamical properties.
Goings, Joshua J.; Li, Xiaosong; Caricato, Marco; Frisch, Michael J.
2014-10-28
Methods for fast and reliable computation of electronic excitation energies are in short supply, and little is known about their systematic performance. This work reports a comparison of several low-scaling approximations to the equation of motion coupled cluster singles and doubles (EOM–CCSD) and linear-response coupled cluster singles and doubles (LR–CCSD) equations with other single reference methods for computing the vertical electronic transition energies of 11 small organic molecules. The methods, including second order equation-of-motion many-body perturbation theory (EOM–MBPT2) and its partitioned variant, are compared to several valence and Rydberg singlet states. We find that the EOM–MBPT2 method was rarely more than a tenth of an eV from EOM–CCSD calculated energies, yet demonstrates a performance gain of nearly 30%. The partitioned equation-of-motion approach, P–EOM–MBPT2, which is an order of magnitude faster than EOM–CCSD, outperforms the CIS(D) and CC2 in the description of Rydberg states. CC2, on the other hand, excels at describing valence states where P–EOM–MBPT2 does not. The difference between the CC2 and P–EOM–MBPT2 can ultimately be traced back to how each method approximates EOM–CCSD and LR–CCSD. The results suggest that CC2 and P–EOM–MBPT2 are complementary: CC2 is best suited for the description of valence states while P–EOM–MBPT2 proves to be a superior O(N{sup 5}) method for the description of Rydberg states.
NASA Astrophysics Data System (ADS)
Hohenstein, Edward G.; Kokkila, Sara I. L.; Parrish, Robert M.; Martínez, Todd J.
2013-03-01
The second-order approximate coupled cluster singles and doubles method (CC2) is a valuable tool in electronic structure theory. Although the density fitting approximation has been successful in extending CC2 to larger molecules, it cannot address the steep O(N^5) scaling with the number of basis functions, N. Here, we introduce the tensor hypercontraction (THC) approximation to CC2 (THC-CC2), which reduces the scaling to O(N^4) and the storage requirements to O(N^2). We present an algorithm to efficiently evaluate the THC-CC2 correlation energy and demonstrate its quartic scaling. This implementation of THC-CC2 uses a grid-based least-squares THC (LS-THC) approximation to the density-fitted electron repulsion integrals. The accuracy of the CC2 correlation energy under these approximations is shown to be suitable for most practical applications.
Bozkaya, Uğur; Sherrill, C David
2016-05-01
An efficient implementation is presented for analytic gradients of the coupled-cluster singles and doubles (CCSD) method with the density-fitting approximation, denoted DF-CCSD. Frozen core terms are also included. When applied to a set of alkanes, the DF-CCSD analytic gradients are significantly accelerated compared to conventional CCSD for larger molecules. The efficiency of our DF-CCSD algorithm arises from the acceleration of several different terms, which are designated as the "gradient terms": computation of particle density matrices (PDMs), generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the relaxed PDMs and GFM, back-transformation of PDMs and GFM to the atomic orbital (AO) basis, and evaluation of gradients in the AO basis. For the largest member of the alkane set (C10H22), the computational times for the gradient terms (with the cc-pVTZ basis set) are 2582.6 (CCSD) and 310.7 (DF-CCSD) min, respectively, a speed up of more than 8-folds. For gradient related terms, the DF approach avoids the usage of four-index electron repulsion integrals. Based on our previous study [U. Bozkaya, J. Chem. Phys. 141, 124108 (2014)], our formalism completely avoids construction or storage of the 4-index two-particle density matrix (TPDM), using instead 2- and 3-index TPDMs. The DF approach introduces negligible errors for equilibrium bond lengths and harmonic vibrational frequencies. PMID:27155621
NASA Astrophysics Data System (ADS)
Bozkaya, Uǧur; Sherrill, C. David
2016-05-01
An efficient implementation is presented for analytic gradients of the coupled-cluster singles and doubles (CCSD) method with the density-fitting approximation, denoted DF-CCSD. Frozen core terms are also included. When applied to a set of alkanes, the DF-CCSD analytic gradients are significantly accelerated compared to conventional CCSD for larger molecules. The efficiency of our DF-CCSD algorithm arises from the acceleration of several different terms, which are designated as the "gradient terms": computation of particle density matrices (PDMs), generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the relaxed PDMs and GFM, back-transformation of PDMs and GFM to the atomic orbital (AO) basis, and evaluation of gradients in the AO basis. For the largest member of the alkane set (C10H22), the computational times for the gradient terms (with the cc-pVTZ basis set) are 2582.6 (CCSD) and 310.7 (DF-CCSD) min, respectively, a speed up of more than 8-folds. For gradient related terms, the DF approach avoids the usage of four-index electron repulsion integrals. Based on our previous study [U. Bozkaya, J. Chem. Phys. 141, 124108 (2014)], our formalism completely avoids construction or storage of the 4-index two-particle density matrix (TPDM), using instead 2- and 3-index TPDMs. The DF approach introduces negligible errors for equilibrium bond lengths and harmonic vibrational frequencies.
NASA Astrophysics Data System (ADS)
Gwaltney, Steven R.; Sherrill, C. David; Head-Gordon, Martin; Krylov, Anna I.
2000-09-01
We present a general perturbative method for correcting a singles and doubles coupled-cluster energy. The coupled-cluster wave function is used to define a similarity-transformed Hamiltonian, which is partitioned into a zeroth-order part that the reference problem solves exactly plus a first-order perturbation. Standard perturbation theory through second-order provides the leading correction. Applied to the valence optimized doubles (VOD) approximation to the full-valence complete active space self-consistent field method, the second-order correction, which we call (2), captures dynamical correlation effects through external single, double, and semi-internal triple and quadruple substitutions. A factorization approximation reduces the cost of the quadruple substitutions to only sixth order in the size of the molecule. A series of numerical tests are presented showing that VOD(2) is stable and well-behaved provided that the VOD reference is also stable. The second-order correction is also general to standard unwindowed coupled-cluster energies such as the coupled-cluster singles and doubles (CCSD) method itself, and the equations presented here fully define the corresponding CCSD(2) energy.
Coupled Cluster Methods in Lattice Gauge Theory
NASA Astrophysics Data System (ADS)
Watson, Nicholas Jay
Available from UMI in association with The British Library. Requires signed TDF. The many body coupled cluster method is applied to Hamiltonian pure lattice gauge theories. The vacuum wavefunction is written as the exponential of a single sum over the lattice of clusters of gauge invariant operators at fixed relative orientation and separation, generating excitations of the bare vacuum. The basic approximation scheme involves a truncation according to geometrical size on the lattice of the clusters in the wavefunction. For a wavefunction including clusters up to a given size, all larger clusters generated in the Schrodinger equation are discarded. The general formalism is first given, including that for excited states. Two possible procedures for discarding clusters are considered. The first involves discarding clusters describing excitations of the bare vacuum which are larger than those in the given wavefunction. The second involves rearranging the clusters so that they describe fluctuations of the gauge invariant excitations about their self-consistently calculated expectation values, and then discarding fluctuations larger then those in the given wavefunction. The coupled cluster method is applied to the Z_2 and Su(2) models in 2 + 1D. For the Z_2 model, the first procedure gives poor results, while the second gives wavefunctions which explicitly display a phase transition with critical couplings in good agreement with those obtained by other methods. For the SU(2) model, the first procedure also gives poor results, while the second gives vacuum wavefunctions valid at all couplings. The general properties of the wavefunctions at weak coupling are discussed. Approximations with clusters spanning up to four plaquettes are considered. Excited states are calculated, yielding mass gaps with fair scaling properties. Insight is obtained into the form of the wavefunctions at all couplings.
Diagrammatic Vibrational Coupled-Cluster
NASA Astrophysics Data System (ADS)
Faucheaux, Jacob A.; Hirata, So
2015-06-01
A diagrammatic vibrational coupled-cluster method for calculation of zero-point energies and an equation-of-motion coupled-cluster method for calculation of anharmonic vibrational frequencies are developed. The methods, which we refer to as XVCC and EOM-XVCC respectively, rely on the size-extensive vibrational self-consistient field (XVSCF) method for reference wave functions. The methods retain the efficiency advantages of XVSCF making them suitable for applications to large molecules and solids, while they are numerically shown to accurately predict zero-point energies and frequencies of small molecules as well. In particular, EOM-XVCC is shown to perform well for modes which undergo Fermi resonance where traditional perturbative methods fail. Rules for the systematic generation and interpretation of the XVCC and EOM-XVCC diagrams to any order are presented.
Pair extended coupled cluster doubles
Henderson, Thomas M.; Scuseria, Gustavo E.; Bulik, Ireneusz W.
2015-06-07
The accurate and efficient description of strongly correlated systems remains an important challenge for computational methods. Doubly occupied configuration interaction (DOCI), in which all electrons are paired and no correlations which break these pairs are permitted, can in many cases provide an accurate account of strong correlations, albeit at combinatorial computational cost. Recently, there has been significant interest in a method we refer to as pair coupled cluster doubles (pCCD), a variant of coupled cluster doubles in which the electrons are paired. This is simply because pCCD provides energies nearly identical to those of DOCI, but at mean-field computational cost (disregarding the cost of the two-electron integral transformation). Here, we introduce the more complete pair extended coupled cluster doubles (pECCD) approach which, like pCCD, has mean-field cost and reproduces DOCI energetically. We show that unlike pCCD, pECCD also reproduces the DOCI wave function with high accuracy. Moreover, pECCD yields sensible albeit inexact results even for attractive interactions where pCCD breaks down.
Friese, Daniel H; Hättig, Christof; Ruud, Kenneth
2012-01-21
An implementation of two-photon absorption matrix elements using the approximate second-order coupled-cluster singles and doubles model CC2 is presented. In this implementation we use the resolution-of-the-identity approximation for the two-electron repulsion integrals to reduce the computational cost. To avoid storage of large arrays we introduce in addition a numerical Laplace transformation of orbital energy denominators for the response of the doubles amplitudes. The error due to the numerical Laplace transformation is found to be negligible. Using this new implementation, we performed a series of benchmark calculations on substituted benzene and azobenzene derivatives to get reference values for TD-DFT results. We show that results obtained with the Coulomb-attenuated B3LYP functional are in reasonable agreement with the coupled-cluster results, whereas other density functionals which do not have a long-range correction give considerably less accurate results. Applications to the AF240 dye molecule and a weakly bound molecular tweezer complex demonstrate that this new RI-CC2 implementation allows for the first time to compute two-photon absorption cross sections with a correlated wave function method for molecules with more than 70 atoms and to apply this method for benchmarking TD-DFT calculations on molecules which are of particular relevance for experimental studies of two-photon absorption. PMID:22130199
NASA Technical Reports Server (NTRS)
Rendell, Alistair P.; Lee, Timothy J.
1991-01-01
The analytic energy gradient for the single and double excitation coupled-cluster (CCSD) wave function has been reformulated and implemented in a new set of programs. The reformulated set of gradient equations have a smaller computational cost than any previously published. The iterative solution of the linear equations and the construction of the effective density matrices are fully vectorized, being based on matrix multiplications. The new method has been used to investigate the Cl2O2 molecule, which has recently been postulated as an important intermediate in the destruction of ozone in the stratosphere. In addition to reporting computational timings, the CCSD equilibrium geometries, harmonic vibrational frequencies, infrared intensities, and relative energetics of three isomers of Cl2O2 are presented.
Singlet-paired coupled cluster theory for open shells.
Gomez, John A; Henderson, Thomas M; Scuseria, Gustavo E
2016-06-28
Restricted single-reference coupled cluster theory truncated to single and double excitations accurately describes weakly correlated systems, but often breaks down in the presence of static or strong correlation. Good coupled cluster energies in the presence of degeneracies can be obtained by using a symmetry-broken reference, such as unrestricted Hartree-Fock, but at the cost of good quantum numbers. A large body of work has shown that modifying the coupled cluster ansatz allows for the treatment of strong correlation within a single-reference, symmetry-adapted framework. The recently introduced singlet-paired coupled cluster doubles (CCD0) method is one such model, which recovers correct behavior for strong correlation without requiring symmetry breaking in the reference. Here, we extend singlet-paired coupled cluster for application to open shells via restricted open-shell singlet-paired coupled cluster singles and doubles (ROCCSD0). The ROCCSD0 approach retains the benefits of standard coupled cluster theory and recovers correct behavior for strongly correlated, open-shell systems using a spin-preserving ROHF reference. PMID:27369507
Single System Image Cluster Management
Energy Science and Technology Software Center (ESTSC)
2004-02-13
Cluster computing has quickly proven itself to be a capable workhorse for a wide variety of production computing tasks; however, setting up and maintaining a cluster still requires significantly more effort than administrating just a single machine. As computing hardware descreases in price and cluster sizes grow, it is becoming increasingly important to manage clusters cleverly so that a system administration effort can "scale" as well. To ease the task of mananging many machines, administratorsmore » often deploy an environment that is homogeneous across all nodes of a cluster, and maintain a snapshot of the filesystem as a 'master image'. However due to operational, behavioral, and physical constraints, many nodes often require numerous deviations from the master image in order to operate as desired.« less
Azar, R. Julian; Head-Gordon, Martin
2012-01-14
We propose a wave function-based method for the decomposition of intermolecular interaction energies into chemically-intuitive components, isolating both mean-field- and explicit correlation-level contributions. We begin by solving the locally-projected self-consistent field for molecular interactions equations for a molecular complex, obtaining an intramolecularly polarized reference of self-consistently optimized, absolutely-localized molecular orbitals (ALMOs), determined with the constraint that each fragment MO be composed only of atomic basis functions belonging to its own fragment. As explicit inter-electronic correlation is integral to an accurate description of weak forces underlying intermolecular interaction potentials, namely, coordinated fluctuations in weakly interacting electronic densities, we add dynamical correlation to the ALMO polarized reference at the coupled-cluster singles and doubles level, accounting for explicit dispersion and charge-transfer effects, which map naturally onto the cluster operator. We demonstrate the stability of energy components with basis set extension, follow the hydrogen bond-breaking coordinate in the C{sub s}-symmetry water dimer, decompose the interaction energies of dispersion-bound rare gas dimers and other van der Waals complexes, and examine charge transfer-dominated donor-acceptor interactions in borane adducts. We compare our results with high-level calculations and experiment when possible.
Seniority zero pair coupled cluster doubles theory
Stein, Tamar; Henderson, Thomas M.; Scuseria, Gustavo E.
2014-06-07
Coupled cluster theory with single and double excitations accurately describes weak electron correlation but is known to fail in cases of strong static correlation. Fascinatingly, however, pair coupled cluster doubles (p-CCD), a simplified version of the theory limited to pair excitations that preserve the seniority of the reference determinant (i.e., the number of unpaired electrons), has mean field computational cost and is an excellent approximation to the full configuration interaction (FCI) of the paired space provided that the orbital basis defining the pairing scheme is adequately optimized. In previous work, we have shown that optimization of the pairing scheme in the seniority zero FCI leads to a very accurate description of static correlation. The same conclusion extends to p-CCD if the orbitals are optimized to make the p-CCD energy stationary. We here demonstrate these results with numerous examples. We also explore the contributions of different seniority sectors to the coupled cluster doubles (CCD) correlation energy using different orbital bases. We consider both Hartree-Fock and Brueckner orbitals, and the role of orbital localization. We show how one can pair the orbitals so that the role of the Brueckner orbitals at the CCD level is retained at the p-CCD level. Moreover, we explore ways of extending CCD to accurately describe strongly correlated systems.
Coupled-cluster calculations of nucleonic matter
NASA Astrophysics Data System (ADS)
Hagen, G.; Papenbrock, T.; Ekström, A.; Wendt, K. A.; Baardsen, G.; Gandolfi, S.; Hjorth-Jensen, M.; Horowitz, C. J.
2014-01-01
Background: The equation of state (EoS) of nucleonic matter is central for the understanding of bulk nuclear properties, the physics of neutron star crusts, and the energy release in supernova explosions. Because nuclear matter exhibits a finely tuned saturation point, its EoS also constrains nuclear interactions. Purpose: This work presents coupled-cluster calculations of infinite nucleonic matter using modern interactions from chiral effective field theory (EFT). It assesses the role of correlations beyond particle-particle and hole-hole ladders, and the role of three-nucleon forces (3NFs) in nuclear matter calculations with chiral interactions. Methods: This work employs the optimized nucleon-nucleon (NN) potential NNLOopt at next-to-next-to leading order, and presents coupled-cluster computations of the EoS for symmetric nuclear matter and neutron matter. The coupled-cluster method employs up to selected triples clusters and the single-particle space consists of a momentum-space lattice. We compare our results with benchmark calculations and control finite-size effects and shell oscillations via twist-averaged boundary conditions. Results: We provide several benchmarks to validate the formalism and show that our results exhibit a good convergence toward the thermodynamic limit. Our calculations agree well with recent coupled-cluster results based on a partial wave expansion and particle-particle and hole-hole ladders. For neutron matter at low densities, and for simple potential models, our calculations agree with results from quantum Monte Carlo computations. While neutron matter with interactions from chiral EFT is perturbative, symmetric nuclear matter requires nonperturbative approaches. Correlations beyond the standard particle-particle ladder approximation yield non-negligible contributions. The saturation point of symmetric nuclear matter is sensitive to the employed 3NFs and the employed regularization scheme. 3NFs with nonlocal cutoffs exhibit a
NASA Astrophysics Data System (ADS)
Scuseria, Gustavo E.
1991-01-01
The analytic energy gradient for the singles and doubles coupled cluster method including a perturbative correction due to triple excitations [CCSD(T)] is formulated and computationally implemented. Encouraged by the recent success in reproducing the experimental equilibrium structure and vibrational frequencies of ozone, the new CCSD(T) gradient method is tested with two other ``difficult'' quantum chemistry problems: FOOF and Cr2. With the largest basis set employed in this work [triple zeta plus two sets of polarization functions (TZ2Pf)] at the CCSD(T) level of theory, the predictions for the O-O and O-F bond lengths in FOOF are 1.218 and 1.589 Å, respectively. These figures are in good agreement with the experimental values 1.216 and 1.575 Å. Based on CCSD calculations with even larger basis sets, it is concluded that the error of 0.014 Å in the O-F bond length at the TZ2Pf/CCSD(T) level of theory is due to the remaining basis set deficiency. On the other hand, the CCSD(T) prediction for the equilibrium bond length of Cr2 (1.604 Å), obtained with a large (10s8p3d2f1g) basis set capable of achieving the Hartree-Fock limit, is still 0.075 Å shorter than experiment, clearly indicating the importance of higher than connected triple excitations in a single-reference treatment of this particular problem.
Toward open-shell nuclei with coupled-cluster theory
Jansen, G. R.; Hjorth-Jensen, M.; Hagen, G.; Papenbrock, T.
2011-05-15
We develop a method based on equation-of-motion coupled-cluster theory to describe properties of open-shell nuclei with A{+-}2 nucleons outside a closed shell. We perform proof-of-principle calculations for the ground states of the helium isotopes {sup 3-6}He and the first excited 2{sup +} state in {sup 6}He. The comparison with exact results from matrix diagonalization in small model spaces demonstrates the accuracy of the coupled-cluster methods. Three-particle-one-hole excitations of {sup 4}He play an important role for the accurate description of {sup 6}He. For the open-shell nucleus {sup 6}He, the computational cost of the method is comparable with the coupled-cluster singles-and-doubles approximation while its accuracy is similar to the coupled-cluster with singles, doubles, and triples excitations.
Equation-of-motion coupled cluster perturbation theory revisited
Eriksen, Janus J. Jørgensen, Poul; Olsen, Jeppe; Gauss, Jürgen
2014-05-07
The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally converges towards the full configuration interaction energy limit. The series is based on a Møller-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby remedying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz.
Bravaya, Ksenia B.; Zuev, Dmitry; Epifanovsky, Evgeny; Krylov, Anna I.
2013-03-28
Theory and implementation of complex-scaled variant of equation-of-motion coupled-cluster method for excitation energies with single and double substitutions (EOM-EE-CCSD) is presented. The complex-scaling formalism extends the EOM-EE-CCSD model to resonance states, i.e., excited states that are metastable with respect to electron ejection. The method is applied to Feshbach resonances in atomic systems (He, H{sup -}, and Be). The dependence of the results on one-electron basis set is quantified and analyzed. Energy decomposition and wave function analysis reveal that the origin of the dependence is in electron correlation, which is essential for the lifetime of Feshbach resonances. It is found that one-electron basis should be sufficiently flexible to describe radial and angular electron correlation in a balanced fashion and at different values of the scaling parameter, {theta}. Standard basis sets that are optimized for not-complex-scaled calculations ({theta} = 0) are not sufficiently flexible to describe the {theta}-dependence of the wave functions even when heavily augmented by additional sets.
Hirata, So; Yanai, Takeshi; De Jong, Wibe A.; Nakajima, Takahito; Hirao, Kimihiko
2004-02-15
Coupled-cluster methods including through and up to the connected single, double, triple, and quadruple substitutions (CCSD, CCSDT, and CCSDTQ) have been automatically derived and implemented for sequential and parallel executions for use in conjunction with a one-component third-order Douglas-Kroll (DK3) approximation for relativistic corrections. A combination of the converging electron-correlation methods, the accurate relativistic reference wave functions, and the use of systematic basis sets tailored to the relativistic approximation has been shown to predict the experimental singlet-triplet separations within 0.02 eV (0.5 kcal/mol) for five triatomic hydrides (CH2, NH2+, SiH2, PH2+, and AsH2+), the experimental bond lengths within 0.002 angstroms, rotational constants within 0.02 cm-1, vibration-rotation constants within 0.01 cm-1, centrifugal distortion constants within 2 %, harmonic vibration frequencies within 9 cm-1 (0.4 %), anharmonic vibrational constants within 2 cm-1, and dissociation energies within 0.03 eV (0.8 kcal/mol) for twenty diatomic hydrides (BH, CH, NH, OH, FH, AlH, SiH, PH, SH, ClH, GaH, GeH, AsH, SeH, BrH, InH, SnH, SbH, TeH, and IH) containing main-group elements across the second through fifth periods of the periodic table. In these calculations, spin-orbit effects on dissociation energies, which were assumed to be additive, were estimated from the measured spin-orbit coupling constants of atoms and diatomic molecules, and an electronic energy in the complete-basis-set, complete-electron-correlation limit has been extrapolated by the formula which was in turn based on the exponential-Gaussian extrapolation formula of the basis set dependence.
Ab initio Bogoliubov coupled cluster theory
NASA Astrophysics Data System (ADS)
Signoracci, Angelo; Hagen, Gaute; Duguet, Thomas
2014-09-01
Coupled cluster (CC) theory has become a standard method in nuclear theory for realistic ab initio calculations of medium mass nuclei, but remains limited by its requirement of a Slater determinant reference state which reasonably approximates the nuclear system of interest. Extensions of the method, such as equation-of-motion CC, permit the calculation of nuclei with one or two nucleons added or removed from a doubly magic core, yet still only a few dozen nuclei are accessible with modern computational restrictions. In order to extend the applicability of ab initio methods to open-shell systems, the superfluid nature of nuclei must be taken into account. By utilizing Bogoliubov algebra and employing spontaneous symmetry breaking with respect to particle number conservation, superfluid systems can be treated by a single reference state. An ab initio theory to include correlations on top of a Bogoliubov reference state has been developed in the guise of standard CC theory. The formalism and first results of this Bogoliubov coupled cluster theory will be presented to demonstrate the applicability of the method.
Multi-level coupled cluster theory
Myhre, Rolf H.; Koch, Henrik; Sánchez de Merás, Alfredo M. J.
2014-12-14
We present a general formalism where different levels of coupled cluster theory can be applied to different parts of the molecular system. The system is partitioned into subsystems by Cholesky decomposition of the one-electron Hartree-Fock density matrix. In this way the system can be divided across chemical bonds without discontinuities arising. The coupled cluster wave function is defined in terms of cluster operators for each part and these are determined from a set of coupled equations. The total wave function fulfills the Pauli-principle across all borders and levels of electron correlation. We develop the associated response theory for this multi-level coupled cluster theory and present proof of principle applications. The formalism is an essential tool in order to obtain size-intensive complexity in the calculation of local molecular properties.
NASA Astrophysics Data System (ADS)
Hirata, So; Yanai, Takeshi; de Jong, Wibe A.; Nakajima, Takahito; Hirao, Kimihiko
2004-02-01
Coupled-cluster methods including through and up to the connected single, double, triple, and quadruple substitutions have been derived and implemented automatically for sequential and parallel executions by an algebraic and symbolic manipulation program TCE (TENSOR CONTRACTION ENGINE) for use in conjunction with a one-component third-order Douglas-Kroll approximation for relativistic corrections. A combination of the converging electron-correlation methods, the accurate relativistic reference wave functions, and the use of systematic basis sets tailored to the relativistic approximation has been shown to predict the experimental singlet-triplet separations within 0.02 eV (0.5 kcal/mol) for five triatomic hydrides (CH2, NH2+, SiH2, PH2+, and AsH2+), the experimental bond lengths (re or r0) within 0.002 Å, rotational constants (Be or B0) within 0.02 cm-1, vibration-rotation constants (αe) within 0.01 cm-1, centrifugal distortion constants (De) within 2%, harmonic vibration frequencies (ωe) within 8 cm-1 (0.4%), anharmonic vibrational constants (xωe) within 2 cm-1, and dissociation energies (D00) within 0.02 eV (0.4 kcal/mol) for twenty diatomic hydrides (BH, CH, NH, OH, FH, AlH, SiH, PH, SH, ClH, GaH, GeH, AsH, SeH, BrH, InH, SnH, SbH, TeH, and IH) containing main-group elements across the second through fifth rows of the periodic table. In these calculations, spin-orbit effects on dissociation energies, which were assumed to be additive, were estimated from the measured spin-orbit coupling constants of atoms and diatomic molecules, and an electronic energy in the complete-basis-set, complete-electron-correlation limit has been extrapolated in two ways to verify the robustness of the results: One assuming Gaussian-exponential dependence of total energies on double through quadruple ζ basis sets and the other assuming n-3 dependence of correlation energies on double through quintuple ζ basis sets.
Combining coupled cluster and perturbation theory
NASA Astrophysics Data System (ADS)
Nooijen, Marcel
1999-12-01
Single reference coupled cluster (CC) singles and doubles theory is combined with low-order perturbation theory (PT) to treat ground state electron correlation. Two variants of the general scheme are discussed that differ in the type of amplitudes that are approximated perturbatively and which are treated to infinite order. The combined CC/PT methods to include ground state correlation are merged with equation-of-motion (EOM) and similarity transformed EOM methods to describe excitation spectra of the highly correlated s-tetrazine, MnO4- and Ni(CO)4 systems. It is shown that the computationally efficient CC/PT schemes can reproduce full CCSD results even if perturbation theory by itself is a very poor approximation, as is the case for many transition metal compounds. In a second test CC/PT is applied to determine ground state equilibrium molecular structures and harmonic vibrational frequencies for a set of small molecules. Using either variant of CC/PT, full CCSD geometries are easily recovered, while vibrational frequencies can be more sensitive to details of the approximation.
Coupled-cluster computations of atomic nuclei.
Hagen, G; Papenbrock, T; Hjorth-Jensen, M; Dean, D J
2014-09-01
In the past decade, coupled-cluster theory has seen a renaissance in nuclear physics, with computations of neutron-rich and medium-mass nuclei. The method is efficient for nuclei with product-state references, and it describes many aspects of weakly bound and unbound nuclei. This report reviews the technical and conceptual developments of this method in nuclear physics, and the results of coupled-cluster calculations for nucleonic matter, and for exotic isotopes of helium, oxygen, calcium, and some of their neighbors. PMID:25222372
Coarse-Grained Clustering Dynamics of Heterogeneously Coupled Neurons.
Moon, Sung Joon; Cook, Katherine A; Rajendran, Karthikeyan; Kevrekidis, Ioannis G; Cisternas, Jaime; Laing, Carlo R
2015-12-01
The formation of oscillating phase clusters in a network of identical Hodgkin-Huxley neurons is studied, along with their dynamic behavior. The neurons are synaptically coupled in an all-to-all manner, yet the synaptic coupling characteristic time is heterogeneous across the connections. In a network of N neurons where this heterogeneity is characterized by a prescribed random variable, the oscillatory single-cluster state can transition-through [Formula: see text] (possibly perturbed) period-doubling and subsequent bifurcations-to a variety of multiple-cluster states. The clustering dynamic behavior is computationally studied both at the detailed and the coarse-grained levels, and a numerical approach that can enable studying the coarse-grained dynamics in a network of arbitrarily large size is suggested. Among a number of cluster states formed, double clusters, composed of nearly equal sub-network sizes are seen to be stable; interestingly, the heterogeneity parameter in each of the double-cluster components tends to be consistent with the random variable over the entire network: Given a double-cluster state, permuting the dynamical variables of the neurons can lead to a combinatorially large number of different, yet similar "fine" states that appear practically identical at the coarse-grained level. For weak heterogeneity we find that correlations rapidly develop, within each cluster, between the neuron's "identity" (its own value of the heterogeneity parameter) and its dynamical state. For single- and double-cluster states we demonstrate an effective coarse-graining approach that uses the Polynomial Chaos expansion to succinctly describe the dynamics by these quickly established "identity-state" correlations. This coarse-graining approach is utilized, within the equation-free framework, to perform efficient computations of the neuron ensemble dynamics. PMID:26458901
Photoionization cross section by Stieltjes imaging applied to coupled cluster Lanczos pseudo-spectra
NASA Astrophysics Data System (ADS)
Cukras, Janusz; Coriani, Sonia; Decleva, Piero; Christiansen, Ove; Norman, Patrick
2013-09-01
A recently implemented asymmetric Lanczos algorithm for computing (complex) linear response functions within the coupled cluster singles (CCS), coupled cluster singles and iterative approximate doubles (CC2), and coupled cluster singles and doubles (CCSD) is coupled to a Stieltjes imaging technique in order to describe the photoionization cross section of atoms and molecules, in the spirit of a similar procedure recently proposed by Averbukh and co-workers within the Algebraic Diagrammatic Construction approach. Pilot results are reported for the atoms He, Ne, and Ar and for the molecules H2, H2O, NH3, HF, CO, and CO2.
Photoionization cross section by Stieltjes imaging applied to coupled cluster Lanczos pseudo-spectra
Cukras, Janusz; Coriani, Sonia; Decleva, Piero; Christiansen, Ove; Norman, Patrick
2013-09-07
A recently implemented asymmetric Lanczos algorithm for computing (complex) linear response functions within the coupled cluster singles (CCS), coupled cluster singles and iterative approximate doubles (CC2), and coupled cluster singles and doubles (CCSD) is coupled to a Stieltjes imaging technique in order to describe the photoionization cross section of atoms and molecules, in the spirit of a similar procedure recently proposed by Averbukh and co-workers within the Algebraic Diagrammatic Construction approach. Pilot results are reported for the atoms He, Ne, and Ar and for the molecules H{sub 2}, H{sub 2}O, NH{sub 3}, HF, CO, and CO{sub 2}.
