Quantum Monte Carlo Study of Weakly Interacting Many-Electron Systems

Quantum Monte Carlo (QMC) methods are playing an increasingly important role for providing benchmark results for testing more approximate electronic structure and force field methods. Two particular variants of QMC, the variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) methods, have been applied to study the many-electron systems. All-electron calculations using QMC methods are performed to study the ground-state energy of the Be atom with single-determinant and multi-determinant trial functions, the binding energy of the water dimer, and the binding energy of the water-benzene complex. All of the DMC results achieve good agreement with high level ab initio methods and experiments. The QMC method with pseudopotentials is used to calculate the electron binding energies of two forms of (H2O)6. It is found that the DMC method, when using either Hartree-Fock or density functional theory trial functions, gives electron binding energies in excellent agreement with the results of large basis set CCSD(T) calculations. Pseudopotential QMC methods are also used to study the interactions of the water-benzene, water-anthracene, and water-coronene complexes. The dissociation energies of water-acene complexes of the DMC calculations agree with several other high level quantum calculations. Localized orbitals represented as spline functions are used to reduce the computational cost of the calculations for larger water-acene complexes. The prospects of using this approach to determine the interaction energy between water and graphite are discussed. In addition, we introduce correlation-consistent Gaussian-type orbital basis sets for use with the Casino Dirac-Fock pseudopotentials. These basis sets give low variances in VMC calculations and lead to significantly improved convergence compared to non-optimized basis sets in DMC calculations. We also examine the performance of two methods, the locality approximation (LA) and T-move, that have been designed for dealing with the problems associated with the use of non-local pseudopotentials in quantum Monte Carlo calculations. The two approaches give binding energies of water dimer that agree within the statistical errors. However, the convergence behavior of the DMC calculations is better behaved when using the T-move approach