Introduction to the Diffusion Monte Carlo Method

In this paper the Diffusion Monte Carlo (DMC) method is applied to the confined hydrogen atom with different confinement geometries. This approach is validated using the much studied spherical and cylindrical confinements and then applied to cubical and squared ones, for which data are not available, as new applications of the method relevant to solid state physics. The energy eigenvalues of the ground state and one low-lying excited state are reported as a function of the ch...

We present a method for optimizing the location of the fermion ground-state nodes using a combination of diffusion Monte Carlo (DMC) and projected gradient descent (PGD). A PGD iteration shifts the parameters of an arbitrary node-fixing trial function in the opposite direction of the DMC energy gradient, while maintaining the cusp condition for atomic electrons. The energy gradient is calculated from DMC walker distributions by one of three methods we derive from an exact ana...

The VB-QMC method is presented in this chapter. It consists of using in quantum Monte Carlo (QMC) approaches with a wave function expressed as a usually short expansion of classical Valence-Bond (VB) structures supplemented by a Jastrow factor to account for dynamical correlation. Two variants exist: the VB-VMC (using variational Monte Carlo) and VB-DMC (using diffusion Monte Carlo) methods. QMC algorithms circumvent the notorious non-orthogonality issue of classical VB appro...

We present ground and excited state energies obtained from Diffusion Monte Carlo (DMC) calculations, using accurate multiconfiguration wave functions, for $N$ electrons ($N\le13$) confined to a circular quantum dot. We analyze the electron-electron pair correlation functions and compare the density and correlation energies to the predictions of local spin density approximation theory (LSDA). The DMC estimated change in electrochemical potential as function of the number of el...

We have employed the steepest descent method to optimise the variational ground state quantum Monte Carlo wave function for He, Li, Be, B and C atoms. We have used both the direct energy minimisation and the variance minimisation approaches. Our calculations show that in spite of receiving insufficient attention, the steepest descent method can successfully minimise the wave function. All the derivatives of the trial wave function respect to spatial coordinates and variationa...

Ground state energies and chemical potentials of parahydrogen clusters are calculated from 3 to 40 molecules using the diffusion Monte Carlo technique with two different pH2-pH2 interactions. This calculation improves a previous one by the inclusion of three-body correlations in the importance sampling, by the time step adjustement and by a better estimation of the statistical errors. Apart from the cluster with 13 molecules, no other magic clusters are predicted, in contrast...

We present a stepwise adaptive-timestep version of the Quantum Jump (Monte Carlo wave-function) algorithm. Our method has proved to remain robust even for problems where the integrating implementation of the Quantum Jump method is numerically problematic. The only specific parameter of our algorithm is the single a priori parameter of the Quantum Jump method, the maximal allowed total jump probability per timestep. We study the convergence of ensembles of trajectories to the ...

Digital quantum computers provide a computational framework for solving the Schr\"{o}dinger equation for a variety of many-particle systems. Quantum computing algorithms for the quantum simulation of these systems have recently witnessed remarkable growth, notwithstanding the limitations of existing quantum hardware, especially as a tool for electronic structure computations in molecules. In this review, we provide a self-contained introduction to emerging algorithms for the ...

In this paper we present the Uppsala Quantum Chemistry package (UQUANTCHEM), a new and versatile computational platform with capabilities ranging from simple Hartree-Fock calculations to state of the art First principles Extended Lagrangian Born Oppenheimer Molecular Dynamics (XL- BOMD) and diffusion quantum Monte Carlo (DMC). The UQUANTCHEM package is distributed under the general public license and can be directly downloaded from the code web-site. Together with a presentat...

QMCPACK is an open source quantum Monte Carlo package for ab-initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wave functions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. Th...