Quantum Monte Carlo studies on small molecules

Abstract

The Variational Monte Carlo (VMC) and Fixed-Node Diffusion Monte Carlo (FNDMC) methods have been examined, through studies on small molecules. New programs have been written which implement the (by now) standard algorithms for VMC and FNDMC. We have employed and investigated throughout our studies the accuracy of the common Slater–Jastrow trial wave function. Firstly, we have studied a range of sizes of the Jastrow correlation function of the Boys–Handy form, obtained using our optimization program with analytical derivatives of the central moments in the local energy. Secondly, we have studied the effects of Slater-type orbitals (STOs) that display the exact cusp behaviour at nuclei. The orbitals make up the all important trial determinant, which determines the fixed nodal surface. We report all-electron calculations for the ground state energies of Li₂, Be₂, H₂O, NH₃, CH₄ and H₂CO, in all cases but one with accuracy in excess of 95%. Finally, we report an investigation of the ground state energies, dissociation energies and ionization potentials of NH and NH⁺. Recent focus paid in the literature to these species allow for an extensive comparison with other ab initio methods. We obtain accurate properties for the species and reveal a favourable tendency for fixed-node and other systematic errors to cancel. As a result of our accurate predictions, we are able to obtain a value for the heat of formation of NH, which agrees to within less than 1 kcal mol⁻¹ to other ab initio techniques and 0.2 kcal mol⁻¹ of the experimental value.

Acknowledgements

PTAG would like to convey his gratitude to Professor Garnet Kin-Lic Chan for his mentorship, insight, and programming expertise during the first part of this research. The study of NH was prompted by discussion with Professor P. Tosi, University of Trento during a visit by WAL in 2005. WAL was supported by the Director, Office of Basic Energy Sciences, Chemical Sciences Division of the US Department of Energy under Contract No. DE-AC03-76SF00098; PTAG also received support from the aforementioned source for a visit to Berkeley during the course of this research.