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Article Dans Une Revue Advances in Quantum Chemistry Année : 2016

Introduction to the variational and diffusion Monte Carlo methods

Résumé

We provide a pedagogical introduction to the two main variants of real-space quantum Monte Carlo methods for electronic-structure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on the subject, we review in depth the Metropolis-Hastings algorithm used in VMC for sampling the square of an approximate wave function, discussing details important for applications to electronic systems. We also review in detail the more sophisticated DMC algorithm within the fixed-node approximation, introduced to avoid the infamous Fermionic sign problem, which allows one to sample a more accurate approximation to the ground-state wave function. Throughout this review, we discuss the statistical methods used for evaluating expectation values and statistical uncertainties. In particular, we show how to estimate nonlinear functions of expectation values and their statistical uncertainties.
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Dates et versions

hal-01183633 , version 1 (10-08-2015)

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Julien Toulouse, Roland Assaraf, C. J. Umrigar. Introduction to the variational and diffusion Monte Carlo methods. Advances in Quantum Chemistry, 2016, Electron Correlation in Molecules – ab initio Beyond Gaussian Quantum Chemistry, 73, pp.285. ⟨10.1016/bs.aiq.2015.07.003⟩. ⟨hal-01183633⟩
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