Applications of quantum Monte Carlo methods in condensed systems

Abstract

The quantum Monte Carlo methods represent a powerful and broadly applicable computational tool for finding very accurate solutions of the stationary Schrödinger equation for atoms, molecules, solids and a variety of model systems. The algorithms are intrinsically parallel and are able to take full advantage of the present-day high-performance computing systems. This review article concentrates on the fixed-node/fixed-phase diffusion Monte Carlo method with emphasis on its applications to electronic structure of solids and other extended many-particle systems.

Accurate barrier heights using diffusion Monte Carlo

“…In the literature, there are benchmarks of the energies of atomic systems [3][4][5][6], small molecules including transition metals [7][8][9][10][11], and large benchmark studies have been performed on the G1 set of 55 molecules [12,13]. A review of applications of DMC to chemical systems is available from Austin et al [14], and a review of applications of DMC to bulk systems is available from Kolorenč and Mitas [15] as well as Wagner and Ceperley [2]. Atomic studies find agreement with experiments on order of 0.23 kcal/mol for ionization potentials, on order of 2.3 kcal/mol for electron affinity, and on order 3 kcal/mol for atomization energies.…”

Optimized Structure and Vibrational Properties by Error Affected Potential Energy Surfaces

“…Within QMC, the energy of correlated molecular systems can be calculated with an accuracy in line with experimental data and with the most accurate traditional quantum chemistry methods [42][43][44][45][46][47][48][49][50][51][52] but with a computational cost scaling with the size of the system as facilities 53 ) should make QMC an optimal choice for accurate calculations of molecular geometries and vibrational properties. On the other hand, the underlying stochastic nature of the Monte Carlo algorithms is reflected in the fact that QMC energies and forces are affected by a stochastic error, which slowly decreases as the square root of the computational time.…”

Spin-orbit interactions in electronic structure quantum Monte Carlo methods

“…For broken time-reversal Hamiltonians or for twisted boundary conditions [1] with inherently complex eigenstates, the fixed-node condition has been generalized to the fixed-phase approximation [2]. Benchmark quality results for both models and real materials have been obtained in many settings such as molecules, solids, non-covalently bonded complexes, ultracold condensates and other systems [3,4].Electronic structure QMC calculations are usually done with particle spins being assigned fixed labels, up or down. Since spins commute with Hamiltonians without explicit spin terms, the problem simplifies to the spatial solution of the stationary Schrödinger equation.…”