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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.
We present the extension of variational Monte Carlo (VMC) to the calculation of electronic excitation energies and oscillator strengths using time-dependent linear-response theory. By exploiting the analogy existing between the linear method for wave
The disiloxane molecule is a prime example of silicate compounds containing the Si-O-Si bridge. The molecule is of significant interest within the field of quantum chemistry, owing to the difficulty in theoretically predicting its properties. Herein,
We calculate the linear and non-linear susceptibilities of periodic longitudinal chains of hydrogen dimers with different bond-length alternations using a diffusion quantum Monte Carlo approach. These quantities are derived from the changes in electr
We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker--Campbell--Hausdorff expansion of the similarity transformed Hamiltonian by construction of coupled cluster diagrams on
We present an overview of the variational and diffusion quantum Monte Carlo methods as implemented in the CASINO program. We particularly focus on developments made in the last decade, describing state-of-the-art quantum Monte Carlo algorithms and so