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arXiv · 1706.07588

Optimizing the energy with quantum Monte Carlo: A lower numerical scaling for Jastrow-Slater expansions

Roland Assaraf·Saverio Moroni·Claudia Filippi
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Abstract

We present an improved formalism for quantum Monte Carlo calculations of energy derivatives and properties (e.g. the interatomic forces), with a multideterminant Jastrow-Slater function. As a function of the number $N_e$ of Slater determinants, the numerical scaling of $O(N_e)$ per derivative we have recently reported is here lowered to $O(N_e)$ for the entire set of derivatives. As a function of the number of electrons $N$, the scaling to optimize the wave function and the geometry of a molecular system is lowered to $O(N^3)+O(N N_e)$, the same as computing the energy alone in the sampling process. The scaling is demonstrated on linear polyenes up to C$_{60}$H$_{62}$ and the efficiency of the method is illustrated with the structural optimization of butadiene and octatetraene with Jastrow-Slater wave functions comprising as many as 200000 determinants and 60000 parameters.

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Roland Assaraf, Saverio Moroni, Claudia Filippi. 2017-06-23. Optimizing the energy with quantum Monte Carlo: A lower numerical scaling for Jastrow-Slater expansions. https://arxiv.org/abs/1706.07588

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