[Show abstract][Hide abstract] ABSTRACT: 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.
The Journal of Chemical Physics 07/2015; 143(4):041101. DOI:10.1063/1.4927247 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
Journal of Chemical Theory and Computation 05/2015; 11(7):150527125244004. DOI:10.1021/acs.jctc.5b00086 · 5.50 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The DIIS (direct inversion of the iterative subspace) convergence acceleration algorithm is used in most electronic structure programs to solve the nonlinear coupled cluster amplitude equations. When DIIS is used the storage of previous trial vectors may become a bottleneck and discarding trial vectors may lead to a degradation of the convergence or even divergence. We discuss an alternative way of storing information from trial vectors where only the last 3 trial vectors are needed to maintain the convergence of the full set of previous trial vectors and which only requires minor modifications of an existing DIIS code.
Journal of Chemical Theory and Computation 04/2015; 11(4):150403071611007. DOI:10.1021/ct501114q · 5.50 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The time-dependent Schrödinger equation for a time-periodic perturbation is recasted into a Hermitian eigenvalue equation, where the quasi-energy is an eigenvalue and the time-periodic regular wave function an eigenstate. From this Hermitian eigenvalue equation, a rigorous and transparent formulation of response function theory is developed where (i) molecular properties are defined as derivatives of the quasi-energy with respect to perturbation strengths, (ii) the quasi-energy can be determined from the time-periodic regular wave function using a variational principle or via projection, and (iii) the parametrization of the unperturbed state can differ from the parametrization of the time evolution of this state. This development brings the definition of molecular properties and their determination on par for static and time-periodic perturbations and removes inaccuracies and inconsistencies of previous response function theory formulations. The development where the parametrization of the unperturbed state and its time evolution may differ also extends the range of the wave function models for which response functions can be determined. The simplicity and universality of the presented formulation is illustrated by applying it to the configuration interaction (CI) and the coupled cluster (CC) wave function models and by introducing a new model-the coupled cluster configuration interaction (CC-CI) model-where a coupled cluster exponential parametrization is used for the unperturbed state and a linear parametrization for its time evolution. For static perturbations, the CC-CI response functions are shown to be the analytical analogues of the static molecular properties obtained from finite field equation-of-motion coupled cluster (EOMCC) energy calculations. The structural similarities and differences between the CI, CC, and CC-CI response functions are also discussed with emphasis on linear versus non-linear parametrizations and the size-extensivity of the obtained molecular properties.
The Journal of Chemical Physics 03/2015; 142(11):114109. DOI:10.1063/1.4913364 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We propose the Same Number Of Optimized Parameters (SNOOP) scheme as an alternative to the counterpoise method for treating basis set superposition errors in calculations of intermolecular interaction
energies. The key point of the SNOOP scheme is to enforce that the number of optimized wave function parameters for the noninteracting system is the same as for the interacting system. This ensures a delicate balance between the quality of the monomer and dimer finite basis set calculations. We compare the SNOOP scheme to the uncorrected and counterpoise schemes theoretically as well as numerically. Numerical results for second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster with single, double, and approximate triple excitations (CCSD(T)) show that the SNOOP scheme in general outperforms the uncorrected and counterpoise approaches. Furthermore, we show that SNOOP interaction
energies calculated using a given basis set are of similar quality as those determined by basis set extrapolation of counterpoise-corrected results obtained at a similar computational cost.
The Journal of Chemical Physics 03/2015; 142(11):114116. DOI:10.1063/1.4915141 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Recently, we proposed a novel Lagrangian-based perturbation series-the CCSD(T-n) series-which systematically corrects the coupled cluster singles and doubles (CCSD) energy in orders of the Møller-Plesset fluctuation potential for effects due to triple excitations. In the present study, we report numerical results for the CCSD(T-n) series up through fourth order which show the predicted convergence trend throughout the series towards the energy of its target, the coupled cluster singles, doubles, and triples (CCSDT) model. Since effects due to the relaxation of the CCSD singles and doubles amplitudes enter the CCSD(T-n) series at fourth order (the CCSD(T-4) model), we are able to separate these effects from the total energy correction and thereby emphasize their crucial importance. Furthermore, we illustrate how the ΛCCSD[T]/(T) and CCSD[T]/(T) models, which in slightly different manners augment the CCSD energy by the [T] and (T) corrections rationalized from many-body perturbation theory, may be viewed as approximations to the second-order CCSD(T-2) model. From numerical comparisons with the CCSD(T-n) models, we show that the extraordinary performance of the ΛCCSD[T]/(T) and CCSD[T]/(T) models relies on fortuitous, yet rather consistent, cancellations of errors. As a side product of our investigations, we are led to reconsider the asymmetric ΛCCSD[T] model due to both its rigorous theoretical foundation and its performance, which is shown to be similar to that of the CCSD(T) model for systems at equilibrium geometry and superior to it for distorted systems. In both the calculations at equilibrium and distorted geometries, however, the ΛCCSD[T] and CCSD(T) models are shown to be outperformed by the fourth-order CCSD(T-4) model.
