A ground state potential energy surface for H2 using Monte Carlo methods

Abstract

Abstract Although more accurate values of ground-state electronic energies of the clamped-nucleus H2 molecule have been obtained in analytic variational calculations with explicitly correlated wavefunctions, the Monte Carlo variational calculations reported in this paper provide a useful alternative to analytic calculations. Aside from confirming energies, they may be used in straightforward and simple independent calculations of the quantities needed for nonadiabatic diagonal corrections, relativistic corrections, and radiative corrections to the Born-Oppenheimer potential energy curve. The trial functions used were symmetric exponential functions of products of electron-electron and electron-nucleus distances with integer exponents and up to 128 adjustable parameters optimized to minimize a combination of the energy and its variance. The calculations were carried out for 24 internuclear distances in the range of 0.2 to 10.0 bohr, and they gave energies typically 1-3 microhartrees above analytic variational values with uncertainties typically less than 1 microhartree. Most interesting are the correction terms, which are not variational and were found to confirm earlier values within 1 microhartree. Binding energies calculated for several vibration-rotation levels of H2 using the calculated potential energy curve were found in excellent agreement with those determined from spectroscopic measurements. The authors proposed that the Monte Carlo techniques used be generalized to larger systems for which analytic integrations are much more difficult.