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Ab initio quantum Monte Carlo (QMC) techniques [1], such as variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC), are state-of-the-art numerical methods to obtain highly accurate many-body wave functions. These methods are essential when tackling challenging compounds that cannot be treated correctly within the Density Functional Theory (DFT) framework. In this seminar, I will talk about an overview of ab initio QMC methods and introduce our QMC packages, TurboRVB [2] and TurboGenius [3]. I will also talk about recent algorithmic progress in atomic force calculations using QMC. One of the major drawbacks that hinders widespread QMC applications, especially in the materials science community, is the lack of an affordable scheme to compute atomic forces consistent with the derivatives of the potential energy surface, a.k.a. unbiased atomic forces. This is trivial within the DFT framework, but it is one of the long-standing problems in QMC. Very recently, we have proposed a very efficient method to obtain unbiased atomic forces and pressures in the Variational Monte Carlo (VMC) framework, exploiting the gauge-invariant and locality properties of its geminal representation [4]. I will demonstrate the effectiveness of our method for Hydrogen and Chlorine molecules and for the cubic boron nitride crystal.

[1] W. Foulkes, L. Mitas, R. Needs, and G. Rajagopal, Rev. Mod. Phys. 73, 33 (2001).
[2] K. Nakano, et al. J. Chem. Phys. 152, 204121 (2020).
[3] K. Nakano, et al. J. Chem. Phys. 159, 224801 (2023).
[4] K. Nakano, et al. arXiv:2312.17608 (2023).

 

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