The Journal of Chemical Physics 01/2015; 142(1):014102. DOI:10.1063/1.4904754 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Second quantization formalism is introduced for an efficient description of molecular electronic systems in the nonrelativistic limit and an explicit description of electron spin. Spin orbitals are functions of three continuous spatial coordinates and one discrete spin coordinate. Quantum-mechanical operators may be classified according to how they affect the orbital and spin parts of wave functions. The operators are spin-free or spinless operator, pure spin operator and mixed operator. The author adopts the theory of spin tensor operators for angular momentum in quantum mechanics and develops a useful set of tools for the construction and classification of states and operators with definite spin symmetry properties. Singlet excitation operators play an important role in the second-quantization treatment of molecular electronic structure. This chapter shows how a basis of spin eigenfunctions can set up by taking linear combinations of Slater determinants.
[Show abstract][Hide abstract] ABSTRACT: 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 Moller-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. (C) 2014 AIP Publishing LLC.
The Journal of Chemical Physics 05/2014; 140(17):174114. DOI:10.1063/1.4873138 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree-Fock, Kohn-Sham, multiconfigurational self-consistent-field, Møller-Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.
[Show abstract][Hide abstract] ABSTRACT: Using the coupled cluster Lagrangian technique, we have determined perturbative corrections to the coupled cluster singles and doubles (CCSD) energy that converge towards the coupled cluster singles, doubles, and triples (CCSDT) and coupled cluster singles, doubles, triples, and quadruples (CCSDTQ) energies, considering the CCSD state as the unperturbed reference state and the fluctuation potential as the perturbation. Since the Lagrangian technique is utilized, the energy corrections satisfy Wigner's 2n + 1 rule for the cluster amplitudes and the 2n + 2 rule for the Lagrange multipliers. The energy corrections define the CCSD perturbation series, CCSD(T-n) and CCSD(TQ-n), which are term-wise size extensive to any order in the perturbation. A detailed comparison of the CCSD(TQ-n) series and the CC(2)PT(n) series of Hirata et al. [J. Chem. Phys. 114, 3919 (2001)] has been performed, revealing some deficiencies of the latter related to the target energy of the series and its lack of size extensivity.
The Journal of Chemical Physics 02/2014; 140(6):064108. DOI:10.1063/1.4862501 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A common perception about molecular systems with a nonlocal electronic structure (as manifested by a nonlocal Hartree–Fock (HF) density matrix), such as conjugated π-systems, is that they can only be described in terms of nonlocal molecular orbitals. This view is mostly founded on chemical intuition, and further, this view is strengthened by traditional approaches for obtaining local occupied and virtual orbital spaces, such as the occupied Pipek–Mezey orbitals, and projected atomic orbitals. In this article, we discuss the limitations for localizability of HF orbitals in terms of restrictions posed by the delocalized character of the underlying density matrix for the molecular system and by the orthogonality constraint on the molecular orbitals. We show that the locality of the orbitals, in terms of nonvanishing charge distributions of orbitals centered far apart, is much more strongly affected by the orthogonality constraint than by the physical requirement that the occupied orbitals must represent the electron density. Thus, the freedom of carrying out unitary transformations among the orbitals provides the flexibility to obtain highly local occupied and virtual molecular orbitals, even for molecular systems with a nonlocal density matrix, provided that a proper localization function is used. As an additional consideration, we clear up the common misconception that projected atomic orbitals in general are more local than localized orthogonal virtual orbitals.
Non-Linear Optical Properties of Matter: From molecules to condensed phases, Edited by Manthos G. Papadopoulos and Andrzej J. Sadlej and Jerzy Leszczynski, 10/2013: pages 51-99; Springer., ISBN: 1-4020-4849-1
[Show abstract][Hide abstract] ABSTRACT: The shielding and indirect spin-spin coupling tensors are calculated for HCN, HNC, CH3CN, and CH3NC, using large atomic basis sets and multiconfiguration wavefunctions that contain the most important correlation effects. The isotropic and anisotropic components of the tensors are compared with experimental data. Deviations between the calculated and experimental results appear to be largely due to vibrational and solvent effects.
