Virtual Orbital Many-Body Expansions: A Possible Route towards the Full Configuration Interaction Limit

Eriksen, Janus J.; Lipparini, Filippo; Gauß, Jürgen

doi:10.1021/acs.jpclett.7b02075

Cited by 83 publications

(109 citation statements)

References 62 publications

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“…Those determinants {|Φ µ } that are doubly excited from |Φ ν ∈ P (k) are never accessed if 86 However, those determinants of high energies may become unimportant even though they satisfy condition (63). Therefore, the variational space determined by the integral-driven selection (63) is usually larger than that determined by the coefficientdriven selection (62), particularly when large basis sets are used (NB: this problem can partly be resolved by introducing an approximate denominator to condition (63), see the Supporting Information of Ref. 87 ).…”

Section: Selection Of Ocfgs and Csfsmentioning

confidence: 99%

“…5). After this integral-driven screening, the individual CSFs {|Iµ } of the selected oCFGs {I} are further selected using their (approximate) first-order coefficients (64) (NB: the approximation arises from the restriction (65) on the summation over J in the numerator), just like condition (62). Moreover, as indicated by the relation ε k = 1 2 ε k−1 , the integral-threshold ε k is to be reduced by a factor of two with each iteration, meaning that the external oCFG space Q is accessed incrementally (i.e., Q(ε k )).…”

Section: Selection Of Ocfgs and Csfsmentioning

confidence: 99%

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Iterative Configuration Interaction with Selection

Zhang

Liu

Hoffmann

2020

J. Chem. Theory Comput.

112

160

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Even when starting with a very poor initial guess, the iterative configuration interaction (iCI) approach [J. Chem. Theory Comput. 12, 1169] for strongly correlated electrons can converge from above to full CI (FCI) very quickly by constructing and diagonalizing a very small Hamiltonian matrix at each macro/micro-iteration. However, as a direct solver of the FCI problem, iCI scales exponentially with respect to the numbers of electrons and orbitals. The problem can be mitigated by observing that a vast number of configurations have little weights in the wave function and hence do not contribute discernibly to the correlation energy. The real questions are then (a) how to identify those important configurations as early as possible in the calculation and (b) how to account for the residual contributions of those unimportant configurations. It 1 arXiv:1911.12506v2 [physics.chem-ph] 6 Jan 2020is generally true that if a high-quality yet compact variational space can be determined for describing the static correlation, a low-order treatment of the residual dynamic correlation would then be sufficient. While this is common to all selected CI schemes, the 'iCI with selection' scheme presented here has the following distinctive features:(1) Full spin symmetry is always maintained by taking configuration state functions (CSF) as the many-electron basis. (2) Although the selection is performed on individual CSFs, it is orbital configurations (oCFG) that are used as the organizing units. (3) Given a coefficient pruning-threshold C min (which determines the size of the variational space for static correlation), the selection of important oCFGs/CSFs is performed iteratively until convergence. (4) At each iteration for the growth of the wave function, the first-order interacting space is decomposed into disjoint subspaces, so as to reduce memory requirement on one hand and facilitate parallelization on the other. (5) Upper bounds (which involve only two-electron integrals) for the interactions between doubly connected oCFG pairs are used to screen each first-order interacting subspace before the first-order coefficients of individual CSFs are evaluated. (6) Upon convergence of the static correlation for a given C min , dynamic correlation is estimated by using the state-specific Epstein-Nesbet second-order perturbation theory (PT2). The efficacy of the iCIPT2 scheme is demonstrated numerically by benchmark examples, including C 2 , O 2 , Cr 2 and C 6 H 6 .

