Continuum variational and diffusion quantum Monte Carlo calculations

This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The algorithms are intrinsically parallel and well-suited to petascale computers, and the computational cost scales as a polynomial of the number of particles. A guide to the systems and topics which have been investigated using these methods is given. The bulk of the article is devoted to an overview of the basic quantum Monte Carlo methods, the forms and optimisation of wave functions, performing calculations within periodic boundary conditions, using pseudopotentials, excited-state calculations, sources of calculational inaccuracy, and calculating energy differences and forces

Framework for constructing generic Jastrow correlation factors

We have developed a flexible framework for constructing Jastrow factors which allows for the introduction of terms involving arbitrary numbers of particles. The use of various three- and four-body Jastrow terms in quantum Monte Carlo calculations is investigated, including a four-body van der Waals-like term, and anisotropic terms. We have tested these Jastrow factors on one- and two-dimensional homogeneous electron gases, the Be, B, and O atoms, and the BeH, H$_2$O, N$_2$, and H$_2$ molecules. Our optimized Jastrow factors retrieve more than 90% of the fixed-node diffusion Monte Carlo correlation energy in variational Monte Carlo for each system studied.Comment: 17 pages, 4 figure

Quantum Monte Carlo study of a positron in an electron gas

Quantum Monte Carlo calculations of the relaxation energy, pair-correlation function, and annihilating-pair momentum density are presented for a positron immersed in a homogeneous electron gas. We find smaller relaxation energies and contact pair-correlation functions in the important low-density regime than predicted by earlier studies. Our annihilating-pair momentum densities have almost zero weight above the Fermi momentum due to the cancellation of electron-electron and electron-positron correlation effects

Quantum Monte Carlo study of the energetics of the rutile, anatase, brookite, and columbite TiO2_{2} polymorphs

The relative energies of the low-pressure rutile, anatase, and brookite polymorphs and the high-pressure columbite polymorph of TiO$_{2}$ have been calculated as a function of temperature using the diffusion quantum Monte Carlo (DMC) method and density functional theory (DFT). The vibrational energies are found to be important on the scale of interest and significant quartic anharmonicity is found in the rutile phase. Static-lattice DFT calculations predict that anatase is lower in energy than rutile, in disagreement with experiment. The accurate description of electronic correlations afforded by DMC calculations and the inclusion of anharmonic vibrational effects contribute to stabilizing rutile with respect to anatase. Our calculations predict a phase transition from anatase to rutile TiO$_{2}$ at 630±210 K.J.R.T., P.L.R., and R.J.N. acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant No. EP/J017639/1. B.M. acknowledges support from Robinson College, Cambridge, and the Cambridge Philosophical Society for a Henslow Research Fellowship. R.M. is grateful for financial support from MEXT-KAKENHI Grants No. 26287063, No. 25600156, and No. 22104011, and a grant from the Asahi Glass Foundation. Computational resources were provided by the Archer facility of the U.K.'s national high-performance computing service (for which access was obtained via the UKCP consortium, EPSRC Grant No. EP/K014560/1), by the Center for Information Science of the JAIST, and by the K-computer (supported by the Computational Materials Science Initiative, CMSI/Japan, under Projects No. hp120086, No. hp140150, and No. hp150014)

Inhomogeneous backflow transformations in quantum Monte Carlo calculations

An inhomogeneous backflow transformation for many-particle wave functions is presented and applied to electrons in atoms, molecules, and solids. We report variational and diffusion quantum Monte Carlo VMC and DMC energies for various systems and study the computational cost of using backflow wave functions. We find that inhomogeneous backflow transformations can provide a substantial increase in the amount of correlation energy retrieved within VMC and DMC calculations. The backflow transformations significantly improve the wave functions and their nodal surfaces.Comment: ~20 pages, 11 figure

Strategies for improving the efficiency of quantum Monte Carlo calculations

We describe a number of strategies for minimizing and calculating accurately the statistical uncertainty in quantum Monte Carlo calculations. We investigate the impact of the sampling algorithm on the efficiency of the variational Monte Carlo method. We then propose a technique to maximize the efficiency of the linear extrapolation of diffusion Monte Carlo results to zero time step, finding that a relative time-step ratio of 1:4 is optimal. Finally, we discuss the removal of serial correlation from data sets by reblocking, setting out criteria for the choice of block length and quantifying the effects of the uncertainty in the estimated correlation length