Quantum Monte Carlo methods for electronic structure calculations

Shiwei Zhang

Shiwei Zhang

Jeongnim Kim, Andrew Baczewski, Todd D Beaudet +45 more

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 wavefunctions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary-field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit and graphical processing unit systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://qmcpack.org.

R. N. Barnett, William A. Lester

Nicholas D. M. Hine

This thesis comprises a trio of separate yet thematically-linked investigations within the field of electronic structure that address challenging problems to which quantum Monte Carlo, the most accurate electronic structure method capable of treating large extended systems, has been applied only rarely or indeed never before. The first is the study of polarization and localization in many body systems. Density functional and variational quantum Monte Carlo methods are used to examine the behaviour of the many-electron localization length near band insulator to metal transitions in various oneand two-dimensional model systems. We examine when the localization length, known to be infinite in metals and finite in insulators and assumed to diverge at a metal-insulator transition, serves as a useful diagnostic of the transition. We also present a novel derivation of the formulae for polarization and localization in many body systems that expresses the connection of these two quantities to the concept of Many Body Wannier Functions. The second is a study of the surface energy of the electron gas. The electron gas, or ‘jellium’, is an important benchmark system for electronic structure methods and serves as a simple model for metals. We apply diffusion Monte Carlo (DMC), and a new method for determining surface energies without an unreliable comparison of bulk and slab results, to the calculation of the surface energy. Our method improves on previous calculations in a number of ways and removes many sources of error that plagued previous calculations. The final study applies DMC to the properties, specifically the formation energy, of point defects in Alumina. Alumina is an important technological material, and there are many important unanswered questions relating to its properties that stem from the behaviour and concentration of its point defects. We address many of the problems associated with the calculation of formation energies with electronic structure calculations, and present the first calculations of formation energies of charged point defects in DMC.

Carl W. Greeff, R. N. Barnett, Willard R. Brown +2 more