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Optimization of large determinant expansions in quantum Monte Carlo

Abstract : We present a new method for the optimization of large configuration interaction (CI) expansions in the quantum Monte Carlo (QMC) framework. The central idea here is to replace the non-orthogonal variational optimization of CI coefficients performed in usual QMC calculations by an orthogonal non-Hermitian optimization thanks to the so-called transcorrelated (TC) framework, the two methods yielding the same results in the limit of a complete basis set. By rewriting the TC equations as an effective self-consistent Hermitian problem, our approach requires the sampling of a single quantity per Slater determinant, leading to minimal memory requirements in the QMC code. Using analytical quantities obtained from both the TC framework and the usual CI-type calculations, we also propose improved estimators which reduce the statistical fluctuations of the sampled quantities by more than an order of magnitude. We demonstrate the efficiency of this method on wave functions containing $10^5-10^6$ Slater determinants, using effective core potentials or all-electron calculations. In all the cases, a sub-milliHartree convergence is reached within only two or three iterations of optimization.
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https://hal.archives-ouvertes.fr/hal-03716808
Contributor : Anthony Scemama Connect in order to contact the contributor
Submitted on : Thursday, July 7, 2022 - 5:58:37 PM
Last modification on : Tuesday, September 27, 2022 - 4:22:38 AM

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Abdallah Ammar, Emmanuel Giner, Anthony Scemama. Optimization of large determinant expansions in quantum Monte Carlo. Journal of Chemical Theory and Computation, American Chemical Society, 2022, 18 (9), pp.5325-5336. ⟨10.1021/acs.jctc.2c00556⟩. ⟨hal-03716808⟩

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