Journal of Magnetic Resonance Series A 06/2013; DOI:10.1006/jmra.1995.1128
[Show abstract][Hide abstract] ABSTRACT: For large molecular systems conventional implementations of second order Møller–Plesset (MP2) theory encounter a scaling wall, both memory- and time-wise. We describe how this scaling wall can be removed. We present a massively parallel algorithm for calculating MP2 energies and densities using the divide–expand–consolidate scheme where a calculation on a large system is divided into many small fragment calculations employing local orbital spaces. The resulting algorithm is linear-scaling with system size, exhibits near perfect parallel scalability, removes memory bottlenecks and does not involve any I/O. The algorithm employs three levels of parallelisation combined via a dynamic job distribution scheme. Results on two molecular systems containing 528 and 1056 atoms (4278 and 8556 basis functions) using 47,120 and 94,240 cores are presented. The results demonstrate the scalability of the algorithm both with respect to the number of cores and with respect to system size. The presented algorithm is thus highly suited for large super computer architectures and allows MP2 calculations on large molecular systems to be carried out within a few hours – for example, the correlated calculation on the molecular system containing 1056 atoms took 2.37 hours using 94240 cores.
[Show abstract][Hide abstract] ABSTRACT: Divide-Expand-Consolidate (DEC) is a local correlation method where the inherent locality of the electron correlation problem is used to express the correlated calculation on a large molecular system in terms of small independent fragment calculations employing small subsets of local HF orbitals. A crucial feature of the DEC scheme is that the sizes of the local orbital spaces are determined in a black box manner during the calculation. In this way it is ensured that the correlation energy has been determined to a predefined precision compared to a conventional calculation. In the present work we apply the DEC scheme to calculate the correlation energy as well as the electron density matrix for the insulin molecule using second order Møller-Plesset (MP2) theory. This is the first DEC calculation on a molecular system which is too large to be treated using a conventional MP2 implementation. The fragmentation errors for the insulin DEC calculation are carefully analyzed using internal consistency checks. It is demonstrated that size-intensive properties are determined to the same precision for small and large molecules. For example, the percentage of correlation energy recovered and the error per electron in the correlated density matrix depend only on the predefined precision and not on the molecular size.
[Show abstract][Hide abstract] ABSTRACT: We demonstrate that the divide-expand-consolidate (DEC) scheme – which has previously been used to determine the second-order Møller–Plesset (MP2) correlation energy – can be applied to evaluate the MP2 molecular gradient in a linear-scaling and embarrassingly parallel manner using a set of local Hartree–Fock orbitals. All manipulations of four-index quantities (describing electron correlation effects) are carried out using small local orbital fragment spaces, whereas two-index quantities are treated for the full molecular system. The sizes of the orbital fragment spaces are determined in a black-box manner to ensure that the error in the DEC-MP2 correlation energy compared to a standard MP2 calculation is proportional to a single input threshold denoted the fragment optimization threshold (FOT). The FOT also implicitly controls the error in the DEC-MP2 molecular gradient as substantiated by a theoretical analysis and numerical results. The development of the DEC-MP2 molecular gradient is the initial step towards calculating higher order energy derivatives for large molecular systems using the DEC framework, both at the MP2 level of theory and for more accurate coupled-cluster methods.
The Journal of Chemical Physics 09/2012; 137(11). DOI:10.1063/1.4752432 · 2.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The trust region method has been applied to the minimization of localization functions, and it is shown that both local occupied and local virtual Hartree–Fock (HF) orbitals can be obtained. Because step sizes are size extensive in the trust region method, large steps may be required when the method is applied to large molecular systems. For an exponential parametrization of the localization function only small steps are allowed, and the standard trust radius update therefore has been replaced by a scheme where the direction of the step is determined using a conservative estimate of the trust radius and the length of the step is determined from a line search along the obtained direction. Numerical results for large molecular systems have shown that large steps can then safely be taken, and a robust and nearly monotonic convergence is obtained.
Journal of Chemical Theory and Computation 08/2012; 8(9):3137–3146. DOI:10.1021/ct300473g · 5.50 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Developments in computational molecular electronic structure theory are discussed, emphasizing on molecular response theory based on construction of a many-electron wave function. To establish a variation principle for the quasi-energy in the intermediate normalization, the quasi-energy is calculated subject to the constraint that the intermediately normalized state satisfies the projected Schrödinger equation. The equations of motion for the response functions is used to obtain relations between transition-matrix elements. The studies have also found that eigenvalues are not encountered for electronic systems dominated by a single determinant and may always be removed by extending the excitation manifold. In the formulation by Olsen and Jørgensen, response functions are obtained by applying the Ehrenfest theorem to determine the time evolution of an expectation value for the Hartree-Fock and multi-configurational self-consistent field (MCSCF) states.
Chemical Reviews 01/2012; 112(1):543-631. DOI:10.1021/cr2002239 · 46.57 Impact Factor