Seniority-based coupled cluster theory
Henderson, Thomas M.; Scuseria, Gustavo E.; Bulik, Ireneusz W.; Stein, Tamar
2014-12-28
Doubly occupied configuration interaction (DOCI) with optimized orbitals often accurately describes strong correlations while working in a Hilbert space much smaller than that needed for full configuration interaction. However, the scaling of such calculations remains combinatorial with system size. Pair coupled cluster doubles (pCCD) is very successful in reproducing DOCI energetically, but can do so with low polynomial scaling (N{sup 3}, disregarding the two-electron integral transformation from atomic to molecular orbitals). We show here several examples illustrating the success of pCCD in reproducing both the DOCI energy and wave function and show how this success frequently comes about. What DOCI and pCCD lack are an effective treatment of dynamic correlations, which we here add by including higher-seniority cluster amplitudes which are excluded from pCCD. This frozen pair coupled cluster approach is comparable in cost to traditional closed-shell coupled cluster methods with results that are competitive for weakly correlated systems and often superior for the description of strongly correlated systems.
Seniority-based coupled cluster theory
NASA Astrophysics Data System (ADS)
Henderson, Thomas M.; Bulik, Ireneusz W.; Stein, Tamar; Scuseria, Gustavo E.
2014-12-01
Doubly occupied configuration interaction (DOCI) with optimized orbitals often accurately describes strong correlations while working in a Hilbert space much smaller than that needed for full configuration interaction. However, the scaling of such calculations remains combinatorial with system size. Pair coupled cluster doubles (pCCD) is very successful in reproducing DOCI energetically, but can do so with low polynomial scaling (N3, disregarding the two-electron integral transformation from atomic to molecular orbitals). We show here several examples illustrating the success of pCCD in reproducing both the DOCI energy and wave function and show how this success frequently comes about. What DOCI and pCCD lack are an effective treatment of dynamic correlations, which we here add by including higher-seniority cluster amplitudes which are excluded from pCCD. This frozen pair coupled cluster approach is comparable in cost to traditional closed-shell coupled cluster methods with results that are competitive for weakly correlated systems and often superior for the description of strongly correlated systems.
Yang, Ke; Jalan, Amrit; Green, William H.; Truhlar, Donald G.
2013-01-08
We examine the accuracy of single-reference and multireference correlated wave function methods for predicting accurate energies and potential energy curves of biradicals. The biradicals considered are intermediate species along the bond dissociation coordinates for breaking the F-F bond in F_{2}, the O-O bond in H_{2}O_{2}, and the C-C bond in CH_{3}CH_{3}. We apply a host of single-reference and multireference approximations in a consistent way to the same cases to provide a better assessment of their relative accuracies than was previously possible. The most accurate method studied is coupled cluster theory with all connected excitations through quadruples, CCSDTQ. Without explicit quadruple excitations, the most accurate potential energy curves are obtained by the single-reference RCCSDt method, followed, in order of decreasing accuracy, by UCCSDT, RCCSDT, UCCSDt, seven multireference methods, including perturbation theory, configuration interaction, and coupled-cluster methods (with MRCI+Q being the best and Mk-MR-CCSD the least accurate), four CCSD(T) methods, and then CCSD.
Communication: A simplified coupled-cluster Lagrangian for polarizable embedding.
Krause, Katharina; Klopper, Wim
2016-01-28
A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian. PMID:26827193
A coupled-cluster study of photodetachment cross sections of closed-shell anions
Cukras, Janusz; Decleva, Piero; Coriani, Sonia
2014-11-07
We investigate the performance of Stieltjes Imaging applied to Lanczos pseudo-spectra generated at the coupled cluster singles and doubles, coupled cluster singles and approximate iterative doubles and coupled cluster singles levels of theory in modeling the photodetachment cross sections of the closed shell anions H{sup −}, Li{sup −}, Na{sup −}, F{sup −}, Cl{sup −}, and OH{sup −}. The accurate description of double excitations is found to play a much more important role than in the case of photoionization of neutral species.
Computation of expectation values from vibrational coupled-cluster at the two-mode coupling level
NASA Astrophysics Data System (ADS)
Zoccante, Alberto; Seidler, Peter; Christiansen, Ove
2011-04-01
In this work we show how the vibrational coupled-cluster method at the two-mode coupling level can be used to calculate zero-point vibrational averages of properties. A technique is presented, where any expectation value can be calculated using a single set of Lagrangian multipliers computed solving iteratively a single linear set of equations. Sample calculations are presented which show that the resulting algorithm scales only with the third power of the number of modes, therefore making large systems accessible. Moreover, we present applications to water, pyrrole, and para-nitroaniline.
Nonlocal correlations induced by Hund's coupling: A cluster DMFT study
NASA Astrophysics Data System (ADS)
Nomura, Yusuke; Sakai, Shiro; Arita, Ryotaro
2015-06-01
We study spatial correlation effects in multiorbital systems, especially in a paramagnetic metallic state subject to Hund's coupling. We apply a cluster extension of the dynamical mean-field theory (DMFT) to the three-orbital Hubbard model away from half filling, where previous single-site DMFT studies revealed that local correlation effects caused by Hund's coupling bring about unusual strongly correlated metallic behaviors. We find that Hund's coupling significantly affects the nonlocal correlations too; it strongly modulates the electron distribution in the momentum space so as to make a momentum region almost half filled and hence strongly correlated. It leads to an anomalous electronic state distinct both from the Fermi liquid and the Mott insulator. We identify the mechanism of the anomalous state with the intersite ferromagnetic correlations induced by Hund's coupling.
Approximating electronically excited states with equation-of-motion linear coupled-cluster theory
Byrd, Jason N. Rishi, Varun; Perera, Ajith; Bartlett, Rodney J.
2015-10-28
A new perturbative approach to canonical equation-of-motion coupled-cluster theory is presented using coupled-cluster perturbation theory. A second-order Møller-Plesset partitioning of the Hamiltonian is used to obtain the well known equation-of-motion many-body perturbation theory equations and two new equation-of-motion methods based on the linear coupled-cluster doubles and linear coupled-cluster singles and doubles wavefunctions. These new methods are benchmarked against very accurate theoretical and experimental spectra from 25 small organic molecules. It is found that the proposed methods have excellent agreement with canonical equation-of-motion coupled-cluster singles and doubles state for state orderings and relative excited state energies as well as acceptable quantitative agreement for absolute excitation energies compared with the best estimate theory and experimental spectra.
Ab initio quantum dynamics using coupled-cluster.
Kvaal, Simen
2012-05-21
The curse of dimensionality (COD) limits the current state-of-the-art ab initio propagation methods for non-relativistic quantum mechanics to relatively few particles. For stationary structure calculations, the coupled-cluster (CC) method overcomes the COD in the sense that the method scales polynomially with the number of particles while still being size-consistent and extensive. We generalize the CC method to the time domain while allowing the single-particle functions to vary in an adaptive fashion as well, thereby creating a highly flexible, polynomially scaling approximation to the time-dependent Schrödinger equation. The method inherits size-consistency and extensivity from the CC method. The method is dubbed orbital-adaptive time-dependent coupled-cluster, and is a hierarchy of approximations to the now standard multi-configurational time-dependent Hartree method for fermions. A numerical experiment is also given. PMID:22612082
NASA Astrophysics Data System (ADS)
Kauczor, Joanna; Norman, Patrick; Christiansen, Ove; Coriani, Sonia
2013-12-01
We present a reduced-space algorithm for solving the complex (damped) linear response equations required to compute the complex linear response function for the hierarchy of methods: coupled cluster singles, coupled cluster singles and iterative approximate doubles, and coupled cluster singles and doubles. The solver is the keystone element for the development of damped coupled cluster response methods for linear and nonlinear effects in resonant frequency regions.
Optimized coordinates in vibrational coupled cluster calculations
Thomsen, Bo; Christiansen, Ove; Yagi, Kiyoshi
2014-04-21
The use of variationally optimized coordinates, which minimize the vibrational self-consistent field (VSCF) ground state energy with respect to orthogonal transformations of the coordinates, has recently been shown to improve the convergence of vibrational configuration interaction (VCI) towards the exact full VCI [K. Yagi, M. Keçeli, and S. Hirata, J. Chem. Phys. 137, 204118 (2012)]. The present paper proposes an incorporation of optimized coordinates into the vibrational coupled cluster (VCC), which has in the past been shown to outperform VCI in approximate calculations where similar restricted state spaces are employed in VCI and VCC. An embarrassingly parallel algorithm for variational optimization of coordinates for VSCF is implemented and the resulting coordinates and potentials are introduced into a VCC program. The performance of VCC in optimized coordinates (denoted oc-VCC) is examined through pilot applications to water, formaldehyde, and a series of water clusters (dimer, trimer, and hexamer) by comparing the calculated vibrational energy levels with those of the conventional VCC in normal coordinates and VCI in optimized coordinates. For water clusters, in particular, oc-VCC is found to gain orders of magnitude improvement in the accuracy, exemplifying that the combination of optimized coordinates localized to each monomer with the size-extensive VCC wave function provides a supreme description of systems consisting of weakly interacting sub-systems.
Explicitly correlated coupled-cluster theory with Brueckner orbitals.
Tew, David P
2016-08-21
Brueckner orbitals are the optimal orbitals for use in F12 explicitly correlated coupled-cluster (CC) treatments. A novel approach, Brueckner coupled-cluster doubles with perturbative triples BCCD(T)(F12*) is presented that avoids the expensive re-evaluation of F12 integrals throughout the orbital optimisation and includes a newly derived basis set correction to the Brueckner reference energy. The generalisation of F12 theory to arbitrary non-Hartree-Fock references and to Fock operators that include scalar relativistic effects is also presented. The performance of the new Brueckner F12 method is assessed for a test set of 50 open- and closed-shell reactions and for the ionisation potentials and electron affinities (EAs) of the first-row transition metal atoms. Benchmark basis set limit coupled-cluster singles, doubles and perturbative triples (CCSD(T)) and BCCD(T) values are reported for all energies in the test sets. BCCD(T)(F12*) performs systematically better than CCSD(T)(F12*) for electron affinities where orbital relaxation effects are significant. PMID:27544083
Spencer, James S; Thom, Alex J W
2016-02-28
We describe further details of the stochastic coupled cluster method and a diagnostic of such calculations, the shoulder height, akin to the plateau found in full configuration interaction quantum Monte Carlo. We describe an initiator modification to stochastic coupled cluster theory and show that initiator calculations can at times be extrapolated to the unbiased limit. We apply this method to the 3D 14-electron uniform electron gas and present complete basis set limit values of the coupled cluster singles and doubles (CCSD) and previously unattainable coupled cluster singles and doubles with perturbative triples (CCSDT) correlation energies for up to r(s) = 2, showing a requirement to include triple excitations to accurately calculate energies at high densities. PMID:26931682
Explicitly correlated ring-coupled-cluster-doubles theory
NASA Astrophysics Data System (ADS)
Hehn, Anna-Sophia; Tew, David P.; Klopper, Wim
2015-05-01
The connection between the random-phase approximation and the ring-coupled-cluster-doubles method bridges the gap between density-functional and wave-function theories and the importance of the random-phase approximation lies in both its broad applicability and this linking role in electronic-structure theory. In this contribution, we present an explicitly correlated approach to the random-phase approximation, based on the direct ring-coupled-cluster-doubles ansatz, which overcomes the problem of slow basis-set convergence, inherent to the random-phase approximation. Benchmark results for a test set of 106 molecules and a selection of 10 organic complexes from the S22 test set demonstrate that convergence to within 99% of the basis-set limit is reached for triple-zeta basis sets for atomisation energies, while quadruple-zeta basis sets are required for interaction energies. Corrections due to single excitations into the complementary auxiliary space reduce the basis-set incompleteness error by one order of magnitude, while contributions due to the coupling of conventional and geminal amplitudes are in general negligible. We find that a non-iterative explicitly correlated correction to first order in perturbation theory exhibits the best ratio of accuracy to computational cost.
Explicitly correlated ring-coupled-cluster-doubles theory.
Hehn, Anna-Sophia; Tew, David P; Klopper, Wim
2015-05-21
The connection between the random-phase approximation and the ring-coupled-cluster-doubles method bridges the gap between density-functional and wave-function theories and the importance of the random-phase approximation lies in both its broad applicability and this linking role in electronic-structure theory. In this contribution, we present an explicitly correlated approach to the random-phase approximation, based on the direct ring-coupled-cluster-doubles ansatz, which overcomes the problem of slow basis-set convergence, inherent to the random-phase approximation. Benchmark results for a test set of 106 molecules and a selection of 10 organic complexes from the S22 test set demonstrate that convergence to within 99% of the basis-set limit is reached for triple-zeta basis sets for atomisation energies, while quadruple-zeta basis sets are required for interaction energies. Corrections due to single excitations into the complementary auxiliary space reduce the basis-set incompleteness error by one order of magnitude, while contributions due to the coupling of conventional and geminal amplitudes are in general negligible. We find that a non-iterative explicitly correlated correction to first order in perturbation theory exhibits the best ratio of accuracy to computational cost. PMID:26001446
Explicitly correlated ring-coupled-cluster-doubles theory
Hehn, Anna-Sophia; Klopper, Wim; Tew, David P.
2015-05-21
The connection between the random-phase approximation and the ring-coupled-cluster-doubles method bridges the gap between density-functional and wave-function theories and the importance of the random-phase approximation lies in both its broad applicability and this linking role in electronic-structure theory. In this contribution, we present an explicitly correlated approach to the random-phase approximation, based on the direct ring-coupled-cluster-doubles ansatz, which overcomes the problem of slow basis-set convergence, inherent to the random-phase approximation. Benchmark results for a test set of 106 molecules and a selection of 10 organic complexes from the S22 test set demonstrate that convergence to within 99% of the basis-set limit is reached for triple-zeta basis sets for atomisation energies, while quadruple-zeta basis sets are required for interaction energies. Corrections due to single excitations into the complementary auxiliary space reduce the basis-set incompleteness error by one order of magnitude, while contributions due to the coupling of conventional and geminal amplitudes are in general negligible. We find that a non-iterative explicitly correlated correction to first order in perturbation theory exhibits the best ratio of accuracy to computational cost.
Cluster synchronization induced by one-node clusters in networks with asymmetric negative couplings
Zhang, Jianbao; Ma, Zhongjun; Zhang, Gang
2013-12-15
This paper deals with the problem of cluster synchronization in networks with asymmetric negative couplings. By decomposing the coupling matrix into three matrices, and employing Lyapunov function method, sufficient conditions are derived for cluster synchronization. The conditions show that the couplings of multi-node clusters from one-node clusters have beneficial effects on cluster synchronization. Based on the effects of the one-node clusters, an effective and universal control scheme is put forward for the first time. The obtained results may help us better understand the relation between cluster synchronization and cluster structures of the networks. The validity of the control scheme is confirmed through two numerical simulations, in a network with no cluster structure and in a scale-free network.
Circuit electromechanics with single photon strong coupling
Xue, Zheng-Yuan Yang, Li-Na; Zhou, Jian
2015-07-13
In circuit electromechanics, the coupling strength is usually very small. Here, replacing the capacitor in circuit electromechanics by a superconducting flux qubit, we show that the coupling among the qubit and the two resonators can induce effective electromechanical coupling which can attain the strong coupling regime at the single photon level with feasible experimental parameters. We use dispersive couplings among two resonators and the qubit while the qubit is also driven by an external classical field. These couplings form a three-wave mixing configuration among the three elements where the qubit degree of freedom can be adiabatically eliminated, and thus results in the enhanced coupling between the two resonators. Therefore, our work constitutes the first step towards studying quantum nonlinear effect in circuit electromechanics.
Ab-Initio Coupled-Cluster Study of {sup 16}O
Wloch, M.; Gour, J.R.; Kowalski, K.; Piecuch, P.; Dean, D.J.; Hjorth-Jensen, M.; Papenbrock, T.
2005-06-03
We report converged results for the ground and excited states and matter density of {sup 16}O using realistic two-body nucleon-nucleon interactions and coupled-cluster methods and algorithms developed in quantum chemistry. Most of the binding is obtained with the coupled-cluster singles and doubles approach. Additional binding due to three-body clusters (triples) is minimal. The coupled-cluster method with singles and doubles provides a good description of the matter density, charge radius, charge form factor, and excited states of a one-particle, one-hole nature, but it cannot describe the first-excited 0{sup +} state. Incorporation of triples has no effect on the latter finding.
Multireference coupled-cluster approaches to excited states
NASA Astrophysics Data System (ADS)
Paldus, Josef; Li, Xiangzhu
2015-01-01
We review our recent work on multireference (MR) coupled-cluster (CC) methodology, namely (i) the idea of external corrections that are essential for the so-called reduced MR (RMR) CCSD and RMR-CCSD(T) methods at the single-reference (SR) level and for (N,M)-CCSD at the MR level, and (ii) the concept of the so-called C-conditions for the internal cluster amplitudes at the genuine MR CC state universal (SU) level. The latter concept enables the use of general model spaces (GMSs) while preserving the intermediate normalization and can be employed in any MR CC method that is based on the SU cluster Ansatz of Jeziorski and Monkhorst, including state-selective (SS) approaches, such as the Mukherjee MkCCSD and Brillouin-Wigner BW-CC methods. The performance of the RMR-CCSD(T), GMS-SU-CCSD, GMS-MkCCSD, and (N,M)-CCSD approaches is illustrated on a few typical examples.
Coupled cluster algorithms for networks of shared memory parallel processors
NASA Astrophysics Data System (ADS)
Bentz, Jonathan L.; Olson, Ryan M.; Gordon, Mark S.; Schmidt, Michael W.; Kendall, Ricky A.
2007-05-01
As the popularity of using SMP systems as the building blocks for high performance supercomputers increases, so too increases the need for applications that can utilize the multiple levels of parallelism available in clusters of SMPs. This paper presents a dual-layer distributed algorithm, using both shared-memory and distributed-memory techniques to parallelize a very important algorithm (often called the "gold standard") used in computational chemistry, the single and double excitation coupled cluster method with perturbative triples, i.e. CCSD(T). The algorithm is presented within the framework of the GAMESS [M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.J. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S. Su, T.L. Windus, M. Dupuis, J.A. Montgomery, General atomic and molecular electronic structure system, J. Comput. Chem. 14 (1993) 1347-1363]. (General Atomic and Molecular Electronic Structure System) program suite and the Distributed Data Interface [M.W. Schmidt, G.D. Fletcher, B.M. Bode, M.S. Gordon, The distributed data interface in GAMESS, Comput. Phys. Comm. 128 (2000) 190]. (DDI), however, the essential features of the algorithm (data distribution, load-balancing and communication overhead) can be applied to more general computational problems. Timing and performance data for our dual-level algorithm is presented on several large-scale clusters of SMPs.
Delay-induced cluster patterns in coupled Cayley tree networks
NASA Astrophysics Data System (ADS)
Singh, A.; Jalan, S.
2013-07-01
We study effects of delay in diffusively coupled logistic maps on the Cayley tree networks. We find that smaller coupling values exhibit sensitiveness to value of delay, and lead to different cluster patterns of self-organized and driven types. Whereas larger coupling strengths exhibit robustness against change in delay values, and lead to stable driven clusters comprising nodes from last generation of the Cayley tree. Furthermore, introduction of delay exhibits suppression as well as enhancement of synchronization depending upon coupling strength values. To the end we discuss the importance of results to understand conflicts and cooperations observed in family business.
Mutual Coupling for each Channel of Cluster Radioactivity
NASA Astrophysics Data System (ADS)
Huang, Yin; Zhang, Hong Fei
2013-11-01
Every kinds of cluster radioactivities have different radioactive features depending on their emitted clusters and daughters nuclei. Thus each decay process can be treated as a radioactive channel, and the channels can be coupled to each other. Therefore some channels are abated or strengthen due to the coupling effects. Here we attempt to find out a way to evaluate the influence of each channel, and then introduce a physical quantity Mi to express this effect.
Single photons from dissipation in coupled cavities
NASA Astrophysics Data System (ADS)
Flayac, H.; Savona, V.
2016-07-01
We propose a single-photon source based on a pair of weakly nonlinear optical cavities subject to a one-directional dissipative coupling. When both cavities are driven by mutually coherent fields, sub-Poissonian light is generated in the target cavity even when the nonlinear energy per photon is much smaller than the dissipation rate. The sub-Poissonian character of the field holds over a delay measured by the inverse photon lifetime, as in the conventional photon blockade, thus allowing single-photon emission under pulsed excitation. We discuss a possible implementation of the dissipative coupling relevant to photonic platforms.
Cluster synchronization modes in an ensemble of coupled chaotic oscillators
NASA Astrophysics Data System (ADS)
Belykh, Vladimir N.; Belykh, Igor V.; Mosekilde, Erik
2001-03-01
Considering systems of diffusively coupled identical chaotic oscillators, an effective method to determine the possible states of cluster synchronization and ensure their stability is presented. The method, which may find applications in communication engineering and other fields of science and technology, is illustrated through concrete examples of coupled biological cell models.
Clustering in delay-coupled smooth and relaxational chemical oscillators
NASA Astrophysics Data System (ADS)
Blaha, Karen; Lehnert, Judith; Keane, Andrew; Dahms, Thomas; Hövel, Philipp; Schöll, Eckehard; Hudson, John L.
2013-12-01
We investigate cluster synchronization in networks of nonlinear systems with time-delayed coupling. Using a generic model for a system close to the Hopf bifurcation, we predict the order of appearance of different cluster states and their corresponding common frequencies depending upon coupling delay. We may tune the delay time in order to ensure the existence and stability of a specific cluster state. We qualitatively and quantitatively confirm these results in experiments with chemical oscillators. The experiments also exhibit strongly nonlinear relaxation oscillations as we increase the voltage, i.e., go further away from the Hopf bifurcation. In this regime, we find secondary cluster states with delay-dependent phase lags. These cluster states appear in addition to primary states with delay-independent phase lags observed near the Hopf bifurcation. Extending the theory on Hopf normal-form oscillators, we are able to account for realistic interaction functions, yielding good agreement with experimental findings.
Combined coupled-cluster and many-body perturbation theories
NASA Astrophysics Data System (ADS)
Hirata, So; Fan, Peng-Dong; Auer, Alexander A.; Nooijen, Marcel; Piecuch, Piotr
2004-12-01
Various approximations combining coupled-cluster (CC) and many-body perturbation theories have been derived and implemented into the parallel execution programs that take into account the spin, spatial (real Abelian), and permutation symmetries and that are applicable to closed- and open-shell molecules. The implemented models range from the CCSD(T), CCSD[T], CCSD(2)T, CCSD(2)TQ, and CCSDT(2)Q methods to the completely renormalized (CR) CCSD(T) and CCSD[T] approaches, where CCSD (CCSDT) stands for the CC method with connected single and double (single, double, and triple) cluster operators, and subscripted or parenthesized 2, T, and Q indicate the perturbation order or the excitation ranks of the cluster operators included in the corrections. The derivation and computer implementation have been automated by the algebraic and symbolic manipulation program TENSOR CONTRACTION ENGINE (TCE). The TCE-synthesized subroutines generate the tensors with the highest excitation rank in a blockwise manner so that they need not be stored in their entirety, while enabling the efficient reuse of other precalculated intermediate tensors defined by prioritizing the memory optimization as well as operation minimization. Consequently, the overall storage requirements for the corrections due to connected triple and quadruple cluster operators scale as O(n4) and O(n6), respectively (n being a measure of the system size). For systems with modest multireference character of their wave functions, we found that the order of accuracy is CCSD
Kowalski, Karol; Valiev, Marat
2008-05-27
A new formalism closely related to the Method of Moment of Coupled-Cluster equations (MMCC) is obtained by embedding approximate coupled cluster (CC) or equation-of-motion CC (EOMCC) formalism into the formalism which uses cluster or excitation operators defined by excitation operators of higher rank with respect to a given approximation. Non-iterative corrections due to triples to the CC / EOMCC with singles and doubles (CCSD / EOMCCSD) reveal structural similarities to the CCSD(T) corrections for the ground state. Linked to our QM/MM module in NWChem this new algorithm is used to study the excited-state potential surfaces of C1₂O molecule in gas-phase and CC1₄ solution.
NASA Astrophysics Data System (ADS)
Tajti, Attila; Szalay, Péter G.
2009-09-01
Theory and implementation for evaluation of the nonadiabatic coupling vector between excited electronic states described by equation-of-motion excitation energy coupled-cluster singles and doubles (EOMEE-CCSD) method is presented. Problems arising from the non-Hermitian nature of the theory are discussed in detail. The performance of the new approach is demonstrated by the nice agreement of the nonadiabatic coupling curves for LiH obtained at the EOMEE-CCSD and MR-CISD levels. Using the tools developed we also present a computational procedure to evaluate the interstate coupling constants used in vibronic coupling theories. As an application of this part of the implementation we present simulation of the electronic absorption spectrum of the pyrazine molecule within the linear vibronic coupling model.
Note: Excited State Studies of Ozone using State-Specific Multireference Coupled Cluster Methods
Bhaskaran-Nair, Kiran; Kowalski, Karol
2012-12-07
Vertical excitation energies obtained with state-specific multi-reference coupled cluster (MRCC) methods are reported for the ozone molecule. Using state-specific MRCC non-iterative methods with singles, doubles, and non-iterative triples (MRCCSD(T)) we obtain 4.40 eV for the challenging doubly excited 21A1 state when using a reliable model space. This estimate is in good agreement with experiment (4.5 eV). We also compare our MRCC results with the excitation energies obtained with high-order equation-of-motion coupled cluster methods
Report of a Workshop on Parallelization of Coupled Cluster Methods
Rodney J. Bartlett Erik Deumens
2008-05-08
The benchmark, ab initio quantum mechanical methods for molecular structure and spectra are now recognized to be coupled-cluster theory. To benefit from the transiiton to tera- and petascale computers, such coupled-cluster methods must be created to run in a scalable fashion. This Workshop, held as a aprt of the 48th annual Sanibel meeting, at St. Simns, Island, GA, addressed that issue. Representatives of all the principal scientific groups who are addressing this topic were in attendance, to exchange information about the problem and to identify what needs to be done in the future. This report summarized the conclusions of the workshop.
ClusterSculptor: Software for Expert-Steered Classification of Single Particle Mass Spectra
Zelenyuk, Alla; Imre, Dan G.; Nam, Eun Ju; Han, Yiping; Mueller, Klaus
2008-08-01
To take full advantage of the vast amount of highly detailed data acquired by single particle mass spectrometers requires that the data be organized according to some rules that have the potential to be insightful. Most commonly statistical tools are used to cluster the individual particle mass spectra on the basis of their similarity. Cluster analysis is a powerful strategy for the exploration of high-dimensional data in the absence of a-priori hypotheses or data classification models, and the results of cluster analysis can then be used to form such models. More often than not, when examining the data clustering results we find that many clusters contain particles of different types and that many particles of one type end up in a number of separate clusters. Our experience with cluster analysis shows that we have a vast amount of non-compiled knowledge and intuition that should be brought to bear in this effort. We will present new software we call ClusterSculptor that provides comprehensive and intuitive framework to aid scientists in data classification. ClusterSculptor uses k-means as the overall clustering engine, but allows tuning its parameters interactively, based on a non-distorted compact visual presentation of the inherent characteristics of the data in high-dimensional space. ClusterSculptor provides all the tools necessary for a high-dimensional activity we call cluster sculpting. ClusterSculptor is designed to be coupled to SpectraMiner, our data mining and visualization software package. The data are first visualized with SpectraMiner and identified problems are exported to ClusterSculptor, where the user steers the reclassification and recombination of clusters of tens of thousands particle mass spectra in real-time. The resulting sculpted clusters can be then imported back into SpectraMiner. Here we will greatly improved single particle chemical speciation in an example of application of this new tool to a number of particle types of atmospheric
Panic evacuation of single pedestrians and couples
NASA Astrophysics Data System (ADS)
Frank, G. A.; Dorso, C. O.
2016-02-01
Understanding the timing requirements for evacuation of people has focused primarily on independent pedestrians rather than pedestrians emotionally connected. However, the main statistical effects observed in crowds, the so-called “faster is slower”, “clever is not always better” and the “low visibility enhancement”, cannot explain the overall behavior of a crowd during an evacuation process when correlated pedestrians due to, for example feelings, are present. Our research addresses this issue and examines the statistical behavior of a mixture of individuals and couples during a (panic) escaping process. We found that the attractive feeling among couples plays an important role in the time delays during the evacuation of a single exit room.
Coupled-Cluster Dynamic Polarizabilities Including Triple Excitations
Hammond, Jeffrey R.; De Jong, Wibe A.; Kowalski, Karol
2008-06-10
Dynamic polarizabilities for open- and closed-shell molecules were obtained using coupled-cluster (CC) linear response theory with full treatment of singles, doubles and triples (CCSDT-LR) with large basis sets utilizing the NWChem software suite. Using four approximate CC methods in conjunction with augmented cc-pVNZ basis sets, we are able to evaluate the convergence in both many-electron and one-electron spaces. For systems with primarily dynamic correlation, the results for CC3 and CCSDT are almost indistinguishable. For systems with more static correlation, the PS(T) approximation [J. Chem. Phs. 127, 164105 (2007) performs better that CC3. Additionally, the PS(T) approach separates the triples contribution to the poles of the response function from the triples amplitudes themselves, and demonstrates that the latter are less important than originally thought Lastly, our results show that the choice of reference (ROHF versus UHF) can have a significant impact on the accuracy of polarizabilities for open-shell systems.
Coupled-cluster based basis sets for valence correlation calculations
NASA Astrophysics Data System (ADS)
Claudino, Daniel; Gargano, Ricardo; Bartlett, Rodney J.
2016-03-01
Novel basis sets are generated that target the description of valence correlation in atoms H through Ar. The new contraction coefficients are obtained according to the Atomic Natural Orbital (ANO) procedure from CCSD(T) (coupled-cluster singles and doubles with perturbative triples correction) density matrices starting from the primitive functions of Dunning et al. [J. Chem. Phys. 90, 1007 (1989); ibid. 98, 1358 (1993); ibid. 100, 2975 (1993)] (correlation consistent polarized valence X-tuple zeta, cc-pVXZ). The exponents of the primitive Gaussian functions are subject to uniform scaling in order to ensure satisfaction of the virial theorem for the corresponding atoms. These new sets, named ANO-VT-XZ (Atomic Natural Orbital Virial Theorem X-tuple Zeta), have the same number of contracted functions as their cc-pVXZ counterparts in each subshell. The performance of these basis sets is assessed by the evaluation of the contraction errors in four distinct computations: correlation energies in atoms, probing the density in different regions of space via
Coupled-cluster based basis sets for valence correlation calculations.
