Direct calculation of interaction-induced molecular properties: An application to the relativistic mass-velocity and Darwin terms in the interaction energy of hydrogen atoms

Interaction-induced properties, including the interaction energy itself, are difficult to compute using explicitly correlated basis functions since bases corresponding to noninteracting atoms are not defined in this case. We propose a direct method of calculation in which no subtraction of exact or approximate atomic properties is required. To test the method we computed the one-electron Darwin and mass-velocity contributions to the interaction energy of two ground-state hydrogen atoms at separations close to the van der Waals minimum in the triplet state. To verify the accuracy at larger distances, we also computed the constants determining the asymptotic long-range behavior of the investigated contributions. Our results, obtained with a Gaussian geminal basis, appear to be more accurate than the results of earlier variational calculations employing explicitly correlated exponential functions. When the same basis sets are employed, our method gives results very close to the so-called monomer-contraction method proposed recently by Cencek [W. Cencek , Phys. Rev. Lett. 95, 23304 (2005)], which confirms the soundness of the latter approach. To extend the validity of our calculations to very large interatomic separations R, we provide damping functions accounting for the retardation effects and producing the correct 1/R-7 long-range decrease of the computed relativistic corrections.