RESUMO
The exchange energy, i.e., the splitting ΔE between gerade and ungerade states in the hydrogen molecule, has proven very difficult in numerical calculation at large internuclear distances R, while the known results are sparse and highly inaccurate. On the other hand, there are conflicting analytical results in the literature concerning its asymptotics. In this work, we develop a flexible and efficient numerical approach using explicitly correlated exponential functions and demonstrate highly accurate exchange energies for internuclear distances as large as 57.5 a.u. This approach may find further applications in calculations of inter-atomic interactions. In particular, our results support the asymptotics form ΔE â¼ R5/2e-2R, but with the leading coefficient being 2σ away from the analytically derived value.
RESUMO
Explicitly correlated quantum chemical calculations require calculations of five types of two-electron integrals beyond the standard electron repulsion integrals. We present a novel scheme, which utilises general ideas of the McMurchie-Davidson technique, to compute these integrals when the so-called "range-separated" correlation factor is used. This correlation factor combines the well-known short range behaviour resulting from the electronic cusp condition, with the exact long-range asymptotics derived for the helium atom [Lesiuk, Jeziorski, and Moszynski, J. Chem. Phys. 139, 134102 (2013)]. Almost all steps of the presented procedure are formulated recursively, so that an efficient implementation and control of the precision are possible. Additionally, the present formulation is very flexible and general, and it allows for use of an arbitrary correlation factor in the electronic structure calculations with minor or no changes.