Claudino, Daniel; Gargano, Ricardo; Bartlett, Rodney J
2016-03-14
Novel basis sets are generated that target the description of valence correlation in atoms H through Ar. The new contraction coefficients are obtained according to the Atomic Natural Orbital (ANO) procedure from CCSD(T) (coupled-cluster singles and doubles with perturbative triples correction) density matrices starting from the primitive functions of Dunning et al. [J. Chem. Phys. 90, 1007 (1989); ibid. 98, 1358 (1993); ibid. 100, 2975 (1993)] (correlation consistent polarized valence X-tuple zeta, cc-pVXZ). The exponents of the primitive Gaussian functions are subject to uniform scaling in order to ensure satisfaction of the virial theorem for the corresponding atoms. These new sets, named ANO-VT-XZ (Atomic Natural Orbital Virial Theorem X-tuple Zeta), have the same number of contracted functions as their cc-pVXZ counterparts in each subshell. The performance of these basis sets is assessed by the evaluation of the contraction errors in four distinct computations: correlation energies in atoms, probing the density in different regions of space via ⟨r(n)⟩ (-3 ≤ n ≤ 3) in atoms, correlation energies in diatomic molecules, and the quality of fitting potential energy curves as measured by spectroscopic constants. All energy calculations with ANO-VT-QZ have contraction errors within "chemical accuracy" of 1 kcal/mol, which is not true for cc-pVQZ, suggesting some improvement compared to the correlation consistent series of Dunning and co-workers. PMID:26979680
Coupled cluster calculations on TiO2 nanoclusters
Berardo, Enrico; Hu, Hanshi; Kowalski, Karol; Zwijnenburg, Martijn A.
2013-08-14
The excitation energies of the four lowest-lying singlet excited states of the TiO2 Ti2O4 and Ti3O6 clusters are calculated by a variety of different Equation-of-Motion Coupled Cluster (EOM-CC) approaches in order to obtain benchmark values for the optical excitations of titanium dioxide clusters. More specifically we investigate what is the effect of the inclusion of triple excitations "triples" in the (EOM-)CC scheme on the calculated excited states of those clusters. While for the monomer and dimer the inclusion of triples causes only a rigid shift in the excitation energies, in the case of the trimer the crossing of the interested states is observed. Coupled cluster approaches where triples are treated perturbatively were found to offer no advantage over EOM-CCSD, whereas the active-space methods (EOM-CCSDt(II/I)) proved to yield results very close to the full EOM-CCSDT, but at a much lower computational cost.
High performance organic photovoltaics with plasmonic-coupled metal nanoparticle clusters.
Park, Hyung Il; Lee, Seunghoon; Lee, Ju Min; Nam, Soo Ah; Jeon, Taewoo; Han, Sang Woo; Kim, Sang Ouk
2014-10-28
Performance enhancement of organic photovoltaics using plasmonic nanoparticles has been limited without interparticle plasmon coupling. We demonstrate high performance organic photovoltaics employing gold nanoparticle clusters with controlled morphology as a plasmonic component. Near-field coupling at the interparticle gaps of nanoparticle clusters gives rise to strong enhancement in localized electromagnetic field, which led to the significant improvement of exciton generation and dissociation in the active layer of organic solar cells. A power conversion efficiency of 9.48% is attained by employing gold nanoparticle clusters at the bottom of the organic active layer. This is one of the highest efficiency values reported thus far for the single active layer organic photovoltaics. PMID:25299878
Motion of clusters of weakly coupled two-dimensional cavity solitons
Rosanov, N. N. Fedorov, S. V.; Shatsev, A. N.
2006-04-15
An analysis of clusters of weakly coupled two-dimensional spatial optical solitons in a large-aperture class A laser with a saturable absorber is developed. The symmetries that control the transverse motion of the clusters are described. Numerical solutions of the governing generalized complex Ginzburg-Landau equation demonstrate the existence of four types of clusters of weakly coupled cavity solitons that correspond to symmetries of transverse intensity distributions and energy flows: (1) stationary (with two mirror symmetry axes), (2) rotating about a stationary center of mass (invariant under rotation), (3) translating without rotation (with a single mirror symmetry axis), and (4) asymmetric ones rotating about a center of mass that moves around a circle (with equal periods of rotation and circular motion)
Computation of Spectroscopic Factors with the Coupled-Cluster Method
Jensen, O.; Hagen, Gaute; Papenbrock, T.; Dean, David Jarvis; Vaagen, J. S.
2010-01-01
We present a calculation of spectroscopic factors within coupled-cluster theory. Our derivation of algebraic equations for the one-body overlap functions are based on coupled-cluster equation-of-motion solutions for the ground and excited states of the doubly magic nucleus with mass number A and the odd-mass neighbor with mass A-1. As a proof-of-principle calculation, we consider ^{16}O and the odd neighbors ^{15}O and ^{15}N, and compute the spectroscopic factor for nucleon removal from ^{16}O. We employ a renormalized low-momentum interaction of the V_{low-k} type derived from a chiral interaction at next-to-next-to-next-to-leading order. We study the sensitivity of our results by variation of the momentum cutoff, and then discuss the treatment of the center of mass.
Coupling between {alpha}-condensed states and normal cluster states
Itagaki, N.; Kokalova, Tz.; Ito, M.; Kimura, M.; Oertzen, W. von
2008-03-15
We have studied the {alpha}-condensed states of {sup 16}O and {sup 20}Ne based on a microscopic {alpha}-cluster model. This was performed by introducing a Monte Carlo technique for the description of the THSR (Tohsaki Horiuchi Schuck Roepke) wave function, which is called the ''virtual THSR'' wave function. Earlier microscopic calculations pointed out the possibility of the existence of four-{alpha}-cluster condensed states. Here, in addition to studying the four-{alpha} case, we also studied the case of five-{alpha} particles, for which the states are shown to be stable around the threshold energy even after taking into account the coupling effect between normal cluster states with {sup 16}O+{alpha} configurations.
Brabec, Jiri; Bhaskaran-Nair, Kiran; Govind, Niranjan; Pittner, Jiri; Kowalski, Karol
2012-11-07
The concept of the model space underlying multireference coupled-cluster (MRCC) formulations is a powerful tool to deal with complex correlation effects for various electronic states. Here, we demonstrate that iterative state-specific MRCC methods (SS-MRCC) based on properly defined model spaces can be used to describe core-level excited states even when canonical Hartree-Fock orbitals are utilized. We show that the SS-MRCC models with single and double excitations (SSMRCCSD) are comparable in accuracy to high-level single reference equation-of-motion coupled cluster (EOMCC) formalism. We also demonstrate that the SS-MRCC methods are capable of providing high accuracy results without experiencing numerical problems of the EOMCC methods.
Orbital spaces in the divide-expand-consolidate coupled cluster method
NASA Astrophysics Data System (ADS)
Ettenhuber, Patrick; Baudin, Pablo; Kjærgaard, Thomas; Jørgensen, Poul; Kristensen, Kasper
2016-04-01
The theoretical foundation for solving coupled cluster singles and doubles (CCSD) amplitude equations to a desired precision in terms of independent fragment calculations using restricted local orbital spaces is reinvestigated with focus on the individual error sources. Four different error sources are identified theoretically and numerically and it is demonstrated that, for practical purposes, local orbital spaces for CCSD calculations can be identified from calculations at the MP2 level. The development establishes a solid theoretical foundation for local CCSD calculations for the independent fragments, and thus for divide-expand-consolidate coupled cluster calculations for large molecular systems with rigorous error control. Based on this theoretical foundation, we have developed an algorithm for determining the orbital spaces needed for obtaining the single fragment energies to a requested precision and numerically demonstrated the robustness and precision of this algorithm.
Multireference state-specific coupled-cluster methods. State-of-the-art and perspectives.
Ivanov, Vladimir V; Lyakh, Dmitry I; Adamowicz, Ludwik
2009-04-14
This work reviews the state-specific multireference coupled-cluster (CC) approaches which have been developed as approximate methods for performing high-level quantum mechanical calculations on quasidegenerate ground and excited states of atomic and molecular systems. The term "quasidegenerate" refers to a state that cannot be described even in the first approximation by a single-determinant wavefunction (a Slater determinant), but requires two or more determinants for this purpose. The main challenge with applying the coupled-cluster theory to such states is in describing the electron correlation effects in the wavefunctions representing these states in a manner that is size-extensive, yet accurate and simple enough so the method can be routinely applied to small and medium-size molecular systems. We are describing how this can be accomplished within a theory that focuses on only one state of the system in a single CC calculation (the state-specific theory). PMID:19325966
Adiabatic transfer of coherences in a cluster of coupled nuclear spins
Lee, Jae-Seung; Cardwell, Kate E.; Khitrin, A. K.
2005-12-15
It is experimentally demonstrated that quantum coherences can be efficiently transferred using adiabatic energy-level crossing. In a cluster of six dipolar-coupled proton spins of benzene, oriented by a liquid-crystalline matrix, a single-quantum coherence between one pair of states has been adiabatically transferred to another pair of states, and the superposition survived even after ten successive energy-level crossings.
Peng, Degao; Steinmann, Stephan N; van Aggelen, Helen; Yang, Weitao
2013-09-14
The recent proposal to determine the (exact) correlation energy based on pairing matrix fluctuations by van Aggelen et al. ["Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random phase approximation," preprint arXiv:1306.4957 (2013)] revived the interest in the simplest approximation along this path: the particle-particle random phase approximation (pp-RPA). In this paper, we present an analytical connection and numerical demonstrations of the equivalence of the correlation energy from pp-RPA and ladder-coupled-cluster doubles. These two theories reduce to identical algebraic matrix equations and correlation energy expressions. The numerical examples illustrate that the correlation energy missed by pp-RPA in comparison with coupled-cluster singles and doubles is largely canceled out when considering reaction energies. This theoretical connection will be beneficial to design density functionals with strong ties to coupled-cluster theories and to study molecular properties at the pp-RPA level relying on well established coupled cluster techniques. PMID:24050333
NASA Astrophysics Data System (ADS)
Coriani, Sonia; Koch, Henrik
2015-11-01
We present a simple scheme to compute X-ray absorption spectra (e.g., near-edge absorption fine structure) and core ionisation energies within coupled cluster linear response theory. The approach exploits the so-called core-valence separation to effectively reduce the excitation space to processes involving at least one core orbital, and it can be easily implemented within any pre-existing coupled cluster code for low energy states. We further develop a perturbation correction that incorporates the effect of the excluded part of the excitation space. The correction is shown to be highly accurate. Test results are presented for a set of molecular systems for which well converged results in full space could be generated at the coupled cluster singles and doubles level of theory only, but the scheme is straightforwardly generalizable to all members of the coupled cluster hierarchy of approximations, including CC3.
Egashira, Kazuhiro; Yamada, Yurika; Kita, Yukiumi; Tachikawa, Masanori
2015-02-07
The magnetic coupling of the chromium dimer cation, Cr{sub 2}{sup +}, has been an outstanding problem for decades. An optical absorption spectrum of Cr{sub 2}{sup +} has been obtained by photodissociation spectroscopy in the photon-energy range from 2.0 to 5.0 eV. Besides, calculations have been performed by the equation-of-motion coupled-cluster singles and doubles method for vertical excitation of the species. Their coincidence supports our assignment that the ground electronic state exhibits a ferromagnetic spin coupling, which is contrary to those of neutral and negatively charged dimers, Cr{sub 2} and Cr{sub 2}{sup −}, in their lowest spin states.
Krause, Katharina; Bauer, Mirko; Klopper, Wim
2016-06-14
Theoretical description of phosphorescence lifetimes in the condensed phase requires a method that takes into account both spin-orbit coupling and solvent-solute interactions. To obtain such a method, we have coupled our recently developed two-component coupled-cluster method with singles and approximated doubles to a polarizable environment. With this new method, we investigate how different solvents effect the electronic phosphorescence energies and lifetimes of 4H-pyran-4-thione. PMID:27158835
Slicing and dicing globular clusters: dynamically evolved single stellar populations
NASA Astrophysics Data System (ADS)
Sippel, Anna C.; Hurley, Jarrod R.
2016-04-01
We utilize direct N-body models of globular clusters including stellar evolution to calculate magnitudes for each star in the Hubble Space Telescope Advanced Camera for Surveys 555, 606 and 814 filters. This enables us to analyse the colour of dynamically evolved single stellar populations over time in colour-magnitude diagrams of both, resolved and integrated globular clusters. We find that the change of integrated cluster colour is driven predominantly by the colour of the brightest stars available and hence by stellar evolution, but not by the removal of low-mass stars. We show that even in mass-segregated clusters, different stellar populations are distributed over the entire cluster. This implies that evolved stars also exist within and outside the half-mass radius.
Mode couplings and resonance instabilities in dust clusters.
Qiao, Ke; Kong, Jie; Oeveren, Eric Van; Matthews, Lorin S; Hyde, Truell W
2013-10-01
The normal modes for three to seven particle two-dimensional (2D) dust clusters in a complex plasma are investigated using an N-body simulation. The ion wakefield downstream of each particle is shown to induce coupling between horizontal and vertical modes. The rules of mode coupling are investigated by classifying the mode eigenvectors employing the Bessel and trigonometric functions indexed by order integers (m, n). It is shown that coupling only occurs between two modes with the same m and that horizontal modes having a higher shear contribution exhibit weaker coupling. Three types of resonances are shown to occur when two coupled modes have the same frequency. Discrete instabilities caused by both the first and third type of resonances are verified and instabilities caused by the third type of resonance are found to induce melting. The melting procedure is observed to go through a two-step process with the solid-liquid transition closely obeying the Lindemann criterion. PMID:24229289
NASA Astrophysics Data System (ADS)
Bartlett, Rodney
2008-04-01
Coupled-cluster (CC) theory derives from the ansatz that the n-particle wavefunction is |ψ>=exp(T)|0>, where T is an excitation operator with |0> some choice of mean-field wavefunction. That is sufficient to obtain energies. But to obtain anything else, we use the CC functional, E=<0|(!+λ)exp(-T)Hexp(T)|0>, whose left and right hand eigenvectors provide energies and associated density matrices for the treatment of properties in CC theory. The introduction of λ makes it possible to obtain the ˜3N forces associated with N atoms in the same time as the energy itself. This is essential information for indentifying the critical points on a potential energy surface and their associated Hessians, for either the prediction of vibrational spectra or to characterize a saddle point (transition state) for a reaction. A generalization of the functional to φ(k) =<0|L(k) exp(-T)Hexp(T)R(k)|0>, provides excitation energies, φ(k) along with excited state left- and right-hand wavefunctions, Finally, with the response functions obtained from these left- and right-hand eigenfunctions, used in closed form, higher-order properties like NMR coupling constants are obtained. In this way, coupled-cluster theory provides a method that addresses all the properties of interest for molecules and their interactions. This development will be the topic of our contribution. For details please see, R. J. Bartlett and M Musial, ``Coupled-cluster theory in quantum chemistry'', Revs. of Modern Phys. 79, 291-352 (2007).
Byrd, Jason N; Lutz, Jesse J; Jin, Yifan; Ranasinghe, Duminda S; Montgomery, John A; Perera, Ajith; Duan, Xiaofeng F; Burggraf, Larry W; Sanders, Beverly A; Bartlett, Rodney J
2016-07-14
The accurate determination of the preferred Si12C12 isomer is important to guide experimental efforts directed towards synthesizing SiC nano-wires and related polymer structures which are anticipated to be highly efficient exciton materials for the opto-electronic devices. In order to definitively identify preferred isomeric structures for silicon carbon nano-clusters, highly accurate geometries, energies, and harmonic zero point energies have been computed using coupled-cluster theory with systematic extrapolation to the complete basis limit for set of silicon carbon clusters ranging in size from SiC3 to Si12C12. It is found that post-MBPT(2) correlation energy plays a significant role in obtaining converged relative isomer energies, suggesting that predictions using low rung density functional methods will not have adequate accuracy. Utilizing the best composite coupled-cluster energy that is still computationally feasible, entailing a 3-4 SCF and coupled-cluster theory with singles and doubles extrapolation with triple-ζ (T) correlation, the closo Si12C12 isomer is identified to be the preferred isomer in the support of previous calculations [X. F. Duan and L. W. Burggraf, J. Chem. Phys. 142, 034303 (2015)]. Additionally we have investigated more pragmatic approaches to obtaining accurate silicon carbide isomer energies, including the use of frozen natural orbital coupled-cluster theory and several rungs of standard and double-hybrid density functional theory. Frozen natural orbitals as a way to compute post-MBPT(2) correlation energy are found to be an excellent balance between efficiency and accuracy. PMID:27421410
NASA Astrophysics Data System (ADS)
Byrd, Jason N.; Lutz, Jesse J.; Jin, Yifan; Ranasinghe, Duminda S.; Montgomery, John A.; Perera, Ajith; Duan, Xiaofeng F.; Burggraf, Larry W.; Sanders, Beverly A.; Bartlett, Rodney J.
2016-07-01
The accurate determination of the preferred Si12C12 isomer is important to guide experimental efforts directed towards synthesizing SiC nano-wires and related polymer structures which are anticipated to be highly efficient exciton materials for the opto-electronic devices. In order to definitively identify preferred isomeric structures for silicon carbon nano-clusters, highly accurate geometries, energies, and harmonic zero point energies have been computed using coupled-cluster theory with systematic extrapolation to the complete basis limit for set of silicon carbon clusters ranging in size from SiC3 to Si12C12. It is found that post-MBPT(2) correlation energy plays a significant role in obtaining converged relative isomer energies, suggesting that predictions using low rung density functional methods will not have adequate accuracy. Utilizing the best composite coupled-cluster energy that is still computationally feasible, entailing a 3-4 SCF and coupled-cluster theory with singles and doubles extrapolation with triple-ζ (T) correlation, the closo Si12C12 isomer is identified to be the preferred isomer in the support of previous calculations [X. F. Duan and L. W. Burggraf, J. Chem. Phys. 142, 034303 (2015)]. Additionally we have investigated more pragmatic approaches to obtaining accurate silicon carbide isomer energies, including the use of frozen natural orbital coupled-cluster theory and several rungs of standard and double-hybrid density functional theory. Frozen natural orbitals as a way to compute post-MBPT(2) correlation energy are found to be an excellent balance between efficiency and accuracy.
NASA Astrophysics Data System (ADS)
Larsen, Helena; Olsen, Jeppe; Hättig, Christof; Jørgensen, Poul; Christiansen, Ove; Gauss, Jürgen
1999-08-01
Static and frequency-dependent polarizabilities and first hyperpolarizabilities have been calculated for HF and Ne using full configuration interaction (FCI) and a hierarchy of coupled cluster models: coupled cluster singles (CCS), an approximate coupled cluster singles and doubles model (CC2), coupled cluster singles and doubles (CCSD), an approximate coupled cluster singles, doubles, and triples model (CC3), and coupled cluster singles, doubles, and triples (CCSDT). A previous study of BH concerning FCI benchmarking has been extended to include CC3 and static CCSDT values. Systematic improvements of the polarizabilities and the hyperpolarizabilities are found going from CCS to CCSD and from CCSD to CC3 or CCSDT. Little or no improvement of the polarizabilities and no improvement of the hyperpolarizabilities are seen when going from CCS to CC2. The CCSD results represent a significant improvement over CCS and CC2 but are again surpassed by the CC3 results which agree very well with the FCI values. The relative error for the static polarizability at the CC3 level is 0.11% for Ne and, respectively, 0.16% and 0.20% for αxx and αzz of HF. For βzzz and βzxx the errors are 0.50% and 1.7%, respectively. Only in the challenging case of BH does CCSDT improve the CC3 values. The dispersion for the polarizabilities and hyperpolarizabilities is predicted with increasing accuracy in the CCS-CC2-CCSD-CC3 sequence as expected from the increasing accuracy of the electronic excitation energies. For all molecules the effect of orbital relaxation has been investigated for the static properties. The inclusion of orbital relaxation gives results that are somewhat different from the unrelaxed results but are in general no improvement.
Simulation of circularly polarized luminescence spectra using coupled cluster theory
McAlexander, Harley R.; Crawford, T. Daniel
2015-04-21
We report the first computations of circularly polarized luminescence (CPL) rotatory strengths at the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) level of theory. Using a test set of eight chiral ketones, we compare both dipole and rotatory strengths for absorption (electronic circular dichroism) and emission to the results from time-dependent density-functional theory (TD-DFT) and available experimental data for both valence and Rydberg transitions. For two of the compounds, we obtained optimized geometries of the lowest several excited states using both EOM-CCSD and TD-DFT and determined that structures and EOM-CCSD transition properties obtained with each structure were sufficiently similar that TD-DFT optimizations were acceptable for the remaining test cases. Agreement between EOM-CCSD and the Becke three-parameter exchange function and Lee-Yang-Parr correlation functional (B3LYP) corrected using the Coulomb attenuating method (CAM-B3LYP) is typically good for most of the transitions, though agreement with the uncorrected B3LYP functional is significantly worse for all reported properties. The choice of length vs. velocity representation of the electric dipole operator has little impact on the EOM-CCSD transition strengths for nearly all of the states we examined. For a pair of closely related β, γ-enones, (1R)-7-methylenebicyclo[2.2.1]heptan-2-one and (1S)-2-methylenebicyclo[2.2.1]heptan-7-one, we find that EOM-CCSD and CAM-B3LYP agree with the energetic ordering of the two possible excited-state conformations, resulting in good agreement with experimental rotatory strengths in both absorption and emission, whereas B3LYP yields a qualitatively incorrect result for the CPL signal of (1S)-2-methylenebicyclo[2.2.1]heptan-7-one. Finally, we predict that one of the compounds considered here, trans-bicyclo[3.3.0]octane-3,7-dione, is unique in that it exhibits an achiral ground state and a chiral first excited state, leading to a strong CPL
High-accuracy coupled cluster calculations of atomic properties
Borschevsky, A.; Yakobi, H.; Eliav, E.; Kaldor, U.
2015-01-22
The four-component Fock-space coupled cluster and intermediate Hamiltonian methods are implemented to evaluate atomic properties. The latter include the spectra of nobelium and lawrencium (elements 102 and 103) in the range 20000-30000 cm{sup −1}, the polarizabilities of elements 112-114 and 118, required for estimating their adsorption enthalpies on surfaces used to separate them in accelerators, and the nuclear quadrupole moments of some heavy atoms. The calculations on superheavy elements are supported by the very good agreement with experiment obtained for the lighter homologues.
Time-dependent coupled-cluster method for atomic nuclei
Pigg, David A; Hagen, Gaute; Nam, Hai Ah; Papenbrock, Thomas F
2012-01-01
We study time-dependent coupled-cluster theory in the framework of nuclear physics. Based on Kvaal's bi-variational formulation of this method [S. Kvaal, arXiv:1201.5548], we explicitly demonstrate that observables that commute with the Hamiltonian are conserved under time evolution. We explore the role of the energy and of the similarity-transformed Hamiltonian under real and imaginary time evolution and relate the latter to similarity renormalization group transformations. Proof-of-principle computations of He-4 and O-16 in small model spaces, and computations of the Lipkin model illustrate the capabilities of the method
Communication: Improved pair approximations in local coupled-cluster methods
Schwilk, Max; Werner, Hans-Joachim; Usvyat, Denis
2015-03-28
In local coupled cluster treatments the electron pairs can be classified according to the magnitude of their energy contributions or distances into strong, close, weak, and distant pairs. Different approximations are introduced for the latter three classes. In this communication, an improved simplified treatment of close and weak pairs is proposed, which is based on long-range cancellations of individually slowly decaying contributions in the amplitude equations. Benchmark calculations for correlation, reaction, and activation energies demonstrate that these approximations work extremely well, while pair approximations based on local second-order Møller-Plesset theory can lead to errors that are 1-2 orders of magnitude larger.
Coupled-cluster theory for atoms and molecules in strong magnetic fields.
Stopkowicz, Stella; Gauss, Jürgen; Lange, Kai K; Tellgren, Erik I; Helgaker, Trygve
2015-08-21
An implementation of coupled-cluster (CC) theory to treat atoms and molecules in finite magnetic fields is presented. The main challenges for the implementation stem from the magnetic-field dependence in the Hamiltonian, or, more precisely, the appearance of the angular momentum operator, due to which the wave function becomes complex and which introduces a gauge-origin dependence. For this reason, an implementation of a complex CC code is required together with the use of gauge-including atomic orbitals to ensure gauge-origin independence. Results of coupled-cluster singles-doubles-perturbative-triples (CCSD(T)) calculations are presented for atoms and molecules with a focus on the dependence of correlation and binding energies on the magnetic field. PMID:26298118
Comparing Effects of Cluster-Coupled Patterns on Opinion Dynamics
NASA Astrophysics Data System (ADS)
Liu, Yun; Si, Xia-Meng; Zhang, Yan-Chao
2012-07-01
Community structure is another important feature besides small-world and scale-free property of complex networks. Communities can be coupled through specific fixed links between nodes, or occasional encounter behavior. We introduce a model for opinion evolution with multiple cluster-coupled patterns, in which the interconnectivity denotes the coupled degree of communities by fixed links, and encounter frequency controls the coupled degree of communities by encounter behaviors. Considering the complicated cognitive system of people, the CODA (continuous opinions and discrete actions) update rules are used to mimic how people update their decisions after interacting with someone. It is shown that, large interconnectivity and encounter frequency both can promote consensus, reduce competition between communities and propagate some opinion successfully across the whole population. Encounter frequency is better than interconnectivity at facilitating the consensus of decisions. When the degree of social cohesion is same, small interconnectivity has better effects on lessening the competence between communities than small encounter frequency does, while large encounter frequency can make the greater degree of agreement across the whole populations than large interconnectivity can.
Nonlinear mode coupling and vibrational energy transfer in Yukawa clusters
NASA Astrophysics Data System (ADS)
Qiao, Ke; Kong, Jie; Matthews, Lorin; Hyde, Truell
2015-11-01
Nonlinear mode coupling and the subsequent vibrational energy transfer that results is an important topic in chemical physics research, ranging from small molecules consisting of several atoms to macromolecules such as those found in proteins and DNA. Nonlinear mode coupling is recognized as the mechanism leading to ergodicity, which is a foundational tenet of statistical mechanics. Over the past two decades, Yukawa systems of particles such as those found in complex plasma, have been shown to be an effective model across a large number of physical systems. In this research, nonlinear mode coupling in Yukawa clusters consisting of 3-10 particles is examined via numerical simulation of the vibrational energy transfer between modes starting from an initial excited state. The relationship between the energy transfer process and the internal resonance between modes having a specified frequency ratio and the temporal evolution of the system to a state of equal energy across all modes, i.e., the state of ergodicity, will be discussed. Support from the NSF and the DOE (award numbers PHY-1262031 and PHY-1414523) is gratefully acknowledged.
Phage cluster relationships identified through single gene analysis
2013-01-01
Background Phylogenetic comparison of bacteriophages requires whole genome approaches such as dotplot analysis, genome pairwise maps, and gene content analysis. Currently mycobacteriophages, a highly studied phage group, are categorized into related clusters based on the comparative analysis of whole genome sequences. With the recent explosion of phage isolation, a simple method for phage cluster prediction would facilitate analysis of crude or complex samples without whole genome isolation and sequencing. The hypothesis of this study was that mycobacteriophage-cluster prediction is possible using comparison of a single, ubiquitous, semi-conserved gene. Tape Measure Protein (TMP) was selected to test the hypothesis because it is typically the longest gene in mycobacteriophage genomes and because regions within the TMP gene are conserved. Results A single gene, TMP, identified the known Mycobacteriophage clusters and subclusters using a Gepard dotplot comparison or a phylogenetic tree constructed from global alignment and maximum likelihood comparisons. Gepard analysis of 247 mycobacteriophage TMP sequences appropriately recovered 98.8% of the subcluster assignments that were made by whole-genome comparison. Subcluster-specific primers within TMP allow for PCR determination of the mycobacteriophage subcluster from DNA samples. Using the single-gene comparison approach for siphovirus coliphages, phage groupings by TMP comparison reflected relationships observed in a whole genome dotplot comparison and confirm the potential utility of this approach to another widely studied group of phages. Conclusions TMP sequence comparison and PCR results support the hypothesis that a single gene can be used for distinguishing phage cluster and subcluster assignments. TMP single-gene analysis can quickly and accurately aid in mycobacteriophage classification. PMID:23777341
NASA Astrophysics Data System (ADS)
Piotto, Giampaolo
2015-08-01
The discovery of multiple stellar populations in globular clusters has revolutionized our view of these objects one thought to be simple, single population stellar systems. Different star formation scenarios have been proposed in order to account for the photometric and spectroscopic properties of the different populations hosted by the single cluster, and some of them imply that the original cluster should have been much more massive than it is now, with a significant fraction of the original stars lost into the environment (Galaxy halo or bulge). Because of this, globular clusters become relevant not only as tracers of the general process of galaxy halo formation, but also possible incubators of most (all?) halo stars.In my talk I will briefly summarize the basic observational facts that made the community at large to accept the idea of population multiplicity.I will also present the newest results coming from an extensive, multi-wavelength astrometric and photometric survey, which includes UV data from ACS and WFC3/HST of close to half of the Milky Way globular clusters. The increasing number of spectroscopic surveys of stars in globular clusters, coupled with the capability of (UV) photometry to distinguish different populations has largely increased our capability to trace the basic chemical properties of the many populations within a single cluster.I will present a census of the presence of multiple populations in GCs, their chemical tagging, radial distribution, and kinematics.Possible correlations of multiple populations characterizing quantities with the main cluster parameters will also be presented. Implications on multiple stellar populations formation will be discussed as well as the still open issues.
Cluster analysis of WIBS single particle bioaerosol data
NASA Astrophysics Data System (ADS)
Robinson, N. H.; Allan, J. D.; Huffman, J. A.; Kaye, P. H.; Foot, V. E.; Gallagher, M.
2012-09-01
Hierarchical agglomerative cluster analysis was performed on single-particle multi-spatial datasets comprising optical diameter, asymmetry and three different fluorescence measurements, gathered using two dual Waveband Integrated Bioaerosol Sensor (WIBS). The technique is demonstrated on measurements of various fluorescent and non-fluorescent polystyrene latex spheres (PSL) before being applied to two separate contemporaneous ambient WIBS datasets recorded in a forest site in Colorado, USA as part of the BEACHON-RoMBAS project. Cluster analysis results between both datasets are consistent. Clusters are tentatively interpreted by comparison of concentration time series and cluster average measurement values to the published literature (of which there is a paucity) to represent: non-fluorescent accumulation mode aerosol; bacterial agglomerates; and fungal spores. To our knowledge, this is the first time cluster analysis has been applied to long term online PBAP measurements. The novel application of this clustering technique provides a means for routinely reducing WIBS data to discrete concentration time series which are more easily interpretable, without the need for any a priori assumptions concerning the expected aerosol types. It can reduce the level of subjectivity compared to the more standard analysis approaches, which are typically performed by simple inspection of various ensemble data products. It also has the advantage of potentially resolving less populous or subtly different particle types. This technique is likely to become more robust in the future as fluorescence-based aerosol instrumentation measurement precision, dynamic range and the number of available metrics is improved.
