The calculation of higher-order energies in the many-body perturbation theory series

Knowles, Peter J.; Somasundram, K.; Handy, Nicholas C.; Hirao, Kimihiko

doi:10.1016/0009-2614(85)85002-8

Cited by 157 publications

(45 citation statements)

References 10 publications

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“…Arbitrary-order perturbation theory (i.e. MBPT-n) has been demonstrated by Knowles and Handy [55,56]. Coupled cluster methods with arbitrary levels of excitation have been implemented by Hirata [57], Kàllay [58], and Olsen [59].…”

Section: Background: Advanced Approaches To Software Development For mentioning

confidence: 99%

Automatic code generation for many-body electronic structure methods: the tensor contraction engine‡‡

et al. 2006

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As both electronic structure methods and the computers on which they are run become increasingly complex, the task of producing robust, reliable, high-performance implementations of methods at a rapid pace becomes increasingly daunting. In this paper we present an overview of the Tensor Contraction Engine (TCE), a unique effort to address issues of both productivity and performance through automatic code generation. The TCE is designed to take equations for many-body methods in a convenient high-level form and acts like an optimizing compiler, producing an implementation tuned to the target computer system and even to the specific chemical problem of interest. We provide examples to illustrate the TCE approach, including the ability to target different parallel programming models, and the effects of particular optimizations. * This paper is dedicated to Prof. Rodney J. Bartlett on the occasion of his 60 th birthday.

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Section: Background: Advanced Approaches To Software Development For mentioning

confidence: 99%

Automatic code generation for many-body electronic structure methods: the tensor contraction engine‡‡

et al. 2006

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“…For this reason, many approaches that guarantee second-order convergence have been developed for MC-SCF [10,[107][108][109][110][111][112][113][114][115][116] and DMRG [117][118][119] calculations. While the Lagrangian formulation (equation (6)) is not correct to second order in the orbitals, it has been recently used for a quadratic convergence OO-CC implementation [84].…”

Section: Summary and Discussionmentioning

confidence: 99%

Orbital optimisation in the perfect pairing hierarchy: applications to full-valence calculations on linear polyacenes

2017

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We describe the implementation of orbital optimization for the models in the perfect pairing hierarchy [Lehtola et al, J. Chem. Phys. 145, 134110 (2016)]. Orbital optimization, which is generally necessary to obtain reliable results, is pursued at perfect pairing (PP) and perfect quadruples (PQ) levels of theory for applications on linear polyacenes, which are believed to exhibit strong correlation in the π space. While local minima and σ-π symmetry breaking solutions were found for PP orbitals, no such problems were encountered for PQ orbitals. The PQ orbitals are used for single-point calculations at PP, PQ and perfect hextuples (PH) levels of theory, both only in the π subspace, as well as in the full σπ valence space. It is numerically demonstrated that the inclusion of single excitations is necessary also when optimized orbitals are used. PH is found to yield good agreement with previously published density matrix renormalization group (DMRG) data in the π space, capturing over 95% of the correlation energy. Full-valence calculations made possible by our novel, efficient code reveal that strong correlations are weaker when larger bases or active spaces are employed than in previous calculations. The largest full-valence PH calculations presented correspond to a (192e,192o) problem.

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“…Investigations into the convergence of the Møller-Plesset perturbation series [8] for the energy of a molecule have also been reported [9]. The Møller-Plesset perturbation series is investigated because of its wide use for the inclusion of electron correlation effects into energy calculations and the significant percentage of the correlation energy that can be achieved.…”

Section: Introductionmentioning

confidence: 99%

Converged Hartree‐Fock and electron correlation calculations using systematically constructed basis sets of primitive Gaussian type functions of s‐symmetry

Shalabi

1996

Elect J Theoret Chem

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SUMMARYThe convergence of the matrix Hartree-Fock energies of Li + , H − and LiH prototype systems and electron correlation energies of LiH are studied when a systematic procedure for the construction of even-tempered basis sets of primitive Gaussian type functions of s-symmetry is employed. It is shown that an accuracy approaching the sub-µ Hartree level can be achieved for the total energies of Li + , H − and LiH within the Hartree-Fock approximation. While an accuracy approaching the sub-µ Hartree level can be achieved for the total energy of LiH within the Møller-Plesset perturbation level, an accuracy approaching the µ Hartree level can be achieved within the configuration interaction level. The Hartree-Fock energies of LiH approach the saturation faster than do the electron correlation energies. The convergence of Møller-Plesset perturbation series was basis set size dependent, but the convergence rate and the related Pople approximation were basis set size independent.

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The calculation of higher-order energies in the many-body perturbation theory series

Cited by 157 publications

References 10 publications

Automatic code generation for many-body electronic structure methods: the tensor contraction engine‡‡

Automatic code generation for many-body electronic structure methods: the tensor contraction engine‡‡

Orbital optimisation in the perfect pairing hierarchy: applications to full-valence calculations on linear polyacenes

Converged Hartree‐Fock and electron correlation calculations using systematically constructed basis sets of primitive Gaussian type functions of s‐symmetry

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