Communication: Multipole approximations of distant pair energies in local correlation methods with pair natural orbitals

Werner, Hans‐Joachim

doi:10.1063/1.4968595

Cited by 43 publications

(77 citation statements)

References 22 publications

(23 reference statements)

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“…It should be pointed out that, when the distance threshold is increased from 5.5 to 6.0 Å, the CIM‐MP2 results are further improved. This result shows that correlation energies between distant electron pairs (beyond 5.5 Å) may be included if very accurate binding energies are needed in some cases.…”

Section: Methodsmentioning

confidence: 92%

Fully optimized implementation of the cluster‐in‐molecule local correlation approach for electron correlation calculations of large systems

2018

J Comput Chem

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A fully optimized implementation of the cluster-in-molecule (CIM) local correlation method for faster and more accurate electron correlation calculations of large systems is reported. The speedup comes from the new procedure of constructing virtual localized molecular orbitals of clusters. In the new procedure, Boughton-Pulay projection method is employed instead of a much more expensive Boys localization procedure. In addition, basis set superposition error correction for binding energy calculations and parallelized electron correlation calculations of clusters are now implemented. Benchmark calculations and illustrative applications at the Møller-Plesset perturbation theory, coupled cluster singles and doubles (CCSD), and CCSD with perturbative triples correction levels show that this newly optimized CIM approach is a reliable theoretical tool for electron correlation calculations of various large chemical systems.

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Section: Methodsmentioning

confidence: 92%

Fully optimized implementation of the cluster‐in‐molecule local correlation approach for electron correlation calculations of large systems

2018

J Comput Chem

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“…Finding the appropriate transformation and amplitude optimization method is however challenging. Another possibility, exploited by Werner in his recent work on dPNOs 38 , is to define a reduced virtual space specifically tailored for dispersion on each monomer. Work is currently underway in our laboratory to find even simpler alternatives yielding dispersion-optimized virtuals.…”

Section: Discussionmentioning

confidence: 99%

“…In PNO-type methods, such a basis is extracted from approximate MP2 amplitudes for each local occupied orbital pair, and we could envision a similar strategy. Recently, Werner specifically investigated distant pairs 38 and found that 3 to 4 distant PNOs (dPNOs) were associated with each occupied orbital. As we mentioned in Section II B, our two-step SVD decomposition applied to a single orbital pair yields PNOs.…”

Section: Properties Of the Virtual Spacementioning

confidence: 99%

“…To our knowledge, a recent paper 38 on improved PNO methods based on iterating the distant CC amplitudes in a reduced virtual correlation space is the first to actually adopt such an approach in practice, and no detailed investigation of a compressed representation for dispersion or long-range electron correlation yet exists. This paper aims to fill this gap, we will compare our numerical results against Pulay's prediction, and against the improved PNO method for long-range correlations 38 in Section IV C.…”

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confidence: 99%

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Compressed representation of dispersion interactions and long-range electronic correlations

Gonthier

Head‐Gordon

2017

The Journal of Chemical Physics

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The description of electron correlation in quantum chemistry often relies on multiindex quantities. Here, we examine a compressed representation of the long-range part of electron correlation, that is associated with dispersion interactions. For this purpose, we perform CCSD computations on localized orbitals, then extract the portion of CCSD amplitudes corresponding to dispersion energies. Using singular value decomposition, we uncover that a very compressed representation of the amplitudes is possible in terms of occupied-virtual geminal pairs located on each monomer. These geminals provide an accurate description of dispersion energies at medium and long distances. The corresponding virtual orbitals are examined by further singular value decompositions of the geminals. We connect each component of the virtual space to the multipole expansion of dispersion energies. Our results are robust with respect to basis set change and hold for systems as large as the benzene-methane dimer.This compressed representation of dispersion energies paves the way to practical and accurate approximations for dispersion, for example in local correlation methods. a) j

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“…Perhaps the most popular localization technique these days is the one based on pair natural orbitals (PNOs) . The idea itself goes back to the seventies and it was revived again in 2009 by Neese and coworkers and has since been taken up by the group of Werner and a number of other groups whose activities will concern us later regarding excited states. The local pair natural orbital (LPNO) formulation again starts off with LMOs for the occupied space, while the virtual space is spanned by PNOs which are obtained from some estimate of the pair density (

D_{ab}^{ij}

), here defined as

D_{ab}^{ij} = {\overset{false˜}{T}}_{ac}^{ij} T_{bc}^{ij} + {\overset{false˜}{T}}_{ca}^{ij} T_{cb}^{ij}, {\overset{false˜}{T}}_{ab}^{ij} = \frac{1}{1 + δ_{ij}} ((), 4 T_{ab}^{ij} - 2 T_{ba}^{ij}) .

…”

Section: Algorithmic Approximationsmentioning

confidence: 99%

Single‐reference coupled cluster methods for computing excitation energies in large molecules: The efficiency and accuracy of approximations

Izsák

2019

WIREs Comput Mol Sci

110

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While methodological developments in the last decade made it possible to compute coupled cluster (CC) energies including excitations up to a perturbative triples correction for molecules containing several hundred atoms, a similar breakthrough has not yet been reported for excited state computations. Accurate CC methods for excited states are still expensive, although some promising candidates for an efficient and accurate excited state CC method have emerged recently. This review examines the various approximation schemes with particular emphasis on their performance for excitation energies and summarizes the best state-of-the-art results which may pave the way for a robust excited state method applicable to molecules of hundreds of atoms.Among these, special attention will be given to exploiting the techniques of similarity transformation, perturbative approximations as well as integral decomposition, local and embedding techniques within the equation of motion CC framework. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Structure and Mechanism > Molecular Structures K E Y W O R D S accuracy, coupled cluster, efficiency, excited states, single reference | INTRODUCTIONIn their lucid review written a few years ago, 1 Sneskov and Christiansen discussed the various coupled cluster (CC) methods available for excited states. Using the systematic machinery of response theory, they described a hierarchy of methods, established a link between response theory and equation of motion (EOM) methods, and finished by discussing a number of approaches that might be used to reduce the computational cost. The present review aims at providing an overview of efficient methods available primarily for large molecules, and hence the emphasis will be laid more upon recent methodological advances which reduce the cost and on the extent this affects the accuracy of these methods. For ground state calculations, choosing a reference method for benchmarks is quite easy, since the CC singles doubles and perturbative triples, or CCSD(T), ansatz 2 is not only widely regarded as the gold standard of quantum chemistry, but it has also recently become possible to compute CCSD(T) energies for molecules containing several hundred atoms. 3 For excited states, progress has been

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Communication: Multipole approximations of distant pair energies in local correlation methods with pair natural orbitals

Cited by 43 publications

References 22 publications

Fully optimized implementation of the cluster‐in‐molecule local correlation approach for electron correlation calculations of large systems

Fully optimized implementation of the cluster‐in‐molecule local correlation approach for electron correlation calculations of large systems

Compressed representation of dispersion interactions and long-range electronic correlations

Single‐reference coupled cluster methods for computing excitation energies in large molecules: The efficiency and accuracy of approximations

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