Coulomb correlation in the H2 molecule: A two-particle density analysis

Abstract

The correlation effect in molecules, and its influence on bonding, is difficult to assess in terms of the traditional Coulomb hole, a concept which has been particularly fruitful in atomic studies. As an alternative, we have studied correlation-induced changes in the two-particle density over a preselected molecular plane. The consequences of different components of correlation can be highlighted by choosing specific fixed locations of a ‘‘test’’ or ‘‘reference’’ electron in relation to the nuclear framework. The ground state of H2 is investigated as the initial example. This simple system is especially interesting since it possesses the prototype homonuclear chemical bond. The analysis was aided by using an energetically reliable correlated wave function expressed as a natural expansion. Due to the first natural orbital being effectively a Brueckner orbital, correlation effects were measured here with respect to the first natural configuration. Besides examining the two-particle density changes over the H2 molecular plane, we also defined and determined the corresponding radial and angular ‘‘planar Coulomb holes,’’ ΔR(r12) and ΔA(ε), respectively. Finally, variations in the relative importance of the ‘‘change of density’’ characteristics, arising from each of the three main components of electron correlation, were mapped out as the test or ‘‘fixed’’ electron was moved across the chosen H2 plane. The procedure adopted here is sufficiently general to be applicable to any electron pair within a polyatomic system—in both position space and momentum space.