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Section: Selection Of Ocfgs and Csfsmentioning

confidence: 99%

Section: Selection Of Ocfgs and Csfsmentioning

confidence: 99%

Iterative Configuration Interaction with Selection

Zhang

Liu

Hoffmann

2020

J. Chem. Theory Comput.

112

160

View full text Add to dashboard Cite

show abstract

“…3 as no changes with respect to the standard formulation of MBE-FCI are introduced whenever the reference space coincides with the HF determinant. 23,24 By virtue of Eq. 3, one is hence left with two distinct choices for the expansion reference:…”

Section: Theorymentioning

confidence: 99%

Many-Body Expanded Full Configuration Interaction. II. Strongly Correlated Regime

Eriksen

Gauß

2019

J. Chem. Theory Comput.

Self Cite

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In this second part of our series on the recently proposed many-body expanded full configuration interaction (MBE-FCI) method, we introduce the concept of multideterminantal expansion references. Through theoretical arguments and numerical validations, the use of this class of starting points is shown to result in a focussed compression of the MBE decomposition of the FCI energy, thus allowing chemical problems dominated by strong correlation to be addressed by the method. The general applicability and performance enhancements of MBE-FCI are verified for standard stress tests such as the bond dissociations in H 2 O, N 2 , C 2 , and a linear H 10 chain. Furthermore, the benefits of employing a multideterminantal expansion reference in accelerating calculations of high accuracy are discussed, with an emphasis on calculations in extended basis sets. As an illustration of this latter quality of the MBE-FCI method, results for H 2 O and C 2 in basis sets ranging from double-to pentuple-ζ quality are presented, demonstrating near-ideal parallel scaling on up to almost 25000 processing units.

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“…[56][57][58] In addition, several incremental schemes that do not yield a wave function have also been recently proposed for the estimation of FCI energies. 59,60 In contrast to both the CAS approach, where the smallness of the feasible active space poses significant limitations, and to the RAS and GAS approaches, which allow for slightly larger active spaces at the cost of having to specify the structure of the wave function -that is often far from trivial -the adaptive approaches can handle large active spaces with minimal user intervention. For instance, the ASCI method which is used in the present work consists of an iterative process in which a new and improved set of determinants is found during each step.…”

Section: A Configuration Interactionmentioning

confidence: 99%

Cluster decomposition of full configuration interaction wave functions: A tool for chemical interpretation of systems with strong correlation

Lehtola

Tubman

Whaley

et al. 2017

The Journal of Chemical Physics

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Approximate full configuration interaction (FCI) calculations have recently become tractable for systems of unforeseen size thanks to stochastic and adaptive approximations to the exponentially scaling FCI problem. The result of an FCI calculation is a weighted set of electronic configurations, which can also be expressed in terms of excitations from a reference configuration. The excitation amplitudes contain information on the complexity of the electronic wave function, but this information is contaminated by contributions from disconnected excitations, i.e. those excitations that are just products of independent lower-level excitations. The unwanted contributions can be removed via a cluster decomposition procedure, making it possible to examine the importance of connected excitations in complicated multireference molecules which are outside the reach of conventional algorithms. We present an implementation of the cluster decomposition analysis and apply it to both true FCI wave functions, as well as wave functions generated from the adaptive sampling CI (ASCI) algorithm. The cluster decomposition is useful for interpreting calculations in chemical studies, as a diagnostic for the convergence of various excitation manifolds, as well as as a guidepost for polynomially scaling electronic structure models. Applications are presented for (i) the double dissociation of water, (ii) the carbon dimer, (iii) the π space of polyacenes, as well as (iv) the chromium dimer. While the cluster amplitudes exhibit rapid decay with increasing rank for the first three systems, even connected octuple excitations still appear important in Cr 2 , suggesting that spin-restricted single-reference coupled-cluster approaches may not be tractable for some problems in transition metal chemistry.

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Virtual Orbital Many-Body Expansions: A Possible Route towards the Full Configuration Interaction Limit

Cited by 83 publications

References 62 publications

Iterative Configuration Interaction with Selection

Iterative Configuration Interaction with Selection

Many-Body Expanded Full Configuration Interaction. II. Strongly Correlated Regime

Cluster decomposition of full configuration interaction wave functions: A tool for chemical interpretation of systems with strong correlation

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