Optimization of large determinant expansions in quantum Monte Carlo

Ammar, Abdallah; Giner, Emmanuel; Scemama, Anthony

doi:10.48550/arxiv.2205.12851

Cited by 2 publications

(3 citation statements)

References 66 publications

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“…The variational step in SCI transforms into the TC framework in obtaining both left-and right eigenvectors of large non symmetric matrices, which requires additional non-Hermitian eigensolver technology. In the present work the latter aspect is by-passed using only Hermitian algorithms thanks to the use of a low-memory footprint self-consistent dressing [81][82][83] of the usual Hamiltonian. Within the near-optimal set-up proposed here, we found that the TC-SCI expansion converges faster both in terms of number of Slater determinants and basis set size.…”

Section: Discussionmentioning

confidence: 99%

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Extension of selected configuration interaction for transcorrelated methods

Ammar¹,

Scemama²,

Giner³

2022

Preprint

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In this work we present an extension of the popular selected configuration interaction (SCI) algorithms to the Transcorrelated (TC) framework. Although we used in this work the recently introduced one-parameter correlation factor [E. Giner, J. Chem. Phys., 154, 084119 (2021)], the theory presented here is valid for any correlation factor. Thanks to the formalization of the non Hermitian TC eigenvalue problem as a search of stationary points for a specific functional depending both on left-and right-functions, we obtain a general framework allowing different choices for both the selection criterion in SCI and the second order perturbative correction to the energy. After numerical investigations on different second-row atomic and molecular systems in increasingly large basis sets, we found that taking into account the non Hermitian character of the TC Hamiltonian in the selection criterion is mandatory to obtain a fast convergence of the TC energy. Also, selection criteria based on either the first order coefficient or the second order energy lead to significantly different convergence rates, which is typically not the case in the usual Hermitian SCI. Regarding the convergence of the total second order perturbation energy, we find that the quality of the left-function used in the equations strongly affects the quality of the results. Within the near-optimal algorithm proposed here we find that the SCI expansion in the TC framework converges faster than the usual SCI both in terms of basis set and number of Slater determinants.

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Section: Discussionmentioning

confidence: 99%

“…Such an approach was originally proposed in Ref. 81 in the context of single reference coupled cluster and more recently applied in the context of multi-reference coupled cluster 82 or quantum Monte Carlo 83 .…”

Section: Obtaining Left-and Right-eigenvectors With Iterative Hermiti...mentioning

confidence: 99%

Extension of selected configuration interaction for transcorrelated methods

Ammar¹,

Scemama²,

Giner³

2022

Preprint

Self Cite

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“…These methods scale fa-vorably with system size (N 4 with N the number of electrons) and naturally parallelize. [27][28][29] In addition, recent improvements in QMC algorithms [30][31][32][33] allow for fast optimization of trial wave functions with thousands of parameters. When using determinant expansions provided by the CIPSI method fully optimized in the presence of a Jastrow factor as trial wave functions, VMC and DMC have been shown to provide accurate excitation energies.…”

Section: Introductionmentioning

confidence: 99%

Double excitation energies from quantum Monte Carlo using state-specific energy optimization

Shepard¹,

Panadés-Barrueta²,

Moroni³

et al. 2022

Preprint

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We show that recently developed quantum Monte Carlo methods, which provide accurate vertical transition energies for single excitations, also successfully treat double excitations. We study the double excitations in medium-sized molecules, some of which are challenging for high level coupled-cluster calculations to model accurately. Our fixednode diffusion Monte Carlo excitation energies are in very good agreement with reliable benchmarks, when available, and provide accurate predictions for excitation energies of difficult systems where reference values are lacking.

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Optimization of large determinant expansions in quantum Monte Carlo

Cited by 2 publications

References 66 publications

Extension of selected configuration interaction for transcorrelated methods

Extension of selected configuration interaction for transcorrelated methods

Double excitation energies from quantum Monte Carlo using state-specific energy optimization

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