Matrix elements in the coupled-cluster approach - With application to low-lying states in Li
NASA Technical Reports Server (NTRS)
Martensson-Pendrill, Ann-Marie; Ynnerman, Anders
1990-01-01
A procedure is suggested for evaluating matrix elements of an operator between wavefunctions in the coupled-cluster form. The use of the exponential ansatz leads to compact exponential expressions also for matrix elements. Algorithms are developed for summing all effects of one-particle clusters and certain chains of two-particle clusters (containing the well-known random-phase approximation as a subset). The treatment of one-particle perturbations in single valence states is investigated in detail. As examples the oscillator strength for the 2s-2p transition in Li as well as the hyperfine structure for the two states are studied and compared to earlier work.
Higher-order diagrammatic vibrational coupled-cluster theory
NASA Astrophysics Data System (ADS)
Faucheaux, Jacob A.; Hirata, So
2015-10-01
Diagrammatically size-consistent and basis-set-free vibrational coupled-cluster (XVCC) theory for both zero-point energies and transition frequencies of a molecule, the latter through the equation-of-motion (EOM) formalism, is defined for an nth-order Taylor-series potential energy surface (PES). Quantum-field-theoretical tools (the rules of normal-ordered second quantization and Feynman-Goldstone diagrams) for deriving their working equations are established. The equations of XVCC and EOM-XVCC including up to the mth-order excitation operators are derived and implemented with the aid of computer algebra in the range of 1 ≤ m ≤ 8. Algorithm optimizations known as strength reduction, intermediate reuse, and factorization are carried out before code generation, reducing the cost scaling of the mth-order XVCC and EOM-XVCC in an nth-order Taylor-series PES (m ≥ n) to the optimal value of O(Nm+⌊n/2⌋), where N is the number of modes. The calculated zero-point energies and frequencies of fundamentals, overtones, and combinations as well as Fermi-resonant modes display rapid and nearly monotonic convergence with m towards the exact values for the PES. The theory with the same excitation rank as the truncation order of the Taylor-series PES (m = n) seems to strike the best cost-accuracy balance, achieving the accuracy of a few tenths of cm-1 for transitions involving (m - 3) modes and of a few cm-1 for those involving (m - 2) modes. The relationships between XVCC and the vibrational coupled-cluster theories of Prasad and coworkers and of Christiansen and coworkers as well as the size-extensive vibrational self-consistent-field and many-body perturbation theories are also elucidated.
Higher-order diagrammatic vibrational coupled-cluster theory.
Faucheaux, Jacob A; Hirata, So
2015-10-01
Diagrammatically size-consistent and basis-set-free vibrational coupled-cluster (XVCC) theory for both zero-point energies and transition frequencies of a molecule, the latter through the equation-of-motion (EOM) formalism, is defined for an nth-order Taylor-series potential energy surface (PES). Quantum-field-theoretical tools (the rules of normal-ordered second quantization and Feynman-Goldstone diagrams) for deriving their working equations are established. The equations of XVCC and EOM-XVCC including up to the mth-order excitation operators are derived and implemented with the aid of computer algebra in the range of 1 ≤ m ≤ 8. Algorithm optimizations known as strength reduction, intermediate reuse, and factorization are carried out before code generation, reducing the cost scaling of the mth-order XVCC and EOM-XVCC in an nth-order Taylor-series PES (m ≥ n) to the optimal value of O(N(m+⌊n/2⌋)), where N is the number of modes. The calculated zero-point energies and frequencies of fundamentals, overtones, and combinations as well as Fermi-resonant modes display rapid and nearly monotonic convergence with m towards the exact values for the PES. The theory with the same excitation rank as the truncation order of the Taylor-series PES (m = n) seems to strike the best cost-accuracy balance, achieving the accuracy of a few tenths of cm(-1) for transitions involving (m - 3) modes and of a few cm(-1) for those involving (m - 2) modes. The relationships between XVCC and the vibrational coupled-cluster theories of Prasad and coworkers and of Christiansen and coworkers as well as the size-extensive vibrational self-consistent-field and many-body perturbation theories are also elucidated. PMID:26450290
NASA Astrophysics Data System (ADS)
Bhaskaran-Nair, Kiran; Kowalski, Karol; Jarrell, Mark; Moreno, Juana; Shelton, William A.
2015-11-01
Polyacenes have attracted considerable attention due to their various applications in organic optoelectronic materials. This study focuses on linear polyacenes and their electron affinity (EA) and ionization potential (IP) properties. We have employed our recent implementation of EA/IP equation of motion coupled cluster singles and doubles (EA/IP-EOMCCSD) methods which are accurate, computationally efficient and are capable of treating large systems employing reasonable basis sets size. The EA/IP results obtained for naphthalene, anthracene, tetracene, pentacene, hexacene and heptacene are in a good agreement with experiment. Comparison between quality of excitation energies obtained from IP-EOMCCSD and EE-EOMCCSD formalisms were also studied.
Sahoo, Bijaya K.; Chaudhuri, Rajat; Das, B. P.; Mukherjee, Debashis
2006-04-28
We report the result of our ab initio calculation of the 6s{sup 2}S{sub 1/2}{yields}5d{sup 2}D{sub 3/2} parity nonconserving electric dipole transition amplitude in {sup 137}Ba{sup +} based on relativistic coupled-cluster theory. Considering single, double, and partial triple excitations, we have achieved an accuracy of less than 1%. If the accuracy of our calculation can be matched by the proposed parity nonconservation experiment in Ba{sup +} for the above transition, then the combination of the two results would provide an independent nonaccelerator test of the standard model of particle physics.
Comparison of coupled-cluster methods which include the effects of connected triple excitations
NASA Technical Reports Server (NTRS)
Scuseria, Gustavo E.; Lee, Timothy J.
1990-01-01
The 'coupled cluster single, double, and triple' (CCSDT) excitation model has been used to ascertain electron correlation energies for 14 different molecules representing a variety of chemical bonds, in conjunction with several methods of this type 'CCSDT-x', which include only an approximate treatment of connected triple excitations; these methods encompass CCSDT-1a, -1b, -2, -3, and -4, as well as the novel CCSD(T). While all methods treat the effects of connected triple excitations iteratively, CCSD(T) approaches then perturbationally. For the 14 molecules considered, the CCSD(T) method's average error relative to CCSDT is substantially lower than any of the CCSDT-x methods.
Optimization of the Coupled Cluster Implementation in NWChem on Petascale Parallel Architectures
Anisimov, Victor; Bauer, Gregory H.; Chadalavada, Kalyana; Olson, Ryan M.; Glenski, Joseph W.; Kramer, William T.; Apra, Edoardo; Kowalski, Karol
2014-09-04
Coupled cluster singles and doubles (CCSD) algorithm has been optimized in NWChem software package. This modification alleviated the communication bottleneck and provided from 2- to 5-fold speedup in the CCSD iteration time depending on the problem size and available memory. Sustained 0.60 petaflop/sec performance on CCSD(T) calculation has been obtained on NCSA Blue Waters. This number included all stages of the calculation from initialization till termination, iterative computation of single and double excitations, and perturbative accounting for triple excitations. In the section of perturbative triples alone, the computation maintained 1.18 petaflop/sec performance level. CCSD computations have been performed on Guanine-Cytosine deoxydinucleotide monophosphate (GC-dDMP) to probe the conformational energy difference in DNA single strand in A- and B-conformations. The computation revealed significant discrepancy between CCSD and classical force fields in prediction of relative energy of A- and B-conformations of GC-dDMP.
Communication: The performance of non-iterative coupled cluster quadruples models.
Eriksen, Janus J; Matthews, Devin A; Jørgensen, Poul; Gauss, Jürgen
2015-07-28
We compare the numerical performance of various non-iterative coupled cluster (CC) quadruples models. The results collectively show how approaches that attempt to correct the CC singles and doubles energy for the combined effect of triple and quadruple excitations all fail at recovering the correlation energy of the full CC singles, doubles, triples, and quadruples (CCSDTQ) model to within sufficient accuracy. Such a level of accuracy is only achieved by models that make corrections to the full CC singles, doubles, and triples (CCSDT) energy for the isolated effect of quadruple excitations of which the CCSDT(Q-3) and CCSDT(Q-4) models of the Lagrangian-based CCSDT(Q-n) perturbation series are found to outperform alternative models that add either of the established [Q] and (Q) corrections to the CCSDT energy. PMID:26233096
Myllys, Nanna; Elm, Jonas; Halonen, Roope; Kurtén, Theo; Vehkamäki, Hanna
2016-02-01
We investigate the utilization of the domain local pair natural orbital coupled cluster (DLPNO-CCSD(T)) method for calculating binding energies of atmospherical molecular clusters. Applied to small complexes of atmospherical relevance we find that the DLPNO method significantly reduces the scatter in the binding energy, which is commonly present in DFT calculations. For medium sized clusters consisting of sulfuric acid and bases the DLPNO method yields a systematic underestimation of the binding energy compared to canonical coupled cluster results. The errors in the DFT binding energies appear to be more random, while the systematic nature of the DLPNO results allows the establishment of a scaling factor, to better mimic the canonical coupled cluster calculations. Based on the trends identified for the small and medium sized systems, we further extend the application of the DLPNO method to large acid - base clusters consisting of up to 10 molecules, which have previously been out of reach with accurate coupled cluster methods. Using the Atmospheric Cluster Dynamics Code (ACDC) we compare the sulfuric acid dimer formation based on the new DLPNO binding energies with previously published RI-CC2/aug-cc-pV(T+d)Z results. We also compare the simulated sulfuric acid dimer concentration as a function of the base concentration with measurement data from the CLOUD chamber and flow tube experiments. The DLPNO method, even after scaling, underpredicts the dimer concentration significantly. Reasons for this are discussed. PMID:26771121
NASA Astrophysics Data System (ADS)
Takashima, Hideaki; Kitajima, Kazutaka; Tanaka, Yoshito; Fujiwara, Hideki; Sasaki, Keiji
2014-02-01
Toward complete coupling between propagating light (PL) and a single localized-surface-plasmon (LSP) nanostructure, we propose a tapered-fiber-coupled microspherical cavity system combining an Au-coated probe tip. This system possesses the unique characteristic of precise adjustability for the fiber-cavity coupling rate and the cavity-plasmon coupling rate, which is indispensable for achieving the critical coupling conditions. We successfully demonstrate the 93% PL coupling into the LSP antenna with an effective area of a 58 nm circle, exceeding the diffraction limit.
Spherical coupled-cluster theory for open-shell nuclei
NASA Astrophysics Data System (ADS)
Jansen, G. R.
2013-08-01
Background: A microscopic description of nuclei is important to understand the nuclear shell model from fundamental principles. This is difficult to achieve for more than the lightest nuclei without an effective approximation scheme.Purpose: Define and evaluate an approximation scheme that can be used to study nuclei that are described as two particles attached to a closed (sub-)shell nucleus.Methods: The equation-of-motion coupled-cluster formalism has been used to obtain ground- and excited-state energies. This method is based on the diagonalization of a non-Hermitian matrix obtained from a similarity transformation of the many-body nuclear Hamiltonian. A chiral interaction at the next-to-next-to-next-to leading order (N3LO) using a cutoff at 500 MeV was used.Results: The ground-state energies of 6Li and 6He were in good agreement with a no-core shell-model calculation using the same interaction. Several excited states were also produced with overall good agreement. Only the Jπ=3+ excited state in 6Li showed a sizable deviation. The ground-state energies of 18O, 18F, and 18Ne were converged but underbound compared to experiment. Moreover, the calculated spectra were converged and comparable to both experiment and shell-model studies in this region. Some excited states in 18O were high or missing in the spectrum. It was also shown that the wave function for both ground and excited states separates into an intrinsic part and a Gaussian for the center-of-mass coordinate. Spurious center-of-mass excitations are clearly identified.Conclusions: Results are converged with respect to the size of the model space and the method can be used to describe nuclear states with simple structure. Especially the ground-state energies were very close to what has been achieved by exact diagonalization. To obtain a closer match with experimental data, effects of three-nucleon forces, the scattering continuum, as well as additional configurations in the coupled-cluster approximations
Cluster analysis of WIBS single-particle bioaerosol data
NASA Astrophysics Data System (ADS)
Robinson, N. H.; Allan, J. D.; Huffman, J. A.; Kaye, P. H.; Foot, V. E.; Gallagher, M.
2013-02-01
Hierarchical agglomerative cluster analysis was performed on single-particle multi-spatial data sets comprising optical diameter, asymmetry and three different fluorescence measurements, gathered using two dual Wideband Integrated Bioaerosol Sensors (WIBSs). The technique is demonstrated on measurements of various fluorescent and non-fluorescent polystyrene latex spheres (PSL) before being applied to two separate contemporaneous ambient WIBS data sets recorded in a forest site in Colorado, USA, as part of the BEACHON-RoMBAS project. Cluster analysis results between both data sets are consistent. Clusters are tentatively interpreted by comparison of concentration time series and cluster average measurement values to the published literature (of which there is a paucity) to represent the following: non-fluorescent accumulation mode aerosol; bacterial agglomerates; and fungal spores. To our knowledge, this is the first time cluster analysis has been applied to long-term online primary biological aerosol particle (PBAP) measurements. The novel application of this clustering technique provides a means for routinely reducing WIBS data to discrete concentration time series which are more easily interpretable, without the need for any a priori assumptions concerning the expected aerosol types. It can reduce the level of subjectivity compared to the more standard analysis approaches, which are typically performed by simple inspection of various ensemble data products. It also has the advantage of potentially resolving less populous or subtly different particle types. This technique is likely to become more robust in the future as fluorescence-based aerosol instrumentation measurement precision, dynamic range and the number of available metrics are improved.
Learning-rate-dependent clustering and self-development in a network of coupled phase oscillators
NASA Astrophysics Data System (ADS)
Niyogi, Ritwik K.; English, L. Q.
2009-12-01
We investigate the role of the learning rate in a Kuramoto Model of coupled phase oscillators in which the coupling coefficients dynamically vary according to a Hebbian learning rule. According to the Hebbian theory, a synapse between two neurons is strengthened if they are simultaneously coactive. Two stable synchronized clusters in antiphase emerge when the learning rate is larger than a critical value. In such a fast learning scenario, the network eventually constructs itself into an all-to-all coupled structure, regardless of initial conditions in connectivity. In contrast, when learning is slower than this critical value, only a single synchronized cluster can develop. Extending our analysis, we explore whether self-development of neuronal networks can be achieved through an interaction between spontaneous neural synchronization and Hebbian learning. We find that self-development of such neural systems is impossible if learning is too slow. Finally, we demonstrate that similar to the acquisition and consolidation of long-term memory, this network is capable of generating and remembering stable patterns.
Local Correlation Calculations Using Standard and Renormalized Coupled-Cluster Methods
NASA Astrophysics Data System (ADS)
Piecuch, Piotr; Li, Wei; Gour, Jeffrey
2009-03-01
Local correlation variants of the coupled-cluster (CC) theory with singles and doubles (CCSD) and CC methods with singles, doubles, and non-iterative triples, including CCSD(T) and the completely renormalized CR-CC(2,3) approach, are developed. The main idea of the resulting CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) methods is the realization of the fact that the total correlation energy of a large system can be obtained as a sum of contributions from the occupied orthonormal localized molecular orbitals and their respective occupied and unoccupied orbital domains. The CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) algorithms are characterized by the linear scaling of the total CPU time with the system size and embarrassing parallelism. By comparing the results of the canonical and CIM-CC calculations for normal alkanes and water clusters, it is demonstrated that the CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) approaches recover the corresponding canonical CC correlation energies to within 0.1 % or so, while offering savings in the computer effort by orders of magnitude. By examining the dissociation of dodecane into C11H23 and CH3 and several lowest-energy structures of the (H2O)n clusters, it is shown that the CIM-CC methods accurately reproduce the relative energetics of the corresponding canonical CC calculations.
Holograms for laser diode: Single mode optical fiber coupling
NASA Technical Reports Server (NTRS)
Fuhr, P. L.
1982-01-01
The low coupling efficiency of semiconductor laser emissions into a single mode optical fibers place a severe restriction on their use. Associated with these conventional optical coupling techniques are stringent alignment sensitivities. Using holographic elements, the coupling efficiency may be increased and the alignment sensitivity greatly reduced. Both conventional and computer methods used in the generation of the holographic couplers are described and diagrammed. The reconstruction geometries used are shown to be somewhat restrictive but substantially less rigid than their conventional optical counterparts. Single and double hologram techniques are examined concerning their respective ease of fabrication and relative merits.
Hu, Hanshi; Bhaskaran-Nair, Kiran; Apra, Edoardo; Govind, Niranjan; Kowalski, Karol
2014-10-02
In this paper we discuss the application of novel parallel implementation of the coupled cluster (CC) and equation-of-motion coupled cluster methods (EOMCC) in calculations of excitation energies of triplet states in beta-carotene. Calculated excitation energies are compared with experimental data, where available. We also provide a detailed description of the new parallel algorithms for iterative CC and EOMCC models involving single and doubles excitations.
Single to quadruple quantum dots with tunable tunnel couplings
Takakura, T.; Noiri, A.; Obata, T.; Yoneda, J.; Yoshida, K.; Otsuka, T.; Tarucha, S.
2014-03-17
We prepare a gate-defined quadruple quantum dot to study the gate-tunability of single to quadruple quantum dots with finite inter-dot tunnel couplings. The measured charging energies of various double dots suggest that the dot size is governed by the gate geometry. For the triple and quadruple dots, we study the gate-tunable inter-dot tunnel couplings. For the triple dot, we find that the effective tunnel coupling between side dots significantly depends on the alignment of the center dot potential. These results imply that the present quadruple dot has a gate performance relevant for implementing spin-based four-qubits with controllable exchange couplings.
Characterizing a nonclassical carbene with coupled cluster methods: cyclobutylidene.
Wang, Xiao; Agarwal, Jay; Schaefer Iii, Henry F
2016-09-21
Carbenes represent a special class of reactive compounds that possess a lone pair of electrons on a carbon atom. Among the myriad examples of carbenes in the literature, cyclobutylidene stands out as a unique nonclassical compound that includes transannular interaction between opposing C1 and C3 carbon atoms within a four-membered ring. On its lowest potential energy surface (X[combining tilde](1)A'), cyclobutylidene quickly rearranges, following three reaction paths: (i) 1,2-H migration; (ii) 1,2-C migration; and, (iii) 1,3-H migration. Herein, this reactivity is examined with high-level coupled-cluster methods [up to CCSDT(Q)]. At this level of theory, combined with extrapolation techniques to obtain energies at the complete basis set (CBS) limit, the long-standing disparity between theoretical and experimental results is resolved. Specifically, cyclobutylidene is predicted to prefer 1,2-C migration rather than 1,2-H migration. Rate constants for the three reaction paths are obtained from canonical variational transition state theory (CVT) and yield reasonable agreement with existing experimental results. Further characterization of cyclobutylidene is also reported: the singlet-triplet gap (ΔES-T) is found to be -9.3 kcal mol(-1) at the CCSDT(Q)/CBS level of theory, and anharmonic vibrational frequencies are determined with second-order vibrational perturbation theory (VPT2). PMID:27539444
Krause, Katharina; Klopper, Wim
2015-03-14
A generalization of the approximated coupled-cluster singles and doubles method and the algebraic diagrammatic construction scheme up to second order to two-component spinors obtained from a relativistic Hartree–Fock calculation is reported. Computational results for zero-field splittings of atoms and monoatomic cations, triplet lifetimes of two organic molecules, and the spin-forbidden part of the UV/Vis absorption spectrum of tris(ethylenediamine)cobalt(III) are presented.
Noniterative Multireference Coupled Cluster Methods on Heterogeneous CPU-GPU Systems
Bhaskaran-Nair, Kiran; Ma, Wenjing; Krishnamoorthy, Sriram; Villa, Oreste; van Dam, Hubertus JJ; Apra, Edoardo; Kowalski, Karol
2013-04-09
A novel parallel algorithm for non-iterative multireference coupled cluster (MRCC) theories, which merges recently introduced reference-level parallelism (RLP) [K. Bhaskaran-Nair, J.Brabec, E. Aprà, H.J.J. van Dam, J. Pittner, K. Kowalski, J. Chem. Phys. 137, 094112 (2012)] with the possibility of accelerating numerical calculations using graphics processing unit (GPU) is presented. We discuss the performance of this algorithm on the example of the MRCCSD(T) method (iterative singles and doubles and perturbative triples), where the corrections due to triples are added to the diagonal elements of the MRCCSD (iterative singles and doubles) effective Hamiltonian matrix. The performance of the combined RLP/GPU algorithm is illustrated on the example of the Brillouin-Wigner (BW) and Mukherjee (Mk) state-specific MRCCSD(T) formulations.
Dynamic Polarizabilities of Polyaromatic Hydrocarbons Using Coupled-Cluster Linear Response Theory
Hammond, Jeffrey R.; Kowalski, Karol; De Jong, Wibe A.
2007-10-14
Coupled-cluster theory with single and double excitations (CCSD) is applied to the calculation of optical properties of large polyaromatic hydrocarbons. Dipole polarizabilities are reported for benzene, pyrene, and the oligoacenes sequence n=2-6. Dynamic polarizabilities were calculated on polyacences as large asa pentacene for a single frequency and for benzene and pyrene at many frequencies. The basis set effect was studied for benzene using a variety of basis sets in the Pople and Dunning families up to aug-cc-pVQZ and the Sadlej p VTZ basis, which was used exclusively for the largest molecules. Optimized geometries were evaluated for some of the compounds using HF, B3LYP, PBE0, MP2 and CCSD to understand the role of bond-length-alteration (BLA). Finally, the polarizability results ere compared to four common density-functionals (B3LYP, BLYP, PBE0, PBE).
Relativistic coupled cluster study of diatomic compounds of Hg, Cn, and Fl
Borschevsky, A.; Pershina, V.; Eliav, E.; Kaldor, U.
2014-08-28
The structure and energetics of eight diatomic heavy-atom molecules are presented. These include the species MAu, M{sub 2}, and MHg, with M standing for the Hg, Cn (element 112), and Fl (element 114) atoms. The infinite-order relativistic 2-component Hamiltonian, known to closely reproduce 4-component results at lower computational cost, is used as framework. High-accuracy treatment of correlation is achieved by using the coupled cluster scheme with single, double, and perturbative triple excitations in large converged basis sets. The calculated interatomic separation and bond energy of Hg{sub 2}, the only compound with known experimental data, are in good agreement with measurements. The binding of Fl to Au is stronger than that of Cn, predicting stronger adsorption on gold surfaces. The bond in the M{sub 2} species is strongest for Fl{sub 2}, being of chemical nature; weaker bonds appear in Cn{sub 2} and Hg{sub 2}, which are bound by van der Waals interactions, with the former bound more strongly due to the smaller van der Waals radius. The same set of calculations was also performed using the relativistic density functional theory approach, in order to test the performance of the latter for these weakly bound systems with respect to the more accurate coupled cluster calculations. It was found that for the MAu species the B3LYP functional provides better agreement with the coupled cluster results than the B88/P86 functional. However, for the M{sub 2} and the MHg molecules, B3LYP tends to underestimate the binding energies.
Relativistic coupled cluster study of diatomic compounds of Hg, Cn, and Fl.
Borschevsky, A; Pershina, V; Eliav, E; Kaldor, U
2014-08-28
The structure and energetics of eight diatomic heavy-atom molecules are presented. These include the species MAu, M2, and MHg, with M standing for the Hg, Cn (element 112), and Fl (element 114) atoms. The infinite-order relativistic 2-component Hamiltonian, known to closely reproduce 4-component results at lower computational cost, is used as framework. High-accuracy treatment of correlation is achieved by using the coupled cluster scheme with single, double, and perturbative triple excitations in large converged basis sets. The calculated interatomic separation and bond energy of Hg2, the only compound with known experimental data, are in good agreement with measurements. The binding of Fl to Au is stronger than that of Cn, predicting stronger adsorption on gold surfaces. The bond in the M2 species is strongest for Fl2, being of chemical nature; weaker bonds appear in Cn2 and Hg2, which are bound by van der Waals interactions, with the former bound more strongly due to the smaller van der Waals radius. The same set of calculations was also performed using the relativistic density functional theory approach, in order to test the performance of the latter for these weakly bound systems with respect to the more accurate coupled cluster calculations. It was found that for the MAu species the B3LYP functional provides better agreement with the coupled cluster results than the B88/P86 functional. However, for the M2 and the MHg molecules, B3LYP tends to underestimate the binding energies. PMID:25173008
Tandon, Santokh S; Bunge, Scott D; Rakosi, Robert; Xu, Zhiqiang; Thompson, Laurence K
2009-09-01
One-pot reactions between 2,6-diformyl-4-methylphenol (DFMP) and 2-aminoethanol (AE) in the presence of cobalt(II) salts [Co(ClO4)2, CoCl2, Co(CH3CO2)2, Co(NO3)2] and sodium azide result in the self-assembly of novel one-dimensional single chain mixed-valence cobalt coordination polymers {[Co2(II)Co2(III) (HL)2(OCH3)2(N3)3]ClO(4).5H2O.CH3OH}n (1), {[Co2(II)Co2(III) (HL)2(OCH3)2(N3)3]Cl.H2O}n (2) in which tetra-cobalt cationic units are bridged by symmetrical 1,3-azides, forming single chains; mixed valence neutral tetranuclear clusters [Co2(II)Co2(III) (HL)2(OCH3)2(N3)4]CH3OH.2H2O (3), [Co2(II)Co2(III)(HL)2(OCH3)2(N3)2(CH3CO2)2].2CH3OH.2H2O (4), and the cationic cluster [Co2(II) Co2(III) (HL)2(OCH3)2(CH3OH)2(N3)2](NO3)2 (5). In all these reactions, H3L, the potentially pentadentate (N2O3), trianionic double Schiff base ligand 2,6-bis[(2-hydroxy-ethylimino)-methyl]-4-methylphenol is formed. The reaction between DFMP and AE in the presence of nickel(ii) salts and sodium azide in methanol-water mixture results in the self-assembly of ferromagnetically coupled hexanuclear complexes [Ni6(H2L)2(HL-1)2(H2O)2(N3)6](ClO4)(2).2CH3OH (6), and [Ni6(H2L)2(HL-1)2(CH3OH)2(N3)6](BF4)2 (7), involving double (H3L) and single (H2L-1) Schiff base ligands, and a neutral tetranuclear complex [Ni4(H2L)2(OCH3)2(CH3CO2)2(N3)2] (8) with only double Schiff-base (H3L). In these complexes, the nature of the anion and the reaction conditions seem to play an important role in directing the formation of tetranuclear, hexanuclear or polymeric clusters. All complexes involve divacant double cubane-type cores containing three to four different types of bridging ligands (phenoxy, azido, methoxy/alkoxy, and acetate). Variable temperature magnetic properties of these spin coupled clusters have been investigated and magneto-structural correlations have been established. PMID:19672499
Datta, Dipayan Gauss, Jürgen
2015-07-07
We report analytical calculations of isotropic hyperfine-coupling constants in radicals using a spin-adapted open-shell coupled-cluster theory, namely, the unitary group based combinatoric open-shell coupled-cluster (COSCC) approach within the singles and doubles approximation. A scheme for the evaluation of the one-particle spin-density matrix required in these calculations is outlined within the spin-free formulation of the COSCC approach. In this scheme, the one-particle spin-density matrix for an open-shell state with spin S and M{sub S} = + S is expressed in terms of the one- and two-particle spin-free (charge) density matrices obtained from the Lagrangian formulation that is used for calculating the analytic first derivatives of the energy. Benchmark calculations are presented for NO, NCO, CH{sub 2}CN, and two conjugated π-radicals, viz., allyl and 1-pyrrolyl in order to demonstrate the performance of the proposed scheme.
Ab initio Bogoliubov coupled cluster theory for open-shell nuclei
Signoracci, Angelo J.; Duguet, Thomas; Hagen, Gaute; Jansen, G. R.
2015-06-29
Background: Ab initio many-body methods have been developed over the past 10 yr to address closed-shell nuclei up to mass A≈130 on the basis of realistic two- and three-nucleon interactions. A current frontier relates to the extension of those many-body methods to the description of open-shell nuclei. Several routes to address open-shell nuclei are currently under investigation, including ideas that exploit spontaneous symmetry breaking. Purpose: Singly open-shell nuclei can be efficiently described via the sole breaking of U(1) gauge symmetry associated with particle-number conservation as a way to account for their superfluid character. While this route was recently followed within the framework of self-consistent Green's function theory, the goal of the present work is to formulate a similar extension within the framework of coupled cluster theory. Methods: We formulate and apply Bogoliubov coupled cluster (BCC) theory, which consists of representing the exact ground-state wave function of the system as the exponential of a quasiparticle excitation cluster operator acting on a Bogoliubov reference state. Equations for the ground-state energy and the cluster amplitudes are derived at the singles and doubles level (BCCSD) both algebraically and diagrammatically. The formalism includes three-nucleon forces at the normal-ordered two-body level. The first BCC code is implemented in m scheme, which will permit the treatment of doubly open-shell nuclei via the further breaking of SU(2) symmetry associated with angular momentum conservation. Results: Proof-of-principle calculations in an N_{max}=6 spherical harmonic oscillator basis for ^{16,18}O and ^{18}Ne in the BCCD approximation are in good agreement with standard coupled cluster results with the same chiral two-nucleon interaction, while ^{20}O and ^{20}Mg display underbinding relative to experiment. The breaking of U(1) symmetry, monitored by computing the variance
Ab initio Bogoliubov coupled cluster theory for open-shell nuclei
Signoracci, Angelo J.; Duguet, Thomas; Hagen, Gaute; Jansen, G. R.
2015-06-29
Background: Ab initio many-body methods have been developed over the past 10 yr to address closed-shell nuclei up to mass A≈130 on the basis of realistic two- and three-nucleon interactions. A current frontier relates to the extension of those many-body methods to the description of open-shell nuclei. Several routes to address open-shell nuclei are currently under investigation, including ideas that exploit spontaneous symmetry breaking. Purpose: Singly open-shell nuclei can be efficiently described via the sole breaking of U(1) gauge symmetry associated with particle-number conservation as a way to account for their superfluid character. While this route was recently followed withinmore » the framework of self-consistent Green's function theory, the goal of the present work is to formulate a similar extension within the framework of coupled cluster theory. Methods: We formulate and apply Bogoliubov coupled cluster (BCC) theory, which consists of representing the exact ground-state wave function of the system as the exponential of a quasiparticle excitation cluster operator acting on a Bogoliubov reference state. Equations for the ground-state energy and the cluster amplitudes are derived at the singles and doubles level (BCCSD) both algebraically and diagrammatically. The formalism includes three-nucleon forces at the normal-ordered two-body level. The first BCC code is implemented in m scheme, which will permit the treatment of doubly open-shell nuclei via the further breaking of SU(2) symmetry associated with angular momentum conservation. Results: Proof-of-principle calculations in an Nmax=6 spherical harmonic oscillator basis for 16,18O and 18Ne in the BCCD approximation are in good agreement with standard coupled cluster results with the same chiral two-nucleon interaction, while 20O and 20Mg display underbinding relative to experiment. The breaking of U(1) symmetry, monitored by computing the variance associated with the particle-number operator, is
Electrochemical Single-Molecule Transistors with Optimized Gate Coupling.
