M. D. Towler

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 wavefunctions and are capable of achieving very high accuracy. The algorithms are intrinsically parallel and well suited to implementation on petascale computers, and the computational cost scales as a polynomial in 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 optimization of wavefunctions, performing calculations under periodic boundary conditions, using pseudopotentials, excited-state calculations, sources of calculational inaccuracy, and calculating energy differences and forces.

Jastrow correlation factor for atoms, molecules, and solids

A form of Jastrow factor is introduced for use in quantum Monte Carlo simulations of finite and periodic systems. Test data are presented for atoms, molecules, and solids, including both all-electron and pseudopotential atoms. We demonstrate that our Jastrow factor is able to retrieve a large fraction of the correlation energy.

Density functional theory in periodic systems using local Gaussian basis sets

This paper describes a new implementation of density functional theory for periodic systems in a basis of local Gaussian functions, including a thorough discussion of the various algorithms. The results of test calculations using this scheme are reported for some representative crystalline solids, with particular emphasis placed on the influence of the various computational parameters used to control the accuracy of the numerical integration of the exchange-correlation potential.

Electronic structure of p-type conducting transparent oxides

Abstract The band structure of p-type transparent conducting oxides CuAlO 2 , CuGaO 2 , CuInO 2 and SrCu 2 O 2 have been calculated by the pseudopotential method within the local density formalism. The band gaps have been found using the B3LYP functional. The minimum indirect gap of CuXO 2 decreases along the series X=Al to In, and the valence band maximum is always at the zone boundary. The band maxima of SrCu 2 O 2 are both at Γ.

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.

Assessing the accuracy of quantum Monte Carlo and density functional theory for energetics of small water clusters

We present a detailed study of the energetics of water clusters (H(2)O)(n) with n ≤ 6, comparing diffusion Monte Carlo (DMC) and approximate density functional theory (DFT) with well converged coupled-cluster benchmarks. We use the many-body decomposition of the total energy to classify the errors of DMC and DFT into 1-body, 2-body and beyond-2-body components. Using both equilibrium cluster configurations and thermal ensembles of configurations, we find DMC to be uniformly much more accurate than DFT, partly because some of the approximate functionals give poor 1-body distortion energies. Even when these are corrected, DFT remains considerably less accurate than DMC. When both 1- and 2-body errors of DFT are corrected, some functionals compete in accuracy with DMC; however, other functionals remain worse, showing that they suffer from significant beyond-2-body errors. Combining the evidence presented here with the recently demonstrated high accuracy of DMC for ice structures, we suggest how DMC can now be used to provide benchmarks for larger clusters and for bulk liquid water.

Carbon clusters near the crossover to fullerene stability

The energetic stability of structural isomers of

Ab initio Hartree-Fock calculations of CaO, VO, MnO and NiO

{\mathrm{C}}_{24},

Quantum Monte Carlo calculations of the dissociation energy of the water dimer.

{\mathrm{C}}_{26},