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. 2024 Jan 11;128(1):281-291.
doi: 10.1021/acs.jpca.3c05109. Epub 2023 Dec 28.

Toward a Stochastic Complete Active Space Second-Order Perturbation Theory

Arta A Safari  1 , Robert J Anderson  1 , Giovanni Li Manni  1
Affiliations

Toward a Stochastic Complete Active Space Second-Order Perturbation Theory

Arta A Safari et al. J Phys Chem A. .

Abstract

In this work, an internally contracted stochastic complete active space second-order perturbation theory, stochastic-CASPT2, is reported. The method relies on stochastically sampled reduced density matrices (RDMs) up to rank four and contractions thereof with the generalized Fock matrix. A new protocol for calculating higher-order RDMs in full configuration interaction quantum Monte Carlo (FCIQMC) has been designed based on (1) restricting sampling of the corresponding excitations to a deterministic subspace, (2) averaging the RDMs from independent dynamics and (3) projecting them onto the closest positive semi-definite matrix. Our protocol avoids previously encountered numerical conditioning problems in the orthogonalization of the perturber overlap matrix stemming from numerical noise. The chromium dimer CASSCF(12,12)/CASPT2 binding curve is computed as a proof of concept.

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Conflict of interest statement

The authors declare no competing financial interest.

Figures

Figure 1
Figure 1
The semi-stochastic subspace partitions the CI space into a principal space (A) containing high-weighted determinants and a residual space (B). Triple and quadruple contributions to higher-order RDMs are only accumulated in the (AA) block, as well as on the diagonal of the (BB) block corresponding to sums of products of instantaneous occupations.
Figure 2
Figure 2
Comparison of the hermiticity error of the averaged F.4RDM and 3RDM, as well as the largest negative eigenvalue of the averaged 3RDM from six independent runs sampled for 20k iterations.
Figure 3
Figure 3
Comparison between the binding curves obtained with 20k and 120k 3RDM sampling iterations. See the text for details.
Figure 4
Figure 4
Eigenvalue distribution of the (a) FOIS overlap matrix across all perturber classes and (b) underlying 3RDMs sampled for 20k iterations at the 2.6 Å geometry.
Figure 5
Figure 5
Mean of the absolute errors across the binding curve of the stochastic-CASPT2 energies.
Figure 6
Figure 6
Estimates of the standard error obtained by resampling 3RDMs from 12 seeds sampled for 120k iterations for the 1.9, 2.3, and 3.0 Å geometries.
See this image and copyright information in PMC

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