Osorio, Henrry M; Catarelli, Samantha; Cea, Pilar; Gluyas, Josef B G; Hartl, František; Higgins, Simon J; Leary, Edmund; Low, Paul J; Martín, Santiago; Nichols, Richard J; Tory, Joanne; Ulstrup, Jens; Vezzoli, Andrea; Milan, David C; Zeng, Qiang
2015-11-18
Electrochemical gating at the single molecule level of viologen molecular bridges in ionic liquids is examined. Contrary to previous data recorded in aqueous electrolytes, a clear and sharp peak in the single molecule conductance versus electrochemical potential data is obtained in ionic liquids. These data are rationalized in terms of a two-step electrochemical model for charge transport across the redox bridge. In this model the gate coupling in the ionic liquid is found to be fully effective with a modeled gate coupling parameter, ξ, of unity. This compares to a much lower gate coupling parameter of 0.2 for the equivalent aqueous gating system. This study shows that ionic liquids are far more effective media for gating the conductance of single molecules than either solid-state three-terminal platforms created using nanolithography, or aqueous media. PMID:26488257
Analytical Energy Gradients for Excited-State Coupled-Cluster Methods
NASA Astrophysics Data System (ADS)
Wladyslawski, Mark; Nooijen, Marcel
The equation-of-motion coupled-cluster (EOM-CC) and similarity transformed equation-of-motion coupled-cluster (STEOM-CC) methods have been firmly established as accurate and routinely applicable extensions of single-reference coupled-cluster theory to describe electronically excited states. An overview of these methods is provided, with emphasis on the many-body similarity transform concept that is the key to a rationalization of their accuracy. The main topic of the paper is the derivation of analytical energy gradients for such non-variational electronic structure approaches, with an ultimate focus on obtaining their detailed algebraic working equations. A general theoretical framework using Lagrange's method of undetermined multipliers is presented, and the method is applied to formulate the EOM-CC and STEOM-CC gradients in abstract operator terms, following the previous work in [P.G. Szalay, Int. J. Quantum Chem. 55 (1995) 151] and [S.R. Gwaltney, R.J. Bartlett, M. Nooijen, J. Chem. Phys. 111 (1999) 58]. Moreover, the systematics of the Lagrange multiplier approach is suitable for automation by computer, enabling the derivation of the detailed derivative equations through a standardized and direct procedure. To this end, we have developed the SMART (Symbolic Manipulation and Regrouping of Tensors) package of automated symbolic algebra routines, written in the Mathematica programming language. The SMART toolkit provides the means to expand, differentiate, and simplify equations by manipulation of the detailed algebraic tensor expressions directly. The Lagrangian multiplier formulation establishes a uniform strategy to perform the automated derivation in a standardized manner: A Lagrange multiplier functional is constructed from the explicit algebraic equations that define the energy in the electronic method; the energy functional is then made fully variational with respect to all of its parameters, and the symbolic differentiations directly yield the explicit
Nooijen, Marcel; Demel, Ondřej; Datta, Dipayan; Kong, Liguo; Shamasundar, K R; Lotrich, V; Huntington, Lee M; Neese, Frank
2014-02-28
The novel multireference equation-of-motion coupled-cluster (MREOM-CC) approaches provide versatile and accurate access to a large number of electronic states. The methods proceed by a sequence of many-body similarity transformations and a subsequent diagonalization of the transformed Hamiltonian over a compact subspace. The transformed Hamiltonian is a connected entity and preserves spin- and spatial symmetry properties of the original Hamiltonian, but is no longer Hermitean. The final diagonalization spaces are defined in terms of a complete active space (CAS) and limited excitations (1h, 1p, 2h, …) out of the CAS. The methods are invariant to rotations of orbitals within their respective subspaces (inactive, active, external). Applications to first row transition metal atoms (Cr, Mn, and Fe) are presented yielding results for up to 524 electronic states (for Cr) with an rms error compared to experiment of about 0.05 eV. The accuracy of the MREOM family of methods is closely related to its favorable extensivity properties as illustrated by calculations on the O2-O2 dimer. The computational costs of the transformation steps in MREOM are comparable to those of closed-shell Coupled Cluster Singles and Doubles (CCSD) approach. PMID:24588141
Nooijen, Marcel; Huntington, Lee M.; Demel, Ondřej; Datta, Dipayan; Kong, Liguo; Shamasundar, K. R.; Lotrich, V.; Neese, Frank
2014-02-28
The novel multireference equation-of-motion coupled-cluster (MREOM-CC) approaches provide versatile and accurate access to a large number of electronic states. The methods proceed by a sequence of many-body similarity transformations and a subsequent diagonalization of the transformed Hamiltonian over a compact subspace. The transformed Hamiltonian is a connected entity and preserves spin- and spatial symmetry properties of the original Hamiltonian, but is no longer Hermitean. The final diagonalization spaces are defined in terms of a complete active space (CAS) and limited excitations (1h, 1p, 2h, …) out of the CAS. The methods are invariant to rotations of orbitals within their respective subspaces (inactive, active, external). Applications to first row transition metal atoms (Cr, Mn, and Fe) are presented yielding results for up to 524 electronic states (for Cr) with an rms error compared to experiment of about 0.05 eV. The accuracy of the MREOM family of methods is closely related to its favorable extensivity properties as illustrated by calculations on the O{sub 2}–O{sub 2} dimer. The computational costs of the transformation steps in MREOM are comparable to those of closed-shell Coupled Cluster Singles and Doubles (CCSD) approach.
Equation-of-motion coupled-cluster method for doubly ionized states with spin-orbit coupling.
Wang, Zhifan; Hu, Shu; Wang, Fan; Guo, Jingwei
2015-04-14
In this work, we report implementation of the equation-of-motion coupled-cluster method for doubly ionized states (EOM-DIP-CC) with spin-orbit coupling (SOC) using a closed-shell reference. Double ionization potentials (DIPs) are calculated in the space spanned by 2h and 3h1p determinants with the EOM-DIP-CC approach at the CC singles and doubles level (CCSD). Time-reversal symmetry together with spatial symmetry is exploited to reduce computational effort. To circumvent the problem of unstable dianion references when diffuse basis functions are included, nuclear charges are scaled. Effect of this stabilization potential on DIPs is estimated based on results from calculations using a small basis set without diffuse basis functions. DIPs and excitation energies of some low-lying states for a series of open-shell atoms and molecules containing heavy elements with two unpaired electrons have been calculated with the EOM-DIP-CCSD approach. Results show that this approach is able to afford a reliable description on SOC splitting. Furthermore, the EOM-DIP-CCSD approach is shown to provide reasonable excitation energies for systems with a dianion reference when diffuse basis functions are not employed. PMID:25877564
Equation-of-motion coupled-cluster method for doubly ionized states with spin-orbit coupling
Wang, Zhifan; Hu, Shu; Guo, Jingwei; Wang, Fan
2015-04-14
In this work, we report implementation of the equation-of-motion coupled-cluster method for doubly ionized states (EOM-DIP-CC) with spin-orbit coupling (SOC) using a closed-shell reference. Double ionization potentials (DIPs) are calculated in the space spanned by 2h and 3h1p determinants with the EOM-DIP-CC approach at the CC singles and doubles level (CCSD). Time-reversal symmetry together with spatial symmetry is exploited to reduce computational effort. To circumvent the problem of unstable dianion references when diffuse basis functions are included, nuclear charges are scaled. Effect of this stabilization potential on DIPs is estimated based on results from calculations using a small basis set without diffuse basis functions. DIPs and excitation energies of some low-lying states for a series of open-shell atoms and molecules containing heavy elements with two unpaired electrons have been calculated with the EOM-DIP-CCSD approach. Results show that this approach is able to afford a reliable description on SOC splitting. Furthermore, the EOM-DIP-CCSD approach is shown to provide reasonable excitation energies for systems with a dianion reference when diffuse basis functions are not employed.
A state-specific partially internally contracted multireference coupled cluster approach.
Datta, Dipayan; Kong, Liguo; Nooijen, Marcel
2011-06-01
A state-specific partially internally contracted multireference coupled cluster approach is presented for general complete active spaces with arbitrary number of active electrons. The dominant dynamical correlation is included via an exponential parametrization of internally contracted cluster operators ( ̂T) which excite electrons from a multideterminantal reference function. The remaining dynamical correlation and relaxation effects are included via a diagonalization of the transformed Hamiltonian ̅Ĥ =e(- ̂T)Ĥe( ̂T) in the multireference configuration interaction singles space in an uncontracted fashion. A new set of residual equations for determining the internally contracted cluster amplitudes is proposed. The second quantized matrix elements of ̅Ĥ , expressed using the extended normal ordering of Kutzelnigg and Mukherjee, are used as the residual equations without projection onto the excited configurations. These residual equations, referred to as the many-body residuals, do not have any near-singularity and thus, should allow one to solve all the amplitudes without discarding any. There are some relatively minor remaining convergence issues that may arise from an attempt to solve all the amplitudes and an initial analysis is provided in this paper. Applications to the bond-stretching potential energy surfaces for N(2), CO, and the low-lying electronic states of C(2) indicate clear improvements of the results using the many-body residuals over the conventional projected residual equations. PMID:21663353
A state-specific partially internally contracted multireference coupled cluster approach
NASA Astrophysics Data System (ADS)
Datta, Dipayan; Kong, Liguo; Nooijen, Marcel
2011-06-01
A state-specific partially internally contracted multireference coupled cluster approach is presented for general complete active spaces with arbitrary number of active electrons. The dominant dynamical correlation is included via an exponential parametrization of internally contracted cluster operators (hat{T}) which excite electrons from a multideterminantal reference function. The remaining dynamical correlation and relaxation effects are included via a diagonalization of the transformed Hamiltonian {{hat{overline{H}}=e^{-hat{T}}hat{H}e^{hat{T}}}} in the multireference configuration interaction singles space in an uncontracted fashion. A new set of residual equations for determining the internally contracted cluster amplitudes is proposed. The second quantized matrix elements of {{hat{overline{H}}}}, expressed using the extended normal ordering of Kutzelnigg and Mukherjee, are used as the residual equations without projection onto the excited configurations. These residual equations, referred to as the many-body residuals, do not have any near-singularity and thus, should allow one to solve all the amplitudes without discarding any. There are some relatively minor remaining convergence issues that may arise from an attempt to solve all the amplitudes and an initial analysis is provided in this paper. Applications to the bond-stretching potential energy surfaces for N2, CO, and the low-lying electronic states of C2 indicate clear improvements of the results using the many-body residuals over the conventional projected residual equations.
Strong Single-Photon Coupling in Superconducting Quantum Magnetomechanics
NASA Astrophysics Data System (ADS)
Via, Guillem; Kirchmair, Gerhard; Romero-Isart, Oriol
2015-04-01
We show that the inductive coupling between the quantum mechanical motion of a superconducting microcantilever and a flux-dependent microwave quantum circuit can attain the strong single-photon nanomechanical coupling regime with feasible experimental parameters. We propose to use a superconducting strip, which is in the Meissner state, at the tip of a cantilever. A pickup coil collects the flux generated by the sheet currents induced by an external quadrupole magnetic field centered at the strip location. The position-dependent magnetic response of the superconducting strip, enhanced by both diamagnetism and demagnetizing effects, leads to a strong magnetomechanical coupling to quantum circuits.
NASA Technical Reports Server (NTRS)
Lee, Timothy J.; Arnold, James O. (Technical Monitor)
1994-01-01
A new spin orbital basis is employed in the development of efficient open-shell coupled-cluster and perturbation theories that are based on a restricted Hartree-Fock (RHF) reference function. The spin orbital basis differs from the standard one in the spin functions that are associated with the singly occupied spatial orbital. The occupied orbital (in the spin orbital basis) is assigned the delta(+) = 1/square root of 2(alpha+Beta) spin function while the unoccupied orbital is assigned the delta(-) = 1/square root of 2(alpha-Beta) spin function. The doubly occupied and unoccupied orbitals (in the reference function) are assigned the standard alpha and Beta spin functions. The coupled-cluster and perturbation theory wave functions based on this set of "symmetric spin orbitals" exhibit much more symmetry than those based on the standard spin orbital basis. This, together with interacting space arguments, leads to a dramatic reduction in the computational cost for both coupled-cluster and perturbation theory. Additionally, perturbation theory based on "symmetric spin orbitals" obeys Brillouin's theorem provided that spin and spatial excitations are both considered. Other properties of the coupled-cluster and perturbation theory wave functions and models will be discussed.
Klopper, W.; Ruscic, B.; Tew, D. P.; Bischoff, F. A.; Wolfsegger, S.; Chemical Sciences and Engineering Division; Univ. Karlsruhe
2008-11-17
The atomization energies of the 105 molecules in the test set of Bakowies [D. Bakowies, J. Chem. Phys. 127 (2007) 084105] have been computed with an estimated standard deviation (from the values compiled in the Active Thermochemical Tables) of {+-}0.1 kJ/mol per valence electron in the molecule. Equilibrium geometries and harmonic vibrational frequencies were calculated at the all-electron CCSD(T)/cc-pCVTZ level, that is, at the level of coupled-cluster theory with singles, doubles and non-iterative triples in a correlation-consistent polarized core-valence triple-zeta basis. Single-point energy calculations were performed at the all-electron CCSD(T) level in a correlation-consistent polarized core-valence quadruple-zeta basis (cc-pCVQZ), and several corrections were added: (i) a correction for the basis-set truncation error, obtained from second-order perturbation theory using Slater-type geminals (MP2-F12 theory), (ii) a correction for the effect of anharmonicity on the zero-point vibrational energy, (iii) a relativistic correction, (iv) a correction for the difference between the full CCSDT model (coupled-cluster theory with singles, doubles and triples) and the CCSD(T) approximation, and (v) a correction for connected quadruple excitations obtained from CCSDT(Q) calculations. The correction for the basis-set truncation error was obtained from MP2-F12 calculations by scaling the MP2 basis-set truncation error by an empirically optimized 'interference factor' of f{sub int} = 0.78. The reference values from the Active Thermochemical Tables for 73 molecules in the test set, the equilibrium geometries, the harmonic vibrational frequencies, and all of the energy corrections represent valuable data for performance assessments of additivity schemes that will be developed in the future, in which the basis-set truncation error will be calculated at the level of coupled-cluster theory using Slater-type geminals (CC-F12 theory). Such a scheme will be free of empirical
Single molecule detection using charge-coupled device array technology
Denton, M.B.
1992-07-29
A technique for the detection of single fluorescent chromophores in a flowing stream is under development. This capability is an integral facet of a rapid DNA sequencing scheme currently being developed by Los Alamos National Laboratory. In previous investigations, the detection sensitivity was limited by the background Raman emission from the water solvent. A detection scheme based on a novel mode of operating a Charge-Coupled Device (CCD) is being developed which should greatly enhance the discrimination between fluorescence from a single molecule and the background Raman scattering from the solvent. Register shifts between rows in the CCD are synchronized with the sample flow velocity so that fluorescence from a single molecule is collected in a single moving charge packet occupying an area approaching that of a single pixel while the background is spread evenly among a large number of pixels. Feasibility calculations indicate that single molecule detection should be achieved with an excellent signal-to-noise ratio.
High-brightness fiber-coupled single emitter arrays
NASA Astrophysics Data System (ADS)
Heinemann, Stefan; Regaard, Boris; Schmidt, Torsten; Lewis, Ben
2009-02-01
Commercial high power fiber coupled diode lasers reach power levels of 200W from a 0.2mm fiber, NA=0.2. 2D fiber coupled single emitter (SE) arrays are described delivering 500W from a 0.2mm fiber. The beam quality of standard 90μm single emitter (SE) is 6mm*mrad (slow axis) and 0.7mm*mrad (fast axis) including errors from fast axis lensing. 3 SEs (24) can be arranged in slow axis (fast axis) to fill the aperture for coupling into a 0.2mm fiber, NA=0.2. For high efficiency, beam shaping optics are avoided. A lens array for slow axis collimation and a focusing optic complete the fiber coupled module. 44 SEs' are arranged as a 2D array, polarization multiplexed and coupled into a 0.2mm fiber, NA=0.2. 62% optical to optical and 75% coupling efficiency are achieved, close to the modeled coupling efficiency of 80%. Alignment tolerances in the system do account for additional losses. Precise manufacturing processes are essential. The SEs on submounts are soldered in one reflow process to a common heatsink and FAC-lensing station automatically aligns the lens based on image processing ensuring minimum total lensing errors (focusing and pointing) of each SE to <15% of total spot size. Tighter tolerances during SE mounting, improved fast axis collimation and a redesigned coupling optic will increase the coupling efficiency to 80% resulting in 410W linear polarized output from the 0.2mm fiber, NA=0.2. Polarization (800W) and dense wavelength multiplexing (1.4kW) open the door to kilowatt level.
Equations of explicitly-correlated coupled-cluster methods.
Shiozaki, Toru; Kamiya, Muneaki; Hirata, So; Valeev, Edward F
2008-06-21
The tensor contraction expressions defining a variety of high-rank coupled-cluster energies and wave functions that include the interelectronic distances (r(12)) explicitly (CC-R12) have been derived with the aid of a newly-developed computerized symbolic algebra smith. Efficient computational sequences to perform these tensor contractions have also been suggested, defining intermediate tensors-some reusable-as a sum of binary tensor contractions. smith can elucidate the index permutation symmetry of intermediate tensors that arise from a Slater-determinant expectation value of any number of excitation, deexcitation and other general second-quantized operators. smith also automates additional algebraic transformation steps specific to R12 methods, i.e. the identification and isolation of the special intermediates that need to be evaluated analytically and the resolution-of-the-identity insertion to facilitate high-dimensional molecular integral computation. The tensor contraction expressions defining the CC-R12 methods including through the connected quadruple excitation operator (CCSDTQ-R12) have been documented and efficient computational sequences have been suggested not just for the ground state but also for excited states via the equation-of-motion formalism (EOM-CC-R12) and for the so-called Lambda equation (Lambda-CC-R12) of the CC analytical gradient theory. Additional equations (the geminal amplitude equation) arise in CC-R12 that need to be solved to determine the coefficients multiplying the r(12)-dependent factors. The operation cost of solving the geminal amplitude equations of rank-k CC-R12 and EOM-CC-R12 (right-hand side) scales as O(n(6)) (k = 2) or O(n(7)) (k > or = 3) with the number of orbitals n and is surpassed by the cost of solving the usual amplitude equations O(n(2k+2)). While the complexity of the geminal amplitude equations of Lambda- and EOM-CC-R12 (left-hand side) nominally scales as O(n(2k+2)), it is less than that of the other O(n(2k
Waveguide-Coupled Superconducting Nanowire Single-Photon Detectors
NASA Technical Reports Server (NTRS)
Beyer, Andrew D.; Briggs, Ryan M.; Marsili, Francesco; Cohen, Justin D.; Meenehan, Sean M.; Painter, Oskar J.; Shaw, Matthew D.
2015-01-01
We have demonstrated WSi-based superconducting nanowire single-photon detectors coupled to SiNx waveguides with integrated ring resonators. This photonics platform enables the implementation of robust and efficient photon-counting detectors with fine spectral resolution near 1550 nm.
Aprà, E; Kowalski, K
2016-03-01
In this paper we discuss the implementation of multireference coupled-cluster formalism with singles, doubles, and noniterative triples (MRCCSD(T)), which is capable of taking advantage of the processing power of the Intel Xeon Phi coprocessor. We discuss the integration of two levels of parallelism underlying the MRCCSD(T) implementation with computational kernels designed to offload the computationally intensive parts of the MRCCSD(T) formalism to Intel Xeon Phi coprocessors. Special attention is given to the enhancement of the parallel performance by task reordering that has improved load balancing in the noniterative part of the MRCCSD(T) calculations. We also discuss aspects regarding efficient optimization and vectorization strategies. PMID:26808463
Connected triple excitations in coupled-cluster calculations of hyperpolarizabilities: Neon
NASA Technical Reports Server (NTRS)
Rice, Julia E.; Scuseria, Gustavo E.; Lee, Timothy J.; Taylor, Peter R.; Almloef, Jan
1992-01-01
We have calculated the second hyperpolarizability gamma of neon using the CCSD(T) method. The accuracy of the CCSD(T) approach has been established by explicit comparison with the single, double and triple excitation coupled-cluster (CCSDT) method using extended basis sets that are known to be adequate for the description of gamma. Our best estimate for gamma(sub 0) of 110 +/- 3 a.u. is in good agreement with other recent theoretical values and with Shelton's recent experimental estimate of 108 +/- 2 a.u. Comparison of the MP2 and CCSD(T) hyperpolarizability values indicates that MP2 gives a very good description of the electron correlation contribution to gamma(sub 0). We have combined MP2 frequency-dependent corrections with the CCSD(T) gamma(sub 0) to yield values of gamma(-2 omega;omega,omega,0) and gamma(exp K)(-omega;omega,0,0).
Bhaskaran-Nair, Kiran; Kowalski, Karol; Jarrell, Mark; Moreno, Juana; Shelton, William A.
2015-11-05
Polyacenes have attracted considerable attention due to their use in organic based optoelectronic materials. Polyacenes are polycyclic aromatic hydrocarbons composed of fused benzene rings. Key to understanding and design of new functional materials is an understanding of their excited state properties starting with their electron affinity (EA) and ionization potential (IP). We have developed a highly accurate and com- putationally e*fficient EA/IP equation of motion coupled cluster singles and doubles (EA/IP-EOMCCSD) method that is capable of treating large systems and large basis set. In this study we employ the EA/IP-EOMCCSD method to calculate the electron affinity and ionization potential of naphthalene, anthracene, tetracene, pentacene, hex- acene and heptacene. We have compared our results with other previous theoretical studies and experimental data. Our EA/IP results are in very good agreement with experiment and when compared with the other theoretical investigations our results represent the most accurate calculations as compared to experiment.
Active-Space Coupled-Cluster Study of Electronic States of Be₃
Kowalski, Karol; Hirata, So; Wloch, M W.; Piecuch, Piotr; Windus, Theresa L.
2005-08-15
An automated implementation of the active-space coupled-cluster (CC) and equation-of-motion (EOM) CC methods with all singles and doubles, and triples defined via active orbitals (CCSDt, EOMCCSDt) employing Tensor Contraction Engine (TCE), is reported. The TCE-generated CCSDt/ codes are parallel and applicable to closed-and open-shell references. The effectiveness of the new code in describing electronic quasi-degeneracies is illustrated by the CCSDt / EOMCCSDt) calculations for the challenging Be₃system, which is characterized by a large number of low-lying excited states dominated by two-electron transitions and significant high order correlation effects in the ground electronic state. Different strategies for defining triple excitation s within the CCSDt / EOMCCSDt) approach are discussed.
Ruprecht 106: The First Single Population Globular Cluster?
NASA Astrophysics Data System (ADS)
Villanova, S.; Geisler, D.; Carraro, G.; Moni Bidin, C.; Muñoz, C.
2013-12-01
All old Galactic globular clusters (GCs) studied in detail to date host at least two generations of stars, where the second is formed from gas polluted by processed material produced by massive stars of the first. This process can happen if the initial mass of the cluster exceeds a threshold above which ejecta are retained and a second generation is formed. A determination of this mass threshold is mandatory in order to understand how GCs form. We analyzed nine red giant branch stars belonging to the cluster Ruprecht 106. Targets were observed with the UVES@VLT2 spectrograph. Spectra cover a wide range and allowed us to measure abundances for light (O, Na, Mg, Al), α (Si, Ca, Ti), iron-peak (Sc, V, Cr, Mn, Fe, Co, Ni, Cu, Zn), and neutron-capture (Y, Zr, Ba, La, Ce, Pr, Nd, Sm, Eu, Dy, Pb) elements. Based on these abundances, we show that Ruprecht 106 is the first convincing example of a single-population GC (i.e., a true simple stellar population), although the sample is relatively small. This result is supported also by an independent photometric test and by the horizontal branch morphology and the dynamical state. It is old (~12 Gyr) and, at odds with other GCs, has no α-enhancement. The material it formed from was contaminated by both s- and r-process elements. The abundance pattern points toward an extragalactic origin. Its present-day mass (M = 104.83 M ⊙) can be assumed as a strong lower limit for the initial mass threshold below which no second generation is formed. Clearly, its initial mass must have been significantly greater, but we have no current constraints on the amount of mass loss during its evolution.
Ruprecht 106: The first single population globular cluster?
Villanova, S.; Geisler, D.; Muñoz, C.; Carraro, G.; Moni Bidin, C.
2013-12-01
All old Galactic globular clusters (GCs) studied in detail to date host at least two generations of stars, where the second is formed from gas polluted by processed material produced by massive stars of the first. This process can happen if the initial mass of the cluster exceeds a threshold above which ejecta are retained and a second generation is formed. A determination of this mass threshold is mandatory in order to understand how GCs form. We analyzed nine red giant branch stars belonging to the cluster Ruprecht 106. Targets were observed with the UVES@VLT2 spectrograph. Spectra cover a wide range and allowed us to measure abundances for light (O, Na, Mg, Al), α (Si, Ca, Ti), iron-peak (Sc, V, Cr, Mn, Fe, Co, Ni, Cu, Zn), and neutron-capture (Y, Zr, Ba, La, Ce, Pr, Nd, Sm, Eu, Dy, Pb) elements. Based on these abundances, we show that Ruprecht 106 is the first convincing example of a single-population GC (i.e., a true simple stellar population), although the sample is relatively small. This result is supported also by an independent photometric test and by the horizontal branch morphology and the dynamical state. It is old (∼12 Gyr) and, at odds with other GCs, has no α-enhancement. The material it formed from was contaminated by both s- and r-process elements. The abundance pattern points toward an extragalactic origin. Its present-day mass (M = 10{sup 4.83} M {sub ☉}) can be assumed as a strong lower limit for the initial mass threshold below which no second generation is formed. Clearly, its initial mass must have been significantly greater, but we have no current constraints on the amount of mass loss during its evolution.
A partial coupling power of single mode fiber fusion
NASA Astrophysics Data System (ADS)
Saktioto, Toto; Ali, Jalil; Rahman, Rosly Abdul; Fadhali, Mohammed; Zainal, Jasman
2008-01-01
Coupled fibers are successfully fabricated by injecting hydrogen flow at 1bar and fused slightly by unstable torch flame in the range of 800-1350°C. Optical parameters may vary significantly over wide range physical properties. Coupling coefficient and refractive index are estimated from the experimental result of the coupling ratio distribution from 1% to 75%. The change of structural and geometrical fiber affects the normalized frequency (V) even for single mode fibers. Coupling ratio as a function of coupling coefficient and separation of fiber axis changes with respect to V at coupling region. V is derived from radius, wavelength and refractive index parameters. Parametric variations are performed on the left and right hand side of the coupling region. At the center of the coupling region V is assumed constant. A partial power is modeled and derived using V, normalized lateral phase constant (u), and normalized lateral attenuation constant, (w) through the second kind of modified Bessel function of the l order, which obeys the normal mode, LP 01 and normalized propagation constant (b). Total power is maintained constant in order to comply with the energy conservation law. The power is integrated through V, u and w over the pulling length range of 7500-9500 μm for 1-D where radial and angle directions are ignored. The core radius of fiber significantly affects V and power partially at coupling region rather than wavelength and refractive index of core and cladding. This model has power phenomena in transmission and reflection for industrial application of coupled fibers.
Cluster Consensus of Nonlinearly Coupled Multi-Agent Systems in Directed Graphs
NASA Astrophysics Data System (ADS)
Lu, Xiao-Qing; Francis, Austin; Chen, Shi-Hua
2010-05-01
We investigate the cluster consensus problem in directed networks of nonlinearly coupled multi-agent systems by using pinning control. Depending on the community structure generated by the group partition of the underlying digraph, various clusters can be made coherently independent by applying feedback injections to a fraction of the agents. Sufficient conditions for cluster consensus are obtained using algebraic graph theory and matrix theory and some simulations results are included to illustrate the method.
NASA Astrophysics Data System (ADS)
Rotstein, Horacio G.; Wu, Hui
2012-09-01
We use simulations and dynamical systems tools to investigate the mechanisms of generation of phase-locked and localized oscillatory cluster patterns in a globally coupled Oregonator model where the activator receives global feedback from the inhibitor, mimicking experimental results observed in the photosensitive Belousov-Zhabotinsky reaction. A homogeneous two-cluster system (two clusters with equal cluster size) displays antiphase patterns. Heterogenous two-cluster systems (two clusters with different sizes) display both phase-locked and localized patterns depending on the parameter values. In a localized pattern the oscillation amplitude of the largest cluster is roughly an order of magnitude smaller than the oscillation amplitude of the smaller cluster, reflecting the effect of self-inhibition exerted by the global feedback term. The transition from phase-locked to localized cluster patterns occurs as the intensity of global feedback increases. Three qualitatively different basic mechanisms, described previously for a globally coupled FitzHugh-Nagumo model, are involved in the generation of the observed patterns. The swing-and-release mechanism is related to the canard phenomenon (canard explosion of limit cycles) in relaxation oscillators. The hold-and-release and hold-and-escape mechanisms are related to the release and escape mechanisms in synaptically connected neural models. The methods we use can be extended to the investigation of oscillatory chemical reactions with other types of non-local coupling.
Rotstein, Horacio G; Wu, Hui
2012-09-14
We use simulations and dynamical systems tools to investigate the mechanisms of generation of phase-locked and localized oscillatory cluster patterns in a globally coupled Oregonator model where the activator receives global feedback from the inhibitor, mimicking experimental results observed in the photosensitive Belousov-Zhabotinsky reaction. A homogeneous two-cluster system (two clusters with equal cluster size) displays antiphase patterns. Heterogenous two-cluster systems (two clusters with different sizes) display both phase-locked and localized patterns depending on the parameter values. In a localized pattern the oscillation amplitude of the largest cluster is roughly an order of magnitude smaller than the oscillation amplitude of the smaller cluster, reflecting the effect of self-inhibition exerted by the global feedback term. The transition from phase-locked to localized cluster patterns occurs as the intensity of global feedback increases. Three qualitatively different basic mechanisms, described previously for a globally coupled FitzHugh-Nagumo model, are involved in the generation of the observed patterns. The swing-and-release mechanism is related to the canard phenomenon (canard explosion of limit cycles) in relaxation oscillators. The hold-and-release and hold-and-escape mechanisms are related to the release and escape mechanisms in synaptically connected neural models. The methods we use can be extended to the investigation of oscillatory chemical reactions with other types of non-local coupling. PMID:22979891
Clustering and phase synchronization in populations of coupled phase oscillators
NASA Astrophysics Data System (ADS)
Cascallares, Guadalupe; Gleiser, Pablo M.
