Diffusion Monte Carlo study of correlation in the hydrogen molecule

The diffusion Monte Carlo (DMC) method shows that correlation in H ₂ produces a set of three spatial changes: (i) an enhancement in the electron density distribution n(r) in the left and right anti-binding regions that include separately the immediate vicinity of each of the two nuclei, (ii) a reduction in n (r) in the binding region intervening between the two nuclei as a counterbalance, and (iii) a concomitant increase in the equilibrium internuclear separation. It is stressed that the correlation energy E ^c(= T^c + V^c) for diatomic molecules be defined by the difference in the total energy between the exact and the Hartree-Fock (HF) variational calculations that are performed at individually optimized internuclear separations. It is this definition that makes it possible to involve a significant contribution from a correlation-induced change in the equilibrium internuclear separation as part of the correlation energy and to relate (i) and (ii) to (iii) in consistency with the electrostatic theorem. The present calculations fulfill the virial theorem to an accuracy of - V/T = 2.00 for DMC and - V^HF/T^HF = 2.000 for HF. The present correlation energy E^c = -0.0408 hartree is not only in good agreement with the most accurate value previously reported, but also can be analyzed into all its components in accordance with the correlational virial theorem 2T ^C + V^c = 0.