2015-10-01
In many species daily rhythms are endogenously generated by groups of coupled neurons that play the role of a circadian pacemaker. The adaptation of the circadian clock to environmental and seasonal changes has been proposed to be regulated by a dual oscillator system. In order to gain insight into this model, we analyzed the synchronization properties of two fully coupled groups of Kuramoto oscillators. Each group has an internal coupling parameter and the interaction between the two groups can be controlled by two parameters allowing for symmetric or non-symmetric coupling. We show that even for such a simple model counterintuitive behaviours take place, such as a global decrease in synchrony when the coupling between the groups is increased. Through a detailed analysis of the local synchronization processes we explain this behaviour.
Symmetry broken and restored coupled-cluster theory: I. Rotational symmetry and angular momentum
NASA Astrophysics Data System (ADS)
Duguet, T.
2015-02-01
We extend coupled-cluster (CC) theory performed on top of a Slater determinant breaking rotational symmetry to allow for the exact restoration of the angular momentum at any truncation order. The main objective relates to the description of near-degenerate finite quantum systems with an open-shell character. As such, the newly developed many-body formalism offers a wealth of potential applications and further extensions dedicated to the ab initio description of, e.g., doubly open-shell atomic nuclei and molecule dissociation. The formalism, which encompasses both single-reference CC theory and projected Hartree-Fock theory as particular cases, permits the computation of usual sets of connected diagrams while consistently incorporating static correlations through the highly non-perturbative restoration of rotational symmetry. Interestingly, the yrast spectroscopy of the system, i.e. the lowest energy associated with each angular momentum, is accessed within a single calculation. A key difficulty presently overcome relates to the necessity to handle generalized energy and norm kernels for which naturally terminating CC expansions could be eventually obtained. The present work focuses on SU(2) but can be extended to any (locally) compact Lie group and to discrete groups, such as most point groups. In particular, the formalism will be soon generalized to U(1) symmetry associated with particle number conservation. This is relevant to Bogoliubov CC theory that was recently applied to singly open-shell nuclei.
NASA Astrophysics Data System (ADS)
Kuptsov, Pavel V.; Kuptsova, Anna V.
2016-04-01
A generalized model of star-like network is suggested that takes into account non-additive coupling and nonlinear transformation of coupling variables. For this model a method of analysis of synchronized cluster stability is developed. Using this method three star-like networks based on Ikeda, predator-prey and Hénon maps are studied.
Communication: A Jastrow factor coupled cluster theory for weak and strong electron correlation
Neuscamman, Eric
2013-11-14
We present a Jastrow-factor-inspired variant of coupled cluster theory that accurately describes both weak and strong electron correlation. Compatibility with quantum Monte Carlo allows for variational energy evaluations and an antisymmetric geminal power reference, two features not present in traditional coupled cluster that facilitate a nearly exact description of the strong electron correlations in minimal-basis N{sub 2} bond breaking. In double-ζ treatments of the HF and H{sub 2}O bond dissociations, where both weak and strong correlations are important, this polynomial cost method proves more accurate than either traditional coupled cluster or complete active space perturbation theory. These preliminary successes suggest a deep connection between the ways in which cluster operators and Jastrow factors encode correlation.
Pinning cluster synchronization in an array of coupled neural networks under event-based mechanism.
Li, Lulu; Ho, Daniel W C; Cao, Jinde; Lu, Jianquan
2016-04-01
Cluster synchronization is a typical collective behavior in coupled dynamical systems, where the synchronization occurs within one group, while there is no synchronization among different groups. In this paper, under event-based mechanism, pinning cluster synchronization in an array of coupled neural networks is studied. A new event-triggered sampled-data transmission strategy, where only local and event-triggering states are utilized to update the broadcasting state of each agent, is proposed to realize cluster synchronization of the coupled neural networks. Furthermore, a self-triggered pinning cluster synchronization algorithm is proposed, and a set of iterative procedures is given to compute the event-triggered time instants. Hence, this will reduce the computational load significantly. Finally, an example is given to demonstrate the effectiveness of the theoretical results. PMID:26829603
A universal state-selective approach to multireference coupled-cluster non-iterative corrections
NASA Astrophysics Data System (ADS)
Kowalski, Karol
2011-05-01
A new form of the asymmetric energy functional for multireference coupled cluster (MRCC) theories is discussed from the point of view of an energy expansion in a quasidegenerate situation. The resulting expansion for the exact electronic energy can be used to define the non-iterative corrections to approximate MRCC approaches. In particular, we show that in the proposed framework the essential part of dynamic correlation can be encapsulated in the so-called correlation Hamiltonian, which in analogy to the effective Hamiltonian, is defined in the model space (M_0). The proper parametrization of the exact/trial wavefunctions leads to the cancellation of the overlap-type numerators and to a connected form of the correlation Hamiltonian and size-extensive energies. Within this parametrization, when the trial wavefunctions are determined without invoking a specific form of the MRCC sufficiency conditions, the ensuing correction can be universally applied to any type of the approximate MRCC method. The analogies with other MRCC triples corrections to MRCC theories with singles and doubles (MRCCSD) are outlined. In particular, we discuss the approach, which in analogy to the Λ-Mk-MRCCSD(T) method [F. A. Evangelista, E. Prochnow, J. Gauss, H. F. Schaefer III, J. Chem. Phys. 132, 074107 (2010)], introduces an approximate form of the triply-excited clusters into the effective and correlation Hamiltonians. Since the discussed corrections can be calculated as a sum of independent reference-related contributions, possible parallel algorithms are also outlined.
Modal Coupling of Single Photon Emitters Within Nanofiber Waveguides.
Gaio, Michele; Moffa, Maria; Castro-Lopez, Marta; Pisignano, Dario; Camposeo, Andrea; Sapienza, Riccardo
2016-06-28
Nanoscale generation of individual photons in confined geometries is an exciting research field aiming at exploiting localized electromagnetic fields for light manipulation. One of the outstanding challenges of photonic systems combining emitters with nanostructured media is the selective channelling of photons emitted by embedded sources into specific optical modes and their transport at distant locations in integrated systems. Here, we show that soft-matter nanofibers, electrospun with embedded emitters, combine subwavelength field localization and large broadband near-field coupling with low propagation losses. By momentum spectroscopy, we quantify the modal coupling efficiency identifying the regime of single-mode coupling. These nanofibers do not rely on resonant interactions, making them ideal for room-temperature operation, and offer a scalable platform for future quantum information technology. PMID:27203403
Modal Coupling of Single Photon Emitters Within Nanofiber Waveguides
2016-01-01
Nanoscale generation of individual photons in confined geometries is an exciting research field aiming at exploiting localized electromagnetic fields for light manipulation. One of the outstanding challenges of photonic systems combining emitters with nanostructured media is the selective channelling of photons emitted by embedded sources into specific optical modes and their transport at distant locations in integrated systems. Here, we show that soft-matter nanofibers, electrospun with embedded emitters, combine subwavelength field localization and large broadband near-field coupling with low propagation losses. By momentum spectroscopy, we quantify the modal coupling efficiency identifying the regime of single-mode coupling. These nanofibers do not rely on resonant interactions, making them ideal for room-temperature operation, and offer a scalable platform for future quantum information technology. PMID:27203403
Coupled resonator filter with single-layer acoustic coupler.
Jamneala, Tiberiu; Small, Martha; Ruby, Rich; Larson, John D
2008-10-01
We discuss the operation of novel coupled-resonator filters with single-layer acoustic couplers. Our analysis employs the physical Mason model for acoustic resonators. Their simpler fabrication process is counterbalanced by the high acoustic attenuation of suitable coupler materials. At high levels of attenuation, both the phase and the acoustic impedance must be treated as complex quantities to accurately predict the filter insertion loss. We demonstrate that the typically poor near-band rejection of coupled resonator filters can be improved at the die level by connecting a small capacitance between the input and output of the filter to produce a pair of tunable transmission minima. We make use of these theoretical findings to fabricate coupled resonators filters operating at 2.45 GHz. PMID:18986880
Photon pair source via two coupling single quantum emitters
NASA Astrophysics Data System (ADS)
Peng, Yong-Gang; Zheng, Yu-Jun
2015-10-01
We study the two coupling two-level single molecules driven by an external field as a photon pair source. The probability of emitting two photons, P2, is employed to describe the photon pair source quality in a short time, and the correlation coefficient RAB is employed to describe the photon pair source quality in a long time limit. The results demonstrate that the coupling single quantum emitters can be considered as a stable photon pair source. Project supported by the National Natural Science Foundation of China (Grand Nos. 91021009, 21073110, and 11374191), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2013AQ020), the Postdoctoral Science Foundation of China (Grant No. 2013M531584), the Doctoral Program of Higher Education of China (Grant Nos. 20130131110005 and 20130131120006), and the Taishan Scholarship Project of Shandong Province, China.
Ellis, Benjamin H; Aggarwal, Somil; Chakraborty, Arindam
2016-01-12
Multicomponent systems are defined as chemical systems that require a quantum mechanical description of two or more different types of particles. Non-Born-Oppenheimer electron-nuclear interactions in molecules, electron-hole interactions in electronically excited nanoparticles, and electron-positron interactions are examples of physical systems that require a multicomponent quantum mechanical formalism. The central challenge in the theoretical treatment of multicomponent systems is capturing the many-body correlation effects that exist not only between particles of identical types (electron-electron) but also between particles of different types (electron-nuclear and electron-hole). In this work, the development and implementation of multicomponent coupled-cluster (mcCC) theory for treating particle-particle correlation in multicomponent systems are presented. This method provides a balanced treatment of many-particle correlation effects in a general multicomponent system while maintaining a size-consistent and size-extensive formalism. The coupled-cluster ansatz presented here is an extension of the electronic structure CCSD formulation for multicomponent systems and is defined as |ΨmcCC⟩ = eT1I+T2I+T1II+T2II+T11I,II+T12I,II+T21I,II+T22I,II|0I0II⟩. The cluster amplitudes in the mcCC wave function were obtained by projecting the mcCC Schrödinger equation onto a direct product space of singly and doubly excited states of type I and II particles and then solving the resulting mcCC equations iteratively. These equations were derived using an automated application of the generalized Wick’s theorem and were implemented using a computer-assisted source code generation approach. The applicability of the mcCC method was demonstrated by calculating ground state energies of multicomponent Hooke's atom and positronium hydride systems as well as by calculating exciton and biexciton binding energies in multiexcitonic systems. For each case, the mcCC results were
NASA Astrophysics Data System (ADS)
Epifanovsky, Evgeny; Klein, Kerstin; Stopkowicz, Stella; Gauss, Jürgen; Krylov, Anna I.
2015-08-01
We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results.
Epifanovsky, Evgeny; Klein, Kerstin; Stopkowicz, Stella; Gauss, Jürgen; Krylov, Anna I
2015-08-14
We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results. PMID:26277122
Epifanovsky, Evgeny; Klein, Kerstin; Gauss, Jürgen; Stopkowicz, Stella; Krylov, Anna I.
2015-08-14
We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results.
Spin-orbit coupling effects in gold clusters: The case of Au13
NASA Astrophysics Data System (ADS)
Flores, Mauricio A.; Menéndez-Proupin, Eduardo
2016-05-01
Non relativistic description of the chemical bonding for heavy atom systems is unrealistic. However, only few relativistic DFT calculations have been reported for gold clusters. In this work, we investigate the effect of the spin-orbit coupling in the structure, relative stability and HOMO-LUMO gap of the lowest-lying isomers of neutral Au13 clusters. Our results show that spin-orbit coupling increases the energy gap between 2D and 3D isomers and a relativistic bond contraction appears. Moreover, the relative energy of some isomers change when the spin-orbit coupling is included.
Quantum tunneling of two coupled single-molecular magnets
NASA Astrophysics Data System (ADS)
Hu, Jianming; Chen, Zhide; Shen, Shunqing
2003-03-01
Jian-Ming Hu, Zhi-De Chen and Shun-Qing Shen Department of Physics, The University of Hong Kong Pokfulam Road, Hong Kong December 02, 2002 Very recently a supramolecular dimer of two single-molecule magnets (SMM) was reported to be synthesized successfully. Two single-molecule magnets are coupled antiferromagnetically to form a supramolecule dimer. We study the coupling effect and tunneling process by the numerical exact diagonalization method. The sweeping rate effect in the derivatives of hysteresis loops has been quantitatively investigated using the modified Landau-Zener model. In addiction we find that exchange coupling between the two SMMs provides a biased field to expel the tunneling between SMMs to two new resonant points via an intermediate state, and direct tunneling is prohibited. The model parameters are calculated for the dimer based on the tunneling process. The outcome indicates that the coupling effect will not change the parameters of each SMM too much at all. This work is supported by a CRCG grant of The University of Hong Kong.
High electronic couplings of single mesitylene molecular junctions.
Komoto, Yuki; Fujii, Shintaro; Nishino, Tomoaki; Kiguchi, Manabu
2015-01-01
We report on an experimental analysis of the charge transport properties of single mesitylene (1,3,5-trimethylbenzene) molecular junctions. The electronic conductance and the current-voltage characteristics of mesitylene molecules wired into Au electrodes were measured by a scanning tunnelling microscopy-based break-junction method at room temperature in a liquid environment. We found the molecular junctions exhibited two distinct conductance states with high conductance values of ca. 10(-1) G 0 and of more than 10(-3) G 0 (G 0 = 2e (2)/h) in the electronic conductance measurements. We further performed a statistical analysis of the current-voltage characteristics of the molecular junctions in the two states. Within a single channel resonant tunnelling model, we obtained electronic couplings in the molecular junctions by fitting the current-voltage characteristics to the single channel model. The origin of the high conductance was attributed to experimentally obtained large electronic couplings of the direct π-bonded molecular junctions (ca. 0.15 eV). Based on analysis of the stretch length of the molecular junctions and the large electronic couplings obtained from the I-V analysis, we proposed two structural models, in which (i) mesitylene binds to the Au electrode perpendicular to the charge transport direction and (ii) mesitylene has tilted from the perpendicular orientation. PMID:26732978
High electronic couplings of single mesitylene molecular junctions
Komoto, Yuki; Nishino, Tomoaki; Kiguchi, Manabu
2015-01-01
Summary We report on an experimental analysis of the charge transport properties of single mesitylene (1,3,5-trimethylbenzene) molecular junctions. The electronic conductance and the current–voltage characteristics of mesitylene molecules wired into Au electrodes were measured by a scanning tunnelling microscopy-based break-junction method at room temperature in a liquid environment. We found the molecular junctions exhibited two distinct conductance states with high conductance values of ca. 10−1 G 0 and of more than 10−3 G 0 (G 0 = 2e 2/h) in the electronic conductance measurements. We further performed a statistical analysis of the current–voltage characteristics of the molecular junctions in the two states. Within a single channel resonant tunnelling model, we obtained electronic couplings in the molecular junctions by fitting the current–voltage characteristics to the single channel model. The origin of the high conductance was attributed to experimentally obtained large electronic couplings of the direct π-bonded molecular junctions (ca. 0.15 eV). Based on analysis of the stretch length of the molecular junctions and the large electronic couplings obtained from the I–V analysis, we proposed two structural models, in which (i) mesitylene binds to the Au electrode perpendicular to the charge transport direction and (ii) mesitylene has tilted from the perpendicular orientation. PMID:26732978
Local Correlation Calculations Using Standard and Renormalized Coupled-Cluster Methods
NASA Astrophysics Data System (ADS)
Li, Wei; Piecuch, Piotr; Gour, Jeffrey R.
2009-03-01
This article discusses our recent effort toward the extension of the linear scaling local correlation approach, termed 'cluster-in-molecule' and abbreviated as CIM [S. Li, J. Ma, and Y. Jiang, J. Comput. Chem. 23, 237 (2002); S. Li, J. Shen, W. Li, and Y. Jiang, J. Chem. Phys. 125, 074109 (2006)], to the coupled-cluster (CC) theory with singles and doubles (CCSD) and CC methods with singles, doubles, and non-iterative triples, including the standard CCSD(T) approach and the completely renormalized CR-CC(2,3) scheme [P. Piecuch and M. Włoch, J. Chem. Phys. 123, 224105 (2005); P. Piecuch, M. Włoch, J. R. Gour, and A. Kinal, Chem. Phys. Lett. 418, 467 (2006)]. As in the earlier CIM work that dealt with the second-order many-body perturbation theory and CC doubles approach, the main idea of the CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) methods is the realization of the fact that the total correlation energy of a large system can be obtained as a sum of contributions from the occupied orthonormal localized molecular orbitals and their respective occupied and unoccupied orbital domains. The CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) methods pursued in this work are characterized by high computational efficiency in both the CIM and CC parts, enabling calculations for much larger systems than previously possible. This is achieved by combining the natural linear scaling and embarrassing parallelism of the CIM ansatz with the vectorized CC codes that rely on recursively generated intermediates and fast matrix multiplication routines. By comparing the results of the canonical and CIM-CC calculations for normal alkanes and water clusters, it is demonstrated that the CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) approaches recover the corresponding canonical CC correlation energies to within 0.1% or so, while offering linear scaling of the computer costs with the system size and savings in the computer effort by orders of magnitude. By examining the dissociation of dodecane into C
Kowalski, K.; Bhaskaran-Nair, K.; Shelton, W. A.
2014-09-07
In this paper we discuss a new formalism for producing an analytic coupled-cluster (CC) Green's function for an N-electron system by shifting the poles of similarity transformed Hamiltonians represented in N - 1 and N + 1 electron Hilbert spaces. Simple criteria are derived for the states in N - 1 and N + 1 electron spaces that are then corrected in the spectral resolution of the corresponding matrix representations of the similarity transformed Hamiltonian. The accurate description of excited state processes within a Green's function formalism would be of significant importance to a number of scientific communities ranging from physics and chemistry to engineering and the biological sciences. This is because the Green's function methodology provides a direct path for not only calculating properties whose underlying origins come from coupled many-body interactions but also provides a straightforward path for calculating electron transport, response, and correlation functions that allows for a direct link with experiment. Finally, as a special case of this general formulation, we discuss the application of this technique for Green's function defined by the CC with singles and doubles representation of the ground-state wave function.
Kowalski, K. Bhaskaran-Nair, K.; Shelton, W. A.
2014-09-07
In this paper we discuss a new formalism for producing an analytic coupled-cluster (CC) Green's function for an N-electron system by shifting the poles of similarity transformed Hamiltonians represented in N − 1 and N + 1 electron Hilbert spaces. Simple criteria are derived for the states in N − 1 and N + 1 electron spaces that are then corrected in the spectral resolution of the corresponding matrix representations of the similarity transformed Hamiltonian. The accurate description of excited state processes within a Green's function formalism would be of significant importance to a number of scientific communities ranging from physics and chemistry to engineering and the biological sciences. This is because the Green's function methodology provides a direct path for not only calculating properties whose underlying origins come from coupled many-body interactions but also provides a straightforward path for calculating electron transport, response, and correlation functions that allows for a direct link with experiment. As a special case of this general formulation, we discuss the application of this technique for Green's function defined by the CC with singles and doubles representation of the ground-state wave function.
Speeding up equation of motion coupled cluster theory with the chain of spheres approximation
NASA Astrophysics Data System (ADS)
Dutta, Achintya Kumar; Neese, Frank; Izsák, Róbert
2016-01-01
In the present paper, the chain of spheres exchange (COSX) approximation is applied to the highest scaling terms in the equation of motion (EOM) coupled cluster equations with single and double excitations, in particular, the terms involving integrals with four virtual labels. It is found that even the acceleration of this single term yields significant computational gains without compromising the desired accuracy of the method. For an excitation energy calculation on a cluster of five water molecules using 585 basis functions, the four virtual term is 9.4 times faster using COSX with a loose grid than using the canonical implementation, which yields a 2.6 fold acceleration for the whole of the EOM calculation. For electron attachment calculations, the four virtual term is 15 times and the total EOM calculation is 10 times faster than the canonical calculation for the same system. The accuracy of the new method was tested using Thiel's test set for excited states using the same settings and the maximum absolute deviation over the whole test set was found to be 12.945 cm-1 (59 μHartree) for excitation energies and 6.799 cm-1 (31 μHartree) for electron attachments. Using MP2 amplitudes for the ground state in combination with the parallel evaluation of the full EOM equations in the manner discussed in this paper enabled us to perform calculations for large systems. Electron affinity values for the two lowest states of a Zn protoporphyrine model compound (224 correlated electrons and 1120 basis functions) were obtained in 3 days 19 h using 4 cores of a Xeon E5-2670 processor allocating 10 GB memory per core. Calculating the lowest two excitation energies for trans-retinal (114 correlated electrons and 539 basis functions) took 1 day 21 h using eight cores of the same processor and identical memory allocation per core.
Speeding up equation of motion coupled cluster theory with the chain of spheres approximation.
Dutta, Achintya Kumar; Neese, Frank; Izsák, Róbert
2016-01-21
In the present paper, the chain of spheres exchange (COSX) approximation is applied to the highest scaling terms in the equation of motion (EOM) coupled cluster equations with single and double excitations, in particular, the terms involving integrals with four virtual labels. It is found that even the acceleration of this single term yields significant computational gains without compromising the desired accuracy of the method. For an excitation energy calculation on a cluster of five water molecules using 585 basis functions, the four virtual term is 9.4 times faster using COSX with a loose grid than using the canonical implementation, which yields a 2.6 fold acceleration for the whole of the EOM calculation. For electron attachment calculations, the four virtual term is 15 times and the total EOM calculation is 10 times faster than the canonical calculation for the same system. The accuracy of the new method was tested using Thiel's test set for excited states using the same settings and the maximum absolute deviation over the whole test set was found to be 12.945 cm(-1) (59 μHartree) for excitation energies and 6.799 cm(-1) (31 μHartree) for electron attachments. Using MP2 amplitudes for the ground state in combination with the parallel evaluation of the full EOM equations in the manner discussed in this paper enabled us to perform calculations for large systems. Electron affinity values for the two lowest states of a Zn protoporphyrine model compound (224 correlated electrons and 1120 basis functions) were obtained in 3 days 19 h using 4 cores of a Xeon E5-2670 processor allocating 10 GB memory per core. Calculating the lowest two excitation energies for trans-retinal (114 correlated electrons and 539 basis functions) took 1 day 21 h using eight cores of the same processor and identical memory allocation per core. PMID:26801015
Parallelization of the Wolff single-cluster algorithm.
Kaupuzs, J; Rimsāns, J; Melnik, R V N
2010-02-01
A parallel [open multiprocessing (OpenMP)] implementation of the Wolff single-cluster algorithm has been developed and tested for the three-dimensional (3D) Ising model. The developed procedure is generalizable to other lattice spin models and its effectiveness depends on the specific application at hand. The applicability of the developed methodology is discussed in the context of the applications, where a sophisticated shuffling scheme is used to generate pseudorandom numbers of high quality, and an iterative method is applied to find the critical temperature of the 3D Ising model with a great accuracy. For the lattice with linear size L=1024, we have reached the speedup about 1.79 times on two processors and about 2.67 times on four processors, as compared to the serial code. According to our estimation, the speedup about three times on four processors is reachable for the O(n) models with n> or =2. Furthermore, the application of the developed OpenMP code allows us to simulate larger lattices due to greater operative (shared) memory available. PMID:20365669
Single Nucleotide Polymorphism Clustering in Systemic Autoimmune Diseases
Charlon, Thomas; Bossini-Castillo, Lara; Carmona, F. David; Di Cara, Alessandro; Wojcik, Jérôme; Voloshynovskiy, Sviatoslav
2016-01-01
Systemic Autoimmune Diseases, a group of chronic inflammatory conditions, have variable symptoms and difficult diagnosis. In order to reclassify them based on genetic markers rather than clinical criteria, we performed clustering of Single Nucleotide Polymorphisms. However naive approaches tend to group patients primarily by their geographic origin. To reduce this “ancestry signal”, we developed SNPClust, a method to select large sources of ancestry-independent genetic variations from all variations detected by Principal Component Analysis. Applied to a Systemic Lupus Erythematosus case control dataset, SNPClust successfully reduced the ancestry signal. Results were compared with association studies between the cases and controls without or with reference population stratification correction methods. SNPClust amplified the disease discriminating signal and the ratio of significant associations outside the HLA locus was greater compared to population stratification correction methods. SNPClust will enable the use of ancestry-independent genetic information in the reclassification of Systemic Autoimmune Diseases. SNPClust is available as an R package and demonstrated on the public Human Genome Diversity Project dataset at https://github.com/ThomasChln/snpclust. PMID:27490238
Single Nucleotide Polymorphism Clustering in Systemic Autoimmune Diseases.
Charlon, Thomas; Martínez-Bueno, Manuel; Bossini-Castillo, Lara; Carmona, F David; Di Cara, Alessandro; Wojcik, Jérôme; Voloshynovskiy, Sviatoslav; Martín, Javier; Alarcón-Riquelme, Marta E
2016-01-01
Systemic Autoimmune Diseases, a group of chronic inflammatory conditions, have variable symptoms and difficult diagnosis. In order to reclassify them based on genetic markers rather than clinical criteria, we performed clustering of Single Nucleotide Polymorphisms. However naive approaches tend to group patients primarily by their geographic origin. To reduce this "ancestry signal", we developed SNPClust, a method to select large sources of ancestry-independent genetic variations from all variations detected by Principal Component Analysis. Applied to a Systemic Lupus Erythematosus case control dataset, SNPClust successfully reduced the ancestry signal. Results were compared with association studies between the cases and controls without or with reference population stratification correction methods. SNPClust amplified the disease discriminating signal and the ratio of significant associations outside the HLA locus was greater compared to population stratification correction methods. SNPClust will enable the use of ancestry-independent genetic information in the reclassification of Systemic Autoimmune Diseases. SNPClust is available as an R package and demonstrated on the public Human Genome Diversity Project dataset at https://github.com/ThomasChln/snpclust. PMID:27490238
Liebermeister, Lars Petersen, Fabian; Münchow, Asmus v.; Burchardt, Daniel; Hermelbracht, Juliane; Tashima, Toshiyuki; Schell, Andreas W.; Benson, Oliver; Meinhardt, Thomas; Krueger, Anke; Stiebeiner, Ariane; Rauschenbeutel, Arno; Weinfurter, Harald; Weber, Markus
2014-01-20
A diamond nano-crystal hosting a single nitrogen vacancy (NV) center is optically selected with a confocal scanning microscope and positioned deterministically onto the subwavelength-diameter waist of a tapered optical fiber (TOF) with the help of an atomic force microscope. Based on this nano-manipulation technique, we experimentally demonstrate the evanescent coupling of single fluorescence photons emitted by a single NV-center to the guided mode of the TOF. By comparing photon count rates of the fiber-guided and the free-space modes and with the help of numerical finite-difference time domain simulations, we determine a lower and upper bound for the coupling efficiency of (9.5 ± 0.6)% and (10.4 ± 0.7)%, respectively. Our results are a promising starting point for future integration of single photon sources into photonic quantum networks and applications in quantum information science.
Sørensen, Lasse K; Olsen, Jeppe; Fleig, Timo
2011-06-01
A string-based coupled-cluster method of general excitation rank and with optimal scaling which accounts for special relativity within the four-component framework is presented. The method opens the way for the treatment of multi-reference problems through an active-space inspired single-reference based state-selective expansion of the model space. The evaluation of the coupled-cluster vector function is implemented by considering contractions of elementary second-quantized operators without setting up the amplitude equations explicitly. The capabilities of the new method are demonstrated in application to the electronic ground state of the bismuth monohydride molecule. In these calculations simulated multi-reference expansions with both doubles and triples excitations into the external space as well as the regular coupled-cluster hierarchy up to full quadruples excitations are compared. The importance of atomic outer core-correlation for obtaining accurate results is shown. Comparison to the non-relativistic framework is performed throughout to illustrate the additional work of the transition to the four-component relativistic framework both in implementation and application. Furthermore, an evaluation of the highest order scaling for general-order expansions is presented. PMID:21663339
NASA Astrophysics Data System (ADS)
Degroote, Matthias; Henderson, Thomas M.; Zhao, Jinmo; Dukelsky, Jorge; Scuseria, Gustavo E.
2016-03-01
We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wave function. In between, we interpolate using a single parameter. The effective Hamiltonian is non-Hermitian and this polynomial similarity transformation theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero. Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit, whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1% across all interaction strengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.
Tunable magnetoresistance in an asymmetrically coupled single-molecule junction.
Warner, Ben; El Hallak, Fadi; Prüser, Henning; Sharp, John; Persson, Mats; Fisher, Andrew J; Hirjibehedin, Cyrus F
2015-03-01
Phenomena that are highly sensitive to magnetic fields can be exploited in sensors and non-volatile memories. The scaling of such phenomena down to the single-molecule level may enable novel spintronic devices. Here, we report magnetoresistance in a single-molecule junction arising from negative differential resistance that shifts in a magnetic field at a rate two orders of magnitude larger than Zeeman shifts. This sensitivity to the magnetic field produces two voltage-tunable forms of magnetoresistance, which can be selected via the applied bias. The negative differential resistance is caused by transient charging of an iron phthalocyanine (FePc) molecule on a single layer of copper nitride (Cu2N) on a Cu(001) surface, and occurs at voltages corresponding to the alignment of sharp resonances in the filled and empty molecular states with the Cu(001) Fermi energy. An asymmetric voltage-divider effect enhances the apparent voltage shift of the negative differential resistance with magnetic field, which inherently is on the scale of the Zeeman energy. These results illustrate the impact that asymmetric coupling to metallic electrodes can have on transport through molecules, and highlight how this coupling can be used to develop molecular spintronic applications. PMID:25622229
Coupling single quantum dots to plasmonic nanocones: optical properties.
Meixner, Alfred J; Jäger, Regina; Jäger, Sebastian; Bräuer, Annika; Scherzinger, Kerstin; Fulmes, Julia; Krockhaus, Sven zur Oven; Gollmer, Dominik A; Kern, Dieter P; Fleischer, Monika
2015-01-01
Coupling a single quantum emitter, such as a fluorescent molecule or a quantum dot (QD), to a plasmonic nanostructure is an important issue in nano-optics and nano-spectroscopy, relevant for a wide range of applications, including tip-enhanced near-field optical microscopy, plasmon enhanced molecular sensing and spectroscopy, and nanophotonic amplifiers or nanolasers, to mention only a few. While the field enhancement of a sharp nanoantenna increasing the excitation rate of a very closely positioned single molecule or QD has been well investigated, the detailed physical mechanisms involved in the emission of a photon from such a system are, by far, less investigated. In one of our ongoing research projects, we try to address these issues by constructing and spectroscopically analysing geometrically simple hybrid heterostructures consisting of sharp gold cones with single quantum dots attached to the very tip apex. An important goal of this work is to tune the longitudinal plasmon resonance by adjusting the cones' geometry to the emission maximum of the core-shell CdSe/ZnS QDs at nominally 650 nm. Luminescence spectra of the bare cones, pure QDs and hybrid systems were distinguished successfully. In the next steps we will further investigate, experimentally and theoretically, the optical properties of the coupled systems in more detail, such as the fluorescence spectra, blinking statistics, and the current results on the fluorescence lifetimes, and compare them with uncoupled QDs to obtain a clearer picture of the radiative and non-radiative processes. PMID:26404008
Preparation of cluster states with endohedral fullerenes in single-walled carbon nanotubes
NASA Astrophysics Data System (ADS)
Hu, Y. M.; Chen, C. Y.; Yang, W. L.; Feng, M.
2012-05-01
We propose two scalable methods for generation of cluster states with arrays of endohedral fullerenes 15N@C60 residing in single-walled carbon nanotubes (SWCNTs) using direct and indirect methods, respectively. The direct method makes use of a series of controlled-phase flip (CPF) gates by electron spin resonance pulses of selective frequencies and durations, where the CPF gates are realized by magnetic-dipole couplings between the electron spins of the nearest-neighbour fullerenes in SWCNTs. The indirect method resorts to auxiliary mobile electron as the flying qubit, which transfers quantum information from one site to another. This greatly releases the requirements for the distance between fullerenes in SWCNTs. The decoherence effect and experimental feasibility are also discussed based on currently available technology.
Laser to single-mode-fiber coupling: A laboratory guide
NASA Technical Reports Server (NTRS)
Ladany, I.
1992-01-01
All the information necessary to achieve reasonably efficient coupling of semiconductor lasers to single mode fibers is collected from the literature, reworked when necessary, and presented in a mostly tabular form. Formulas for determining the laser waist radius and the fiber mode radius are given. Imaging relations connecting these values with the object and image distances are given for three types of lenses: ball, hemisphere, and Gradient Index (GRIN). Sources for these lenses are indicated, and a brief discussion is given about ways of reducing feedback effects.
Carrier doping and interlayer coupling in HTSC single crystals
Kishio, K.; Shimoyama, J.; Kimura, T.; Kotaka, Y.; Kitazawa, K.; Yamafuji, K.; Li, Q.; Suenaga, M.
1994-09-01
Experimental results of the effect of carrier doping on the irreversibility lines in (La,Sr){sub 2}CuO{sub 4{minus}{delta}} and Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8 + {delta}} single crystals are summarized. As a function of Sr or oxygen contents, systematic and dramatic widening of the irreversible regions in the B {minus} T phase diagram was observed in both systems. The present study suggests the critical importance of carrier concentration which directly affects the interlayer coupling strength and dimensionality of the flux line lattice in all the layered HTSC compounds as a universal feature.
Near-Edge X-ray Absorption Fine Structure within Multilevel Coupled Cluster Theory.
Myhre, Rolf H; Coriani, Sonia; Koch, Henrik
2016-06-14
Core excited states are challenging to calculate, mainly because they are embedded in a manifold of high-energy valence-excited states. However, their locality makes their determination ideal for local correlation methods. In this paper, we demonstrate the performance of multilevel coupled cluster theory in computing core spectra both within the core-valence separated and the asymmetric Lanczos implementations of coupled cluster linear response theory. We also propose a visualization tool to analyze the excitations using the difference between the ground-state and excited-state electron densities. PMID:27182829
Current rectification in a single molecule diode: the role of electrode coupling
NASA Astrophysics Data System (ADS)
Sherif, Siya; Rubio-Bollinger, Gabino; Pinilla-Cienfuegos, Elena; Coronado, Eugenio; Cuevas, Juan Carlos; Agraït, Nicolás
2015-07-01
We demonstrate large rectification ratios (\\gt 100) in single-molecule junctions based on a metal-oxide cluster (polyoxometalate), using a scanning tunneling microscope (STM) both at ambient conditions and at low temperature. These rectification ratios are the largest ever observed in a single-molecule junction, and in addition these junctions sustain current densities larger than 105 A cm-2. By following the variation of the I-V characteristics with tip-molecule separation we demonstrate unambiguously that rectification is due to asymmetric coupling to the electrodes of a molecule with an asymmetric level structure. This mechanism can be implemented in other type of molecular junctions using both organic and inorganic molecules and provides a simple strategy for the rational design of molecular diodes.
Current rectification in a single molecule diode: the role of electrode coupling.
Sherif, Siya; Rubio-Bollinger, Gabino; Pinilla-Cienfuegos, Elena; Coronado, Eugenio; Cuevas, Juan Carlos; Agraït, Nicolás
2015-07-24
We demonstrate large rectification ratios (> 100) in single-molecule junctions based on a metal-oxide cluster (polyoxometalate), using a scanning tunneling microscope (STM) both at ambient conditions and at low temperature. These rectification ratios are the largest ever observed in a single-molecule junction, and in addition these junctions sustain current densities larger than 10(5) A cm(-2). By following the variation of the I-V characteristics with tip-molecule separation we demonstrate unambiguously that rectification is due to asymmetric coupling to the electrodes of a molecule with an asymmetric level structure. This mechanism can be implemented in other type of molecular junctions using both organic and inorganic molecules and provides a simple strategy for the rational design of molecular diodes. PMID:26133791
NASA Astrophysics Data System (ADS)
Zhou, Xin; Ishibashi, Koji
2012-09-01
Single charge detection is demonstrated in the capacitively coupled integrated single electron transistors (SETs) in single-walled carbon nanotubes (SWCNTs) quantum dots. Two SETs are fabricated based on two different SWCNTs aligned in parallel, by taking advantage of the aligned growth of SWCNTs and subsequent transfer-printed techniques. In order to make both two SETs be capacitively coupled, a metal finger is fabricated on the top of them. The charge sensing is proved by the response of a detector current in one SWCNT-SET when the number of electrons in the other SWCNT-SET is changed by sweeping the corresponding gate voltages. In this integrated device, shifts of Coulomb oscillation peaks due to the single electron event are also observed.
NASA Technical Reports Server (NTRS)
Lee, Timothy J.; Rendell, Alistair P.
1991-01-01
An efficient formulation of the analytic energy gradient for the single and double excitation coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations is presented. The formulation has a small computational cost, and the algebraic manipulations may be applied generally to the analytic gradient of Moller-Plesset perturbation theory energies. The new formulation has been implemented in an efficient set of programs that utilize highly vectorized algorithms and has been used to investigate the equilibrium structures, harmonic vibrational frequencies, IR intensities, and energy separation of cis- and trans-HONO.
Gopakumar, Geetha; Das, Bhanu Pratap; Chaudhuri, R. K.; Mukherjee, D.; Hirao, K.
2007-01-07
The authors present the results of their calculation for the parity nonconserving 5p{sup 6}6s{sub 1/2}{yields}5p{sup 6}5d{sub 3/2} transition in Ba{sup +} using the relativistic coupled-cluster theory in the singles, doubles, and partial triples approximation. The contributions from the leading intermediate states are explicitly considered. It is found that the largest contribution comes from the |5p{sup 6}6p{sub 1/2}> state. Their results are in reasonable agreement with other calculations.
Valiev, Marat; Kowalski, Karol
2006-12-07
Evolution of the excited state energies of cytosine base in the native DNA environment was investigated using hybrid coupled cluster and classical molecular dynamics approach. The time averaged excitation energies obtained with the variant of the completely renormalized equation-of-motion with singles, doubles, and non-iterative triples approach that includes a bulk of the correlation effects for excited states, are compared with the analogous calculations in the gas phase. Significant blue shifts for the two lowest singlet excitation energies can be observed as a result of interaction of the quantum system with surrounding environment.
NASA Astrophysics Data System (ADS)
Mukherjee, Saikat; Adhikari, Satrajit
2014-08-01
We calculate the adiabatic potential energy surfaces (PESs) and the non-adiabatic coupling terms (NACTs) for the excited electronic states of K3 cluster by MRCI approach using MOLPRO. The NACTs are adapted with molecular symmetry to assign appropriate IREPs so that the elements of the Hamiltonian matrix are totally symmetric. We incorporate those NACTs into three-state adiabatic-to-diabatic transformation (ADT) equations to obtain ADT angles for constructing continuous, single-valued, smooth and symmetric diabatic Hamiltonian matrix, where its elements are fitted with analytic functions. Finally, we demonstrate that the dressed diabatic and adiabatic-via-dressed diabatic PECs show prominent topological effect over dressed adiabatic curves.
Wykes, M; Parambil, R; Beljonne, D; Gierschner, J
2015-09-21
Here, we present a general approach to treating vibronic coupling in molecular crystals based on atomistic simulations of large clusters. Such clusters comprise model aggregates treated at the quantum chemical level embedded within a realistic environment treated at the molecular mechanics level. As we calculate ground and excited state equilibrium geometries and vibrational modes of model aggregates, our approach is able to capture effects arising from coupling to intermolecular degrees of freedom, absent from existing models relying on geometries and normal modes of single molecules. Using the geometries and vibrational modes of clusters, we are able to simulate the fluorescence spectra of aggregates for which the lowest excited state bears negligible oscillator strength (as is the case, e.g., ideal H-aggregates) by including both Franck-Condon (FC) and Herzberg-Teller (HT) vibronic transitions. The latter terms allow the adiabatic excited state of the cluster to couple with vibrations in a perturbative fashion via derivatives of the transition dipole moment along nuclear coordinates. While vibronic coupling simulations employing FC and HT terms are well established for single-molecules, to our knowledge this is the first time they are applied to molecular aggregates. Here, we apply this approach to the simulation of the low-temperature fluorescence spectrum of para-distyrylbenzene single-crystal H-aggregates and draw comparisons with coarse-grained Frenkel-Holstein approaches previously extensively applied to such systems. PMID:26395696
NASA Astrophysics Data System (ADS)
Wykes, M.; Parambil, R.; Beljonne, D.; Gierschner, J.
2015-09-01
Here, we present a general approach to treating vibronic coupling in molecular crystals based on atomistic simulations of large clusters. Such clusters comprise model aggregates treated at the quantum chemical level embedded within a realistic environment treated at the molecular mechanics level. As we calculate ground and excited state equilibrium geometries and vibrational modes of model aggregates, our approach is able to capture effects arising from coupling to intermolecular degrees of freedom, absent from existing models relying on geometries and normal modes of single molecules. Using the geometries and vibrational modes of clusters, we are able to simulate the fluorescence spectra of aggregates for which the lowest excited state bears negligible oscillator strength (as is the case, e.g., ideal H-aggregates) by including both Franck-Condon (FC) and Herzberg-Teller (HT) vibronic transitions. The latter terms allow the adiabatic excited state of the cluster to couple with vibrations in a perturbative fashion via derivatives of the transition dipole moment along nuclear coordinates. While vibronic coupling simulations employing FC and HT terms are well established for single-molecules, to our knowledge this is the first time they are applied to molecular aggregates. Here, we apply this approach to the simulation of the low-temperature fluorescence spectrum of para-distyrylbenzene single-crystal H-aggregates and draw comparisons with coarse-grained Frenkel-Holstein approaches previously extensively applied to such systems.
Wykes, M. Parambil, R.; Gierschner, J.; Beljonne, D.
2015-09-21
Here, we present a general approach to treating vibronic coupling in molecular crystals based on atomistic simulations of large clusters. Such clusters comprise model aggregates treated at the quantum chemical level embedded within a realistic environment treated at the molecular mechanics level. As we calculate ground and excited state equilibrium geometries and vibrational modes of model aggregates, our approach is able to capture effects arising from coupling to intermolecular degrees of freedom, absent from existing models relying on geometries and normal modes of single molecules. Using the geometries and vibrational modes of clusters, we are able to simulate the fluorescence spectra of aggregates for which the lowest excited state bears negligible oscillator strength (as is the case, e.g., ideal H-aggregates) by including both Franck-Condon (FC) and Herzberg-Teller (HT) vibronic transitions. The latter terms allow the adiabatic excited state of the cluster to couple with vibrations in a perturbative fashion via derivatives of the transition dipole moment along nuclear coordinates. While vibronic coupling simulations employing FC and HT terms are well established for single-molecules, to our knowledge this is the first time they are applied to molecular aggregates. Here, we apply this approach to the simulation of the low-temperature fluorescence spectrum of para-distyrylbenzene single-crystal H-aggregates and draw comparisons with coarse-grained Frenkel-Holstein approaches previously extensively applied to such systems.
NASA Astrophysics Data System (ADS)
DeYonker, Nathan J.; Peterson, Kirk A.
2013-04-01
Recent developments in ab initio coupled cluster (CC) theory and correlation consistent basis sets have ushered in an era of unprecedented accuracy when studying the spectroscopy and thermodynamics of molecules containing main group elements. These same developments have recently seen application to heavier inorganic or transition metal-containing species. The present work benchmarks conventional single reference coupled cluster theory (up to full configuration interaction for valence electron correlation and coupled cluster with up to full pentuple excitations (CCSDTQP) for core-valence correlation) and explicitly correlated coupled cluster methods [CC with single, double, and perturbative triple substitutions (CCSD(T)-F12)] for the atomic ionization potentials of the six 4p elements (Ga-Kr), a property with experimental error bars no greater than a few cm-1. When second-order spin orbit coupling effects are included, a composite methodology based on CCSD(T) calculations yielded a mean signed error of just -0.039 kcal mol-1 and a mean unsigned error of 0.043 kcal mol-1. Inclusion of post-CCSD(T) correlation corrections reduced both of these values to -0.008 kcal mol-1 and 0.025 kcal mol-1, respectively, with the latter corresponding to an average error of just 9 cm-1. The maximum signed error in the latter scheme was just -0.043 kcal mol-1 (15 cm-1).
Three coupled qubits in a single superconducting quantum circuit
NASA Astrophysics Data System (ADS)
Chand, Madhavi; Kundu, Suman; Nehra, N.; Raj, Cosmic; Roy, Tanay; Ranadive, A.; Patankar, Meghan P.; Vijay, R.
We propose a new design for a 3-qubit system in the 3D circuit QED architecture. Our design exploits the geometrical symmetry of a single superconducting circuit with three degrees of freedom to generate three coupled qubits. However, only one of these is strongly coupled to the environment while the other two are protected from the Purcell effect. Nevertheless, all three qubits can be measured using the standard dispersive technique. We will present preliminary data on this circuit showing evidence of three distinct qubits that retain the essential properties of a 3D transmon, namely insensitivity to charge noise, sufficient anharmonicity and good coherence times. We will also characterize the coupling of the three qubits to each other, to the environment and to a neighboring transmon qubit. Finally, we will compare our design to previous multi-qubit circuits and discuss possible applications in quantum computing and quantum simulations. Funding: Department of Atomic Energy, Govt. of India; Department of Science and Technology, Govt. of India.
Liakos, Dimitrios G; Neese, Frank
2015-09-01
The recently developed domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)) delivers results that are closely approaching those of the parent canonical coupled cluster method at a small fraction of the computational cost. A recent extended benchmark study established that, depending on the three main truncation thresholds, it is possible to approach the canonical CCSD(T) results within 1 kJ (default setting, TightPNO), 1 kcal/mol (default setting, NormalPNO), and 2-3 kcal (default setting, LoosePNO). Although thresholds for calculations with TightPNO are 2-4 times slower than those based on NormalPNO thresholds, they are still many orders of magnitude faster than canonical CCSD(T) calculations, even for small and medium sized molecules where there is little locality. The computational effort for the coupled cluster step scales nearly linearly with system size. Since, in many instances, the coupled cluster step in DLPNO-CCSD(T) is cheaper or at least not much more expensive than the preceding Hartree-Fock calculation, it is useful to compare the method against modern density functional theory (DFT), which requires an effort comparable to that of Hartree-Fock theory (at least if Hartree-Fock exchange is part of the functional definition). Double hybrid density functionals (DHDF's) even require a MP2-like step. The purpose of this article is to evaluate the cost vs accuracy ratio of DLPNO-CCSD(T) against modern DFT (including the PBE, B3LYP, M06-2X, B2PLYP, and B2GP-PLYP functionals and, where applicable, their van der Waals corrected counterparts). To eliminate any possible bias in favor of DLPNO-CCSD(T), we have chosen established benchmark sets that were specifically proposed for evaluating DFT functionals. It is demonstrated that DLPNO-CCSD(T) with any of the three default thresholds is more accurate than any of the DFT functionals. Furthermore, using the aug-cc-pVTZ basis set and
An efficient and near linear scaling pair natural orbital based local coupled cluster method
NASA Astrophysics Data System (ADS)
Riplinger, Christoph; Neese, Frank
2013-01-01
In previous publications, it was shown that an efficient local coupled cluster method with single- and double excitations can be based on the concept of pair natural orbitals (PNOs) [F. Neese, A. Hansen, and D. G. Liakos, J. Chem. Phys. 131, 064103 (2009), 10.1063/1.3173827]. The resulting local pair natural orbital-coupled-cluster single double (LPNO-CCSD) method has since been proven to be highly reliable and efficient. For large molecules, the number of amplitudes to be determined is reduced by a factor of 105-106 relative to a canonical CCSD calculation on the same system with the same basis set. In the original method, the PNOs were expanded in the set of canonical virtual orbitals and single excitations were not truncated. This led to a number of fifth order scaling steps that eventually rendered the method computationally expensive for large molecules (e.g., >100 atoms). In the present work, these limitations are overcome by a complete redesign of the LPNO-CCSD method. The new method is based on the combination of the concepts of PNOs and projected atomic orbitals (PAOs). Thus, each PNO is expanded in a set of PAOs that in turn belong to a given electron pair specific domain. In this way, it is possible to fully exploit locality while maintaining the extremely high compactness of the original LPNO-CCSD wavefunction. No terms are dropped from the CCSD equations and domains are chosen conservatively. The correlation energy loss due to the domains remains below <0.05%, which implies typically 15-20 but occasionally up to 30 atoms per domain on average. The new method has been given the acronym DLPNO-CCSD ("domain based LPNO-CCSD"). The method is nearly linear scaling with respect to system size. The original LPNO-CCSD method had three adjustable truncation thresholds that were chosen conservatively and do not need to be changed for actual applications. In the present treatment, no additional truncation parameters have been introduced. Any additional truncation
Entangled states decoherence in coupled molecular spin clusters
NASA Astrophysics Data System (ADS)
Troiani, Filippo; Szallas, Attila; Bellini, Valerio; Affronte, Marco
2010-03-01
Localized electron spins in solid-state systems are widely investigated as potential building blocks of quantum devices and computers. While most efforts in the field have been focused on semiconductor low-dimensional structures, molecular antiferromagnets were recently recognized as alternative implementations of effective few-level spin systems. Heterometallic, Cr-based spin rings behave as effective spin-1/2 systems at low temperature and show long decoherence times [1]; besides, they can be chemically linked and magnetically coupled in a controllable fascion [2]. Here, we theoretically investigate the decoherence of the Bell states in such ring dimers, resulting from hyperfine interactions with nuclear spins. Based on a microscopic description of the molecules [3], we simulate the effect of inhomogeneous broadening, spectral diffusion and electron-nuclear entanglement on the electron-spin coherence, estimating the role of the different nuclei (and of possible chemical substitutions), as well as the effect of simple spin-echo sequences. References: [1] F. Troiani, et al., Phys. Rev. Lett. 94, 207208 (2005). [2] G. A. Timco, S: Carretta, F. Troiani et al., Nature Nanotech. 4, 173 (2009). [3] F. Troiani, V. Bellini, and M. Affronte, Phys. Rev. B 77, 054428 (2008).
Eriksen, Janus J; Matthews, Devin A; Jørgensen, Poul; Gauss, Jürgen
2016-05-21
The accuracy at which total energies of open-shell atoms and organic radicals may be calculated is assessed for selected coupled cluster perturbative triples expansions, all of which augment the coupled cluster singles and doubles (CCSD) energy by a non-iterative correction for the effect of triple excitations. Namely, the second- through sixth-order models of the recently proposed CCSD(T-n) triples series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)] are compared to the acclaimed CCSD(T) model for both unrestricted as well as restricted open-shell Hartree-Fock (UHF/ROHF) reference determinants. By comparing UHF- and ROHF-based statistical results for a test set of 18 modest-sized open-shell species with comparable RHF-based results, no behavioral differences are observed for the higher-order models of the CCSD(T-n) series in their correlated descriptions of closed- and open-shell species. In particular, we find that the convergence rate throughout the series towards the coupled cluster singles, doubles, and triples (CCSDT) solution is identical for the two cases. For the CCSD(T) model, on the other hand, not only its numerical consistency, but also its established, yet fortuitous cancellation of errors breaks down in the transition from closed- to open-shell systems. The higher-order CCSD(T-n) models (orders n > 3) thus offer a consistent and significant improvement in accuracy relative to CCSDT over the CCSD(T) model, equally for RHF, UHF, and ROHF reference determinants, albeit at an increased computational cost. PMID:27208931
NASA Astrophysics Data System (ADS)
Eriksen, Janus J.; Matthews, Devin A.; Jørgensen, Poul; Gauss, Jürgen
2016-05-01
The accuracy at which total energies of open-shell atoms and organic radicals may be calculated is assessed for selected coupled cluster perturbative triples expansions, all of which augment the coupled cluster singles and doubles (CCSD) energy by a non-iterative correction for the effect of triple excitations. Namely, the second- through sixth-order models of the recently proposed CCSD(T-n) triples series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)] are compared to the acclaimed CCSD(T) model for both unrestricted as well as restricted open-shell Hartree-Fock (UHF/ROHF) reference determinants. By comparing UHF- and ROHF-based statistical results for a test set of 18 modest-sized open-shell species with comparable RHF-based results, no behavioral differences are observed for the higher-order models of the CCSD(T-n) series in their correlated descriptions of closed- and open-shell species. In particular, we find that the convergence rate throughout the series towards the coupled cluster singles, doubles, and triples (CCSDT) solution is identical for the two cases. For the CCSD(T) model, on the other hand, not only its numerical consistency, but also its established, yet fortuitous cancellation of errors breaks down in the transition from closed- to open-shell systems. The higher-order CCSD(T-n) models (orders n > 3) thus offer a consistent and significant improvement in accuracy relative to CCSDT over the CCSD(T) model, equally for RHF, UHF, and ROHF reference determinants, albeit at an increased computational cost.
Gradients for the partitioned equation-of-motion coupled-cluster method
Gwaltney, S.R.; Bartlett, R.J.
1996-12-31
The Equation-of-Motion Coupled-Cluster method restricted to singles and doubles (EOM-CCSD) is a highly accurate method for calculating excited states of molecules. Errors of 0.1 to 0.3 eV are typical for excitation energies. But a major drawback is that EOM-CCSD is an iterative n{sup 6} method, and for large cases the cost can be prohibitive. For a partitioned EOM-CCSD calculation, the doubles-doubles block of the H matrix is replaced with Ho. Combined with truncating the H matrix at second order (i.e. basing the excited state calculation on a MBPT(2) ground state), the partitioning technique creates an iterative n{sup 5} method for excited states, the P-EOM-MBPT(2) method. In this poster we will present the theory and examples of P-EOM-MBPT(2) gradient calculations. The gradients provide an inexpensive way to look at potential energy surfaces of excited states of molecules.
A universal state-selective approach to multireference coupled-cluster non-iterative corrections
Kowalski, Karol
2011-05-21
A new form of the asymmetric energy functional for the multireference coupled cluster (MRCC) theories is discussed from the point of view of an energy expansion in quasidegenerate situation. The resulting expansion for the exact electronic energy can be used to define the non-iterative corrections to approximate MRCC approaches. In particular, we show that in the proposed framework the essential part of dynamic correlation can be encapsulated in the so-called correlation Hamiltonian, which in analogy to the effective Hamiltonian, is defined in the model space (M0). When the trail wavefunction (wavefunctions) is determined without invoking a specific form of the MRCC sufficiency conditions, the ensuing correction can be universally applied to any type of the approximate MRCC method employing the same excitation manifold. We also discuss several strategies of normalizing trial wavefunctions, which significantly simplify the algebraic structure of the correction. The analogies with other MRCC triples corrections to MRCC theories with singles and doubles are outlined. Possible parallel algorithms for the non-iterative corrections are alsodiscussed.
NASA Astrophysics Data System (ADS)
Hanauer, Matthias; Köhn, Andreas
2012-05-01
Internally contracted multireference coupled cluster (ic-MRCC) methods with perturbative treatment of triple excitations are formulated based on Dyall's definition of a zeroth-order Hamiltonian. The iterative models ic-MRCCSDT-1, ic-MRCC3, and their variants ic-MRCCSD(T), ic-MRCC(3) which determine the energy correction from triples by a non-iterative step are consistent in the single-reference limit with CCSDT-1a, CC3, CCSD(T), and CC(3), respectively. Numerical tests on the potential energy surfaces of BeH2, H2O, and N2 as well as on the structure and harmonic vibrational frequencies of the ozone molecule show that these methods account very well for higher order correlation effects. The ic-MRCCSD(T) method is further applied to the geometry optimization and harmonic frequencies of the symmetric vibrational modes of the binuclear transition metal oxide Ni2O2, to the singlet-triplet splittings of o-, m-, and p-benzyne and to a ring-opening reaction of an azirine compound with the molecular formula C6H7NO. The size of the active spaces used in this study ranges from CAS(2,2) to CAS(8,8). Comparisons of results based on differently sized active spaces indicate that the ic-MRCCSD(T) method provides a highly accurate and efficient treatment of both static and dynamic electron correlation in connection with minimal active spaces.
Ghosh, Debashree
2014-03-07
Hybrid quantum mechanics/molecular mechanics (QM/MM) methods provide an attractive way to closely retain the accuracy of the QM method with the favorable computational scaling of the MM method. Therefore, it is not surprising that QM/MM methods are being increasingly used for large chemical/biological systems. Hybrid equation of motion coupled cluster singles doubles/effective fragment potential (EOM-CCSD/EFP) methods have been developed over the last few years to understand the effect of solvents and other condensed phases on the electronic spectra of chromophores. However, the computational cost of this approach is still dominated by the steep scaling of the EOM-CCSD method. In this work, we propose and implement perturbative approximations to the EOM-CCSD method in this hybrid scheme to reduce the cost of EOM-CCSD/EFP. The timings and accuracy of this hybrid approach is tested for calculation of ionization energies, excitation energies, and electron affinities of microsolvated nucleic acid bases (thymine and cytosine), phenol, and phenolate.
Sharma, Sandeep; Alavi, Ali
2015-09-14
We propose a multireference linearized coupled cluster theory using matrix product states (MPSs-LCC) which provides remarkably accurate ground-state energies, at a computational cost that has the same scaling as multireference configuration interaction singles and doubles, for a wide variety of electronic Hamiltonians. These range from first-row dimers at equilibrium and stretched geometries to highly multireference systems such as the chromium dimer and lattice models such as periodic two-dimensional 1-band and 3-band Hubbard models. The MPS-LCC theory shows a speed up of several orders of magnitude over the usual Density Matrix Renormalization Group (DMRG) algorithm while delivering energies in excellent agreement with converged DMRG calculations. Also, in all the benchmark calculations presented here, MPS-LCC outperformed the commonly used multi-reference quantum chemistry methods in some cases giving energies in excess of an order of magnitude more accurate. As a size-extensive method that can treat large active spaces, MPS-LCC opens up the use of multireference quantum chemical techniques in strongly correlated ab initio Hamiltonians, including two- and three-dimensional solids. PMID:26374008
Brabec, Jiri; Pittner, Jiri; van Dam, Hubertus JJ; Apra, Edoardo; Kowalski, Karol
2012-02-01
A novel algorithm for implementing general type of multireference coupled-cluster (MRCC) theory based on the Jeziorski-Monkhorst exponential Ansatz [B. Jeziorski, H.J. Monkhorst, Phys. Rev. A 24, 1668 (1981)] is introduced. The proposed algorithm utilizes processor groups to calculate the equations for the MRCC amplitudes. In the basic formulation each processor group constructs the equations related to a specific subset of references. By flexible choice of processor groups and subset of reference-specific sufficiency conditions designated to a given group one can assure optimum utilization of available computing resources. The performance of this algorithm is illustrated on the examples of the Brillouin-Wigner and Mukherjee MRCC methods with singles and doubles (BW-MRCCSD and Mk-MRCCSD). A significant improvement in scalability and in reduction of time to solution is reported with respect to recently reported parallel implementation of the BW-MRCCSD formalism [J.Brabec, H.J.J. van Dam, K. Kowalski, J. Pittner, Chem. Phys. Lett. 514, 347 (2011)].
Sharma, Sandeep; Alavi, Ali
2015-09-14
We propose a multireference linearized coupled cluster theory using matrix product states (MPSs-LCC) which provides remarkably accurate ground-state energies, at a computational cost that has the same scaling as multireference configuration interaction singles and doubles, for a wide variety of electronic Hamiltonians. These range from first-row dimers at equilibrium and stretched geometries to highly multireference systems such as the chromium dimer and lattice models such as periodic two-dimensional 1-band and 3-band Hubbard models. The MPS-LCC theory shows a speed up of several orders of magnitude over the usual Density Matrix Renormalization Group (DMRG) algorithm while delivering energies in excellent agreement with converged DMRG calculations. Also, in all the benchmark calculations presented here, MPS-LCC outperformed the commonly used multi-reference quantum chemistry methods in some cases giving energies in excess of an order of magnitude more accurate. As a size-extensive method that can treat large active spaces, MPS-LCC opens up the use of multireference quantum chemical techniques in strongly correlated ab initio Hamiltonians, including two- and three-dimensional solids.
Banik, Subrata; Ravichandran, Lalitha; Brabec, Jiří; Hubač, Ivan; Kowalski, Karol; Pittner, Jiří
2015-03-21
As a further development of the previously introduced a posteriori Universal State-Selective (USS) corrections [K. Kowalski, J. Chem. Phys. 134, 194107 (2011); J. Brabec et al., ibid. 136, 124102 (2012)], we suggest an iterative form of the USS correction by means of correcting effective Hamiltonian matrix elements. We also formulate USS corrections via the left Bloch equations. The convergence of the USS corrections with excitation level towards the full configuration interaction (FCI) limit is also investigated. Various forms of the USS and simplified diagonal USS corrections at the singles and doubles and perturbative triple levels are numerically assessed on several model systems and on the ozone and tetramethyleneethane molecules. It is shown that the iterative USS correction can successfully replace the previously developed a posteriori Brillouin-Wigner coupled cluster size-extensivity correction, while it is not sensitive to intruder states and performs well also in other cases when the a posteriori one fails, like, e.g., for the asymmetric vibration mode of ozone. PMID:25796230
Ghosh, Debashree
2014-03-01
Hybrid quantum mechanics/molecular mechanics (QM/MM) methods provide an attractive way to closely retain the accuracy of the QM method with the favorable computational scaling of the MM method. Therefore, it is not surprising that QM/MM methods are being increasingly used for large chemical/biological systems. Hybrid equation of motion coupled cluster singles doubles/effective fragment potential (EOM-CCSD/EFP) methods have been developed over the last few years to understand the effect of solvents and other condensed phases on the electronic spectra of chromophores. However, the computational cost of this approach is still dominated by the steep scaling of the EOM-CCSD method. In this work, we propose and implement perturbative approximations to the EOM-CCSD method in this hybrid scheme to reduce the cost of EOM-CCSD/EFP. The timings and accuracy of this hybrid approach is tested for calculation of ionization energies, excitation energies, and electron affinities of microsolvated nucleic acid bases (thymine and cytosine), phenol, and phenolate. PMID:24606347
Symmetry breaking in O4(+): An application of the Brueckner coupled-cluster method
NASA Technical Reports Server (NTRS)
Barnes, Leslie A.; Lindh, Roland
1994-01-01
A recent calculation of the antisymmetric stretch frequency for the rectangular structure of quartet O4(+) using the singles and doubles quadratic configuration interaction method with a perturbational estimate of connected triple excitations (QCISD(T)) method gave a value of 3710 cm(exp -1). This anomalous frequency is shown to be a consequence of symmetry breaking effects, which occur even though the QCISD(T) solution derived from a delocalized SCF reference function lies energetically well below the two localized (symmetry-broken) solutions at the equilibrium geometry. The symmetry breaking is almost eliminated at the CCSD level of theory, but the small remaining symmetry breaking effects are magnified at the CCSD(T) level of theory so that the antisymmetric stretch frequency is still significantly in error. The use of the Brueckner coupled cluster method, however, leads to a symmetrical solution which is free of symmetry breaking effects, with an antisymmetric stretch frequency of 1322 cm(exp -1), in good agreement with our earlier calculations using the complete active space self consistent field/complete active space state interaction (CASSCF/CASSI) method.
Origin-independent two-photon circular dichroism calculations in coupled cluster theory.
Friese, Daniel H; Hättig, Christof; Rizzo, Antonio
2016-05-21
We present the first origin-independent approach for the treatment of two-photon circular dichroism (TPCD) using coupled cluster methods. The approach is assessed concerning its behavior on the choice of the basis set and different coupled cluster methods. We also provide a comparison of results from CC2 with those from density functional theory using the CAM-B3LYP functional. Concerning the basis set we note that in most cases an augmented triple zeta basis or a doubly augmented double zeta basis is needed for reasonably converged results. In the comparison of different coupled cluster methods results from CCSD, CC3 and CC2 have been found to be quite similar in most cases, while CCS results differ remarkably from the results at the higher levels. However, this proof-of-principle study also shows that further benchmarking of DFT and CC2 against accurate coupled cluster reference values (e.g. CCSD or CC3) is needed. PMID:27140590
Coupled cluster expansions for the massive Schwinger model in the lattice Hamiltonian formalism
Fang, Xi-Yan; Schutte, D.; Wethkamp, V.; Wichmann, A.
2001-07-01
The coupled cluster method is used to study the lattice massive Schwinger model with staggered fermions. The vacuum energy and mass gaps are calculated. Good agreement is found between these calculations, the exact results in the continuum limit, and the results obtained by other approximation methods.
Protonation and Proton-Coupled Electron Transfer at S-Ligated [4Fe-4S] Clusters
Morris, Wesley D.; Darcy, Julia W.; Mayer, James M.
2015-01-01
Biological [Fe-S] clusters are increasingly recognized to undergo proton-coupled electron transfer (PCET), but the site of protonation, mechanism, and role for PCET remains largely unknown. Here we explore this reactivity with synthetic model clusters. Protonation of the arylthiolate-ligated [4Fe-4S] cluster [Fe4S4(SAr)4]2- (1, SAr = S-2,4-6-(iPr)3C6H2) leads to thiol dissociation, reversibly forming [Fe4S4(SAr)3L]1- (2) + ArSH (L = solvent, and/or conjugate base). Solutions of 2 + ArSH react with the nitroxyl radical TEMPO to give [Fe4S4(SAr)4]1- (1ox) and TEMPOH. This reaction involves PCET coupled to thiolate association and may proceed via the unobserved protonated cluster [Fe4S4(SAr)3(HSAr)]1-(1-H). Similar reactions with this and related clusters proceed comparably. An understanding of the PCET thermochemistry of this cluster system has been developed, encompassing three different redox levels and two protonation states. PMID:25965413
Protonation and Proton-Coupled Electron Transfer at S-Ligated [4Fe-4S] Clusters.
Saouma, Caroline T; Morris, Wesley D; Darcy, Julia W; Mayer, James M
2015-06-15
Biological [Fe-S] clusters are increasingly recognized to undergo proton-coupled electron transfer (PCET), but the site of protonation, mechanism, and role for PCET remains largely unknown. Here we explore this reactivity with synthetic model clusters. Protonation of the arylthiolate-ligated [4Fe-4S] cluster [Fe4 S4 (SAr)4 ](2-) (1, SAr=S-2,4-6-(iPr)3 C6 H2 ) leads to thiol dissociation, reversibly forming [Fe4 S4 (SAr)3 L](1-) (2) and ArSH (L=solvent, and/or conjugate base). Solutions of 2+ArSH react with the nitroxyl radical TEMPO to give [Fe4 S4 (SAr)4 ](1-) (1ox ) and TEMPOH. This reaction involves PCET coupled to thiolate association and may proceed via the unobserved protonated cluster [Fe4 S4 (SAr)3 (HSAr)](1-) (1-H). Similar reactions with this and related clusters proceed comparably. An understanding of the PCET thermochemistry of this cluster system has been developed, encompassing three different redox levels and two protonation states. PMID:25965413
Spin-Orbit Coupling Effects in AumPtn Clusters (m + n = 4).
Moreno, Norberto; Ferraro, Franklin; Flórez, Elizabeth; Hadad, C Z; Restrepo, Albeiro
2016-03-17
A study of AumPtn(m + n = 4) clusters with and without spin-orbit (SO) coupling using scalar relativistic (SR) and two component methods with the ZORA Hamiltonian was carried out. We employed the PW91 functional in conjunction with the all-electron TZ2P basis set. This paper offers a detailed analysis of the SO effects on the cluster geometries, on the LUMO-HOMO gap, on the charge distribution, and on the relative energies for each relativistic method. In general, SO coupling led to an energetic rearrangement of the species, to changes in geometries and structural preferences, to changes in the structural identity of the global minimum for the Au3Pt, AuPt3 and Pt4 cases, and to a reduction of relative energies among the clusters, an effect that appears stronger as the amount of Pt increases. PMID:26894819
Experimental observation of chimera and cluster states in a minimal globally coupled network
NASA Astrophysics Data System (ADS)
Hart, Joseph D.; Bansal, Kanika; Murphy, Thomas E.; Roy, Rajarshi
2016-09-01
A "chimera state" is a dynamical pattern that occurs in a network of coupled identical oscillators when the symmetry of the oscillator population is broken into synchronous and asynchronous parts. We report the experimental observation of chimera and cluster states in a network of four globally coupled chaotic opto-electronic oscillators. This is the minimal network that can support chimera states, and our study provides new insight into the fundamental mechanisms underlying their formation. We use a unified approach to determine the stability of all the observed partially synchronous patterns, highlighting the close relationship between chimera and cluster states as belonging to the broader phenomenon of partial synchronization. Our approach is general in terms of network size and connectivity. We also find that chimera states often appear in regions of multistability between global, cluster, and desynchronized states.
NASA Astrophysics Data System (ADS)
Ashok Kumar, Nanjundan; Kim, Sung Hun; Kim, Jong Tae; Lim, Kwon Taek; Jeong, Yeon Tae
Cluster-like network structures of single-walled carbon nanotubes (SWNTs) were synthesized by chemical grafting poly 2-hydroxyethyl methacrylate (polyHEMA) to the sidewalls of SWNTs. Acid chloride-functionalized tubes were coupled with commercially available HEMA monomer, which was in turn polymerized using a radical initiator. Fourier transform infrared spectroscopy and X-ray photoelectron spectroscopy were used to identify the surface changes on the nanocomposites. Microscopic observations of the nanotube complexes by field emission scanning electron microscopy (FE-SEM) show that the tubes were dispersed and formed cluster-like network, branched structures with less bundling, thus, strongly suggesting a firm coating of the polymer on nanotube walls. The coating was further confirmed by transmission electron microscopy. The thermal properties of the nanotube complex as studied by thermal gravimetric analysis (TGA) revealed that coating enhanced stability of the complex, when compared to that of bulk polyHEMA and pristine SWNTs. The nanotube complexes showed excellent suspension stability when dispersed in organic solvent.
Magnetization reversal of a single cobalt cluster using a RF field pulse
NASA Astrophysics Data System (ADS)
Tamion, A.; Raufast, C.; Bonet, E.; Dupuis, V.; Fournier, T.; Crozes, T.; Bernstein, E.; Wernsdorfer, W.
2010-05-01
Technological improvements require the understanding of dynamical magnetization reversal processes at the nanosecond time scales. In this paper, we present the first magnetization reversal measurements performed on a single cobalt cluster (counting only a thousand of spins), using the micro-superconducting quantum interference device (SQUID) technique by applying a constant magnetic field combined with a radio-frequency (RF) field pulse. First of all, we present the different technical steps necessary to detect the magnetic reversals at low temperature ( T=35 mK) of a well-defined nanoparticle prepared by low energy clusters beam deposition (LECBD). We previously showed that the three-dimensional (3D)-switching Stoner-Wohlfarth astroid represents the magnetic anisotropy of the nanoparticle. Then, an improved device coupled with a gold stripe line, allow us to reverse such macrospin, using a RF pulse. A qualitative understanding of the magnetization reversal by non-linear resonance has been obtained with the Landau-Lifschitz-Gilbert (LLG) equation.
Vicente, R; El Fallah, M S; Casanovas, B; Font-Bardia, M; Escuer, A
2016-06-20
One new Mn(II)2Mn(III)6 cluster exhibiting an S = 17 spin ground state and single-molecule-magnet properties has been designed linking Mn(III)3-salicylaldoximate triangles and tetracoordinated Mn(II) cations by means of end-on azido bridges. The ferromagnetic coupling has been rationalized as a function of their structural parameters. PMID:27227379
Baun, Christian
2016-01-01
Clusters usually consist of servers, workstations or personal computers as nodes. But especially for academic purposes like student projects or scientific projects, the cost for purchase and operation can be a challenge. Single board computers cannot compete with the performance or energy-efficiency of higher-value systems, but they are an option to build inexpensive cluster systems. Because of the compact design and modest energy consumption, it is possible to build clusters of single board computers in a way that they are mobile and can be easily transported by the users. This paper describes the construction of such a cluster, useful applications and the performance of the single nodes. Furthermore, the clusters' performance and energy-efficiency is analyzed by executing the High Performance Linpack benchmark with a different number of nodes and different proportion of the systems total main memory utilized. PMID:27064532
Eriksen, Janus J; Baudin, Pablo; Ettenhuber, Patrick; Kristensen, Kasper; Kjærgaard, Thomas; Jørgensen, Poul
2015-07-14
We propose a reformulation of the traditional (T) triples correction to the coupled cluster singles and doubles (CCSD) energy in terms of local Hartree-Fock (HF) orbitals such that its structural form aligns with our recently developed linear-scaling divide-expand-consolidate (DEC) coupled cluster family of local correlation methods. In a DEC-CCSD(T) calculation, a basis of local occupied and virtual HF orbitals is used to partition the correlated calculation on the full system into a number of independent atomic fragment and pair fragment calculations, each performed within a truncated set of the complete orbital space. In return, this leads to a massively parallel algorithm for the evaluation of the DEC-CCSD(T) correlation energy, which formally scales linearly with the size of the full system and has a tunable precision with respect to a conventional CCSD(T) calculation via a single energy-based input threshold. The theoretical developments are supported by proof of concept DEC-CCSD(T) calculations on a series of medium-sized molecular systems. PMID:26575735
NASA Technical Reports Server (NTRS)
Lee, Timothy J.; Dateo, Christopher E.
2005-01-01
The singles and doubles coupled-cluster method that includes a perturbational estimate of connected triple excitations, denoted CCSD(T), has been used, in conjunction with approximate integral techniques, to compute highly accurate rovibrational spectroscopic constants of cyclopropenylidene, C3H2. The approximate integral technique was proposed in 1994 by Rendell and Lee in order to avoid disk storage and input/output bottlenecks, and today it will also significantly aid in the development of algorithms for distributed memory, massively parallel computer architectures. It is shown in this study that use of approximate integrals does not impact the accuracy of CCSD(T) calculations. In addition, the most accurate spectroscopic data yet for C3H2 is presented based on a CCSD(T)/cc-pVQZ quartic force field that is modified to include the effects of core-valence electron correlation. Cyclopropenylidene is of great astronomical and astrobiological interest because it is the smallest aromatic ringed compound to be positively identified in the interstellar medium, and is thus involved in the prebiotic processing of carbon and hydrogen. The singles and doubles coupled-cluster method that includes a perturbational estimate of
NASA Astrophysics Data System (ADS)
Piecuch, Piotr; Hansen, Jared A.; Ajala, Adeayo O.
2015-10-01
The vertical excitation energies for a comprehensive test set of about 150 singlet excited states of 28 medium-sized organic molecules computed using two variants of the completely renormalised (CR) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and non-iterative triples, abbreviated as δ-CR-EOMCCSD(T), and the analogous two variants of the newer, left-eigenstate δ-CR-EOMCC(2,3) approach are benchmarked against the previously published CASPT2, CC3, and EOMCCSDT-3 results, as well as the suggested theoretical best estimate (TBE) values. The δ-CR-EOMCC approaches are also used to identify and characterise about 50 additional excited states, including several states having substantial two-electron excitation components, which have not been found in the previous work and which can be used in future benchmark studies. It is demonstrated that the non-iterative triples corrections to the EOMCCSD excitation energies defining the relatively inexpensive, single-reference, black-box δ-CR-EOMCC approaches provide significant improvements in the EOMCCSD data, while closely matching the results of the iterative and considerably more expensive CC3 and EOMCCSDT-3 calculations and their CASPT2 and TBE counterparts. It is also shown that the δ-CR-EOMCC methods, especially δ-CR-EOMCC(2,3), are capable of bringing the results of the CC3 and EOMCCSDT-3 calculations to a closer agreement with the CASPT2 and TBE data, demonstrating the utility of the cost-effective δ-CR-EOMCC methods in applications involving molecular electronic spectra. We show that there may exist a relationship between the magnitude of the triples corrections defining δ-CR-EOMCC approaches and the reduced excitation level diagnostic resulting from EOMCCSD.
Piecuch, Piotr; Hansen, Jared A.; Ajala, Adeayo O.
2015-09-15
When vertical energies are excited for a comprehensive test set of about 150 singlet excited states of 28 medium-sized organic molecules computed using two variants of the completely renormalised (CR) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and non-iterative triples, abbreviated as δ-CR-EOMCCSD(T), and the analogous two variants of the newer, left-eigenstate δ-CR-EOMCC(2,3) approach are benchmarked against the previously published CASPT2, CC3, and EOMCCSDT-3 results, as well as the suggested theoretical best estimate (TBE) values. The δ-CR-EOMCC approaches are also used to identify and characterise about 50 additional excited states, including several states having substantial two-electron excitation components, whichmore » have not been found in the previous work and which can be used in future benchmark studies. We demonstrated that the non-iterative triples corrections to the EOMCCSD excitation energies defining the relatively inexpensive, single-reference, black-box δ-CR-EOMCC approaches provide significant improvements in the EOMCCSD data, while closely matching the results of the iterative and considerably more expensive CC3 and EOMCCSDT-3 calculations and their CASPT2 and TBE counterparts. It is also shown that the δ-CR-EOMCC methods, especially δ-CR-EOMCC(2,3), are capable of bringing the results of the CC3 and EOMCCSDT-3 calculations to a closer agreement with the CASPT2 and TBE data, demonstrating the utility of the cost-effective δ-CR-EOMCC methods in applications involving molecular electronic spectra. Finally, we show that there may exist a relationship between the magnitude of the triples corrections defining δ-CR-EOMCC approaches and the reduced excitation level diagnostic resulting from EOMCCSD.« less
A view on coupled cluster perturbation theory using a bivariational Lagrangian formulation.
Kristensen, Kasper; Eriksen, Janus J; Matthews, Devin A; Olsen, Jeppe; Jørgensen, Poul
2016-02-14
We consider two distinct coupled cluster (CC) perturbation series that both expand the difference between the energies of the CCSD (CC with single and double excitations) and CCSDT (CC with single, double, and triple excitations) models in orders of the Møller-Plesset fluctuation potential. We initially introduce the E-CCSD(T-n) series, in which the CCSD amplitude equations are satisfied at the expansion point, and compare it to the recently developed CCSD(T-n) series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)], in which not only the CCSD amplitude, but also the CCSD multiplier equations are satisfied at the expansion point. The computational scaling is similar for the two series, and both are term-wise size extensive with a formal convergence towards the CCSDT target energy. However, the two series are different, and the CCSD(T-n) series is found to exhibit a more rapid convergence up through the series, which we trace back to the fact that more information at the expansion point is utilized than for the E-CCSD(T-n) series. The present analysis can be generalized to any perturbation expansion representing the difference between a parent CC model and a higher-level target CC model. In general, we demonstrate that, whenever the parent parameters depend upon the perturbation operator, a perturbation expansion of the CC energy (where only parent amplitudes are used) differs from a perturbation expansion of the CC Lagrangian (where both parent amplitudes and parent multipliers are used). For the latter case, the bivariational Lagrangian formulation becomes more than a convenient mathematical tool, since it facilitates a different and faster convergent perturbation series than the simpler energy-based expansion. PMID:26874478
Piecuch, Piotr; Hansen, Jared A.; Ajala, Adeayo O.
2015-09-15
When vertical energies are excited for a comprehensive test set of about 150 singlet excited states of 28 medium-sized organic molecules computed using two variants of the completely renormalised (CR) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and non-iterative triples, abbreviated as δ-CR-EOMCCSD(T), and the analogous two variants of the newer, left-eigenstate δ-CR-EOMCC(2,3) approach are benchmarked against the previously published CASPT2, CC3, and EOMCCSDT-3 results, as well as the suggested theoretical best estimate (TBE) values. The δ-CR-EOMCC approaches are also used to identify and characterise about 50 additional excited states, including several states having substantial two-electron excitation components, which have not been found in the previous work and which can be used in future benchmark studies. We demonstrated that the non-iterative triples corrections to the EOMCCSD excitation energies defining the relatively inexpensive, single-reference, black-box δ-CR-EOMCC approaches provide significant improvements in the EOMCCSD data, while closely matching the results of the iterative and considerably more expensive CC3 and EOMCCSDT-3 calculations and their CASPT2 and TBE counterparts. It is also shown that the δ-CR-EOMCC methods, especially δ-CR-EOMCC(2,3), are capable of bringing the results of the CC3 and EOMCCSDT-3 calculations to a closer agreement with the CASPT2 and TBE data, demonstrating the utility of the cost-effective δ-CR-EOMCC methods in applications involving molecular electronic spectra. Finally, we show that there may exist a relationship between the magnitude of the triples corrections defining δ-CR-EOMCC approaches and the reduced excitation level diagnostic resulting from EOMCCSD.
Fransson, Thomas; Coriani, Sonia; Christiansen, Ove; Norman, Patrick
2013-03-28
Near carbon K-edge X-ray absorption fine structure spectra of a series of fluorine-substituted ethenes and acetone have been studied using coupled cluster and density functional theory (DFT) polarization propagator methods, as well as the static-exchange (STEX) approach. With the complex polarization propagator (CPP) implemented in coupled cluster theory, relaxation effects following the excitation of core electrons are accounted for in terms of electron correlation, enabling a systematic convergence of these effects with respect to electron excitations in the cluster operator. Coupled cluster results have been used as benchmarks for the assessment of propagator methods in DFT as well as the state-specific static-exchange approach. Calculations on ethene and 1,1-difluoroethene illustrate the possibility of using nonrelativistic coupled cluster singles and doubles (CCSD) with additional effects of electron correlation and relativity added as scalar shifts in energetics. It has been demonstrated that CPP spectra obtained with coupled cluster singles and approximate doubles (CC2), CCSD, and DFT (with a Coulomb attenuated exchange-correlation functional) yield excellent predictions of chemical shifts for vinylfluoride, 1,1-difluoroethene, trifluoroethene, as well as good spectral features for acetone in the case of CCSD and DFT. Following this, CPP-DFT is considered to be a viable option for the calculation of X-ray absorption spectra of larger π-conjugated systems, and CC2 is deemed applicable for chemical shifts but not for studies of fine structure features. The CCSD method as well as the more approximate CC2 method are shown to yield spectral features relating to π∗-resonances in good agreement with experiment, not only for the aforementioned molecules but also for ethene, cis-1,2-difluoroethene, and tetrafluoroethene. The STEX approach is shown to underestimate π∗-peak separations due to spectral compressions, a characteristic which is inherent to this
NASA Astrophysics Data System (ADS)
Piecuch, Piotr; Włoch, Marta
2005-12-01
Completely renormalized (CR) coupled-cluster (CC) approaches, such as CR-CCSD(T), in which one corrects the standard CC singles and doubles (CCSD) energy for the effects of triply (T) and other higher-than-doubly excited clusters [K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 18 (2000)], are reformulated in terms of the left eigenstates ⟨Φ∣L of the similarity-transformed Hamiltonian of CC theory. The resulting CR-CCSD(T)L or CR-CC(2,3) and other CR-CCL methods are derived from the new biorthogonal form of the method of moments of CC equations (MMCC) in which, in analogy to the original MMCC theory, one focuses on the noniterative corrections to standard CC energies that recover the exact, full configuration-interaction energies. One of the advantages of the biorthogonal MMCC theory, which will be further analyzed and extended to excited states in a separate paper, is a rigorous size extensivity of the basic ground-state CR-CCL approximations that result from it, which was slightly violated by the original CR-CCSD(T) and CR-CCSD(TQ) approaches. This includes the CR-CCSD(T)L or CR-CC(2,3) method discussed in this paper, in which one corrects the CCSD energy by the relatively inexpensive noniterative correction due to triples. Test calculations for bond breaking in HF, F2, and H2O indicate that the noniterative CR-CCSD(T)L or CR-CC(2,3) approximation is very competitive with the standard CCSD(T) theory for nondegenerate closed-shell states, while being practically as accurate as the full CC approach with singles, doubles, and triples in the bond-breaking region. Calculations of the activation enthalpy for the thermal isomerizations of cyclopropane involving the trimethylene biradical as a transition state show that the noniterative CR-CCSD(T)L approximation is capable of providing activation enthalpies which perfectly agree with experiment.
A Comparison of Single Sample and Bootstrap Methods to Assess Mediation in Cluster Randomized Trials
ERIC Educational Resources Information Center
Pituch, Keenan A.; Stapleton, Laura M.; Kang, Joo Youn
2006-01-01
A Monte Carlo study examined the statistical performance of single sample and bootstrap methods that can be used to test and form confidence interval estimates of indirect effects in two cluster randomized experimental designs. The designs were similar in that they featured random assignment of clusters to one of two treatment conditions and…
Hsiao, Chun-Wen; Bai, Meng-Yi; Chang, Yen; Chung, Min-Fan; Lee, Ting-Yin; Wu, Cheng-Tse; Maiti, Barnali; Liao, Zi-Xian; Li, Ren-Ke; Sung, Hsing-Wen
2013-01-01
Myocardial infarction is often associated with abnormalities in electrical function due to a massive loss of functioning cardiomyocytes. This work develops a mesh, consisting of aligned composite nanofibers of polyaniline (PANI) and poly(lactic-co-glycolic acid) (PLGA), as an electrically active scaffold for coordinating the beatings of the cultured cardiomyocytes synchronously. Following doping by HCl, the electrospun fibers could be transformed into a conductive form carrying positive charges, which could then attract negatively charged adhesive proteins (i.e. fibronectin and laminin) and enhance cell adhesion. During incubation, the adhered cardiomyocytes became associated with each other and formed isolated cell clusters; the cells within each cluster elongated and aligned their morphology along the major axis of the fibrous mesh. After culture, expression of the gap-junction protein connexin 43 was clearly observed intercellularly in isolated clusters. All of the cardiomyocytes within each cluster beat synchronously, implying that the coupling between the cells was fully developed. Additionally, the beating rates among these isolated cell clusters could be synchronized via an electrical stimulation designed to imitate that generated in a native heart. Importantly, improving the impaired heart function depends on electrical coupling between the engrafted cells and the host myocardium to ensure their synchronized beating. PMID:23164424
NASA Astrophysics Data System (ADS)
Shen, Jun; Piecuch, Piotr
2012-06-01
After reviewing recent progress in the area of the development of coupled-cluster (CC) methods for quasi-degenerate electronic states that are characterized by stronger non-dynamical correlation effects, including new generations of single- and multi-reference approaches that can handle bond breaking and excited states dominated by many-electron transitions, and after discussing the key elements of the left-eigenstate completely renormalized (CR) CC and equation-of-motion (EOM) CC methods, and the underlying biorthogonal method of moments of CC (MMCC) equations [P. Piecuch, M. Włoch, J. Chem. Phys. 123 (2005) 224105; P. Piecuch, M. Włoch, J.R. Gour, A. Kinal, Chem. Phys. Lett. 418 (2006) 467; M. Włoch, M.D. Lodriguito, P. Piecuch, J.R. Gour, Mol. Phys. 104 (2006) 2149], it is argued that it is beneficial to merge the CR-CC/EOMCC and active-space CC/EOMCC [P. Piecuch, Mol. Phys. 108 (2010) 2987, and references therein] theories into a single formalism. In order to accomplish this goal, the biorthogonal MMCC theory, which provides compact many-body expansions for the differences between the full configuration interaction and CC or, in the case of excited states, EOMCC energies, obtained using conventional truncation schemes in the cluster operator T and excitation operator Rμ, is generalized, so that one can correct the CC/EOMCC energies obtained with arbitrary truncations in T and Rμ for the selected many-electron correlation effects of interest. The resulting moment expansions, defining the new, Flexible MMCC (Flex-MMCC) formalism, and the ensuing CC(P; Q) hierarchy, proposed in the present work, enable one to correct energies obtained in the active-space CC and EOMCC calculations, in which one selects higher many-body components of T and Rμ via active orbitals and which recover much of the relevant non-dynamical and some dynamical electron correlation effects in applications involving potential energy surfaces (PESs) along bond breaking coordinates, for the
NASA Astrophysics Data System (ADS)
Hubert, Mickaël; Olsen, Jeppe; Loras, Jessica; Fleig, Timo
2013-11-01
We present a new implementation of general excitation rank coupled cluster theory for electronically excited states based on the single-reference multi-reference formalism. The method may include active-space selected and/or general higher excitations by means of the general active space concept. It may employ molecular integrals over the four-component Lévy-Leblond Hamiltonian or the relativistic spin-orbit-free four-component Hamiltonian of Dyall. In an initial application to ground- and excited states of the scandium monohydride molecule we report spectroscopic constants using basis sets of up to quadruple-zeta quality and up to full iterative triple excitations in the cluster operators. Effects due to spin-orbit interaction are evaluated using two-component multi-reference configuration interaction for assessing the accuracy of the coupled cluster results.
Hubert, Mickaël; Loras, Jessica; Fleig, Timo; Olsen, Jeppe
2013-11-21
We present a new implementation of general excitation rank coupled cluster theory for electronically excited states based on the single-reference multi-reference formalism. The method may include active-space selected and/or general higher excitations by means of the general active space concept. It may employ molecular integrals over the four-component Lévy-Leblond Hamiltonian or the relativistic spin-orbit-free four-component Hamiltonian of Dyall. In an initial application to ground- and excited states of the scandium monohydride molecule we report spectroscopic constants using basis sets of up to quadruple-zeta quality and up to full iterative triple excitations in the cluster operators. Effects due to spin-orbit interaction are evaluated using two-component multi-reference configuration interaction for assessing the accuracy of the coupled cluster results.
Tracking single particles motion in shaken wet powder clusters
NASA Astrophysics Data System (ADS)
Wenzl, Jennifer; Auernhammer, Guenter K.; Gilson, Laurent
In many industrial branches wet granulate powders, where the particles are connected via an additional binding liquid, are widely used. Amply investigated were model systems, where the binding liquid is homogeneously distributed, i.e. building a connecting capillary network. In contrast wet granulate model systems with an inhomogeneous liquid distribution have been rarely in focus of research. In this work a model system for wet powders was developed, which is suitable for 3D imaging with confocal microscopy. Fluorescent silica particles were immersed in a mixture of two immiscible liquids, one continuous and one binding liquid. In detail a wet powder cluster, where the binding liquid formed droplets was studied in 3D. During applying a mechanical load the motion of the powder particles and the binding liquid droplets was followed. Deformation of the binding liquid droplets led to an increase of its surface area and energy. When the droplet relaxed to an energetically more favored shape upon further cluster deformation, the sudden release of the stored surface energy led to complex powder particle and droplet motions. The model system illustrated the complex dynamics upon shaking, and showed that the binding liquid dominated the cluster dynamics on a local scale.
A comparative study of single reference correlation methods of the coupled-pair type
NASA Astrophysics Data System (ADS)
Wennmohs, Frank; Neese, Frank
2008-01-01
Several variants of coupled electron pair type approximations are compared with respect to their accuracy in the prediction of bond distances, harmonic vibrational frequencies and anharmonic corrections for a range of closed-shell diatomic molecules. In the first part of the paper the coupled-electron pair (CEPA) methods (CEPA/1,2,3) are discussed. Extensions of these methods allow the derivation of the correlation energy from the stationarization of a correlation energy functional (CPF/1,2,3 methods). All methods are formulated as diagonally dressed configuration-interaction with single- and double-excitations (CISD) eigenvalue problems. Averaging the diagonal shifts of the CPF methods in various ways lead to the ACPF and AQCC methods. Several small modifications of the shifts for the single excitations are proposed that enhance the stability of the methods (NCPF/1,2,3, NCEPA/1,2,3, NACPF). The reduced shifts are justified by linear response arguments. The implementation of the methods for a closed-shell ground state is described. In the application part, we first tested the size-consistency, exactness for two-electron systems and unitary invariance of the methods. Extensive numerical studies with polarized quadruple- ζ basis sets are employed to test the accuracy of the coupled pair approaches relative to the more elaborate quadratic CI (QCISD) and coupled-cluster (CCSD and CCSD(T)) approaches. Not surprisingly, the CCSD(T) method is the most accurate approach on average. However, the proposed NCPF/1 variant led to even smaller average errors for bond distances (˜0.2 pm relative to ˜0.3 pm for CCSD(T)) while predicting still accurate harmonic frequencies (av. Error ˜25 cm -1 for NCPF/1, ˜8 cm -1 for CCSD(T) and ˜45 cm -1 for CCSD). All coupled pair methods are more accurate than present day DFT approaches (BP86, B3LYP). The exception is the recently proposed double-hybrid B2PLYP functional that approaches the coupled pair performance. Some more difficult