Electron pair density in the lowest 1Σu+ and 1Σg+ states of H2

We demonstrate and advocate the use of observable quantities derived from the two-electron reduced density matrix - pair densities, conditional densities, and exchange-correlation holes - as signatures of the type of electron correlation in a chemical bond. The prototype cases of the lowest (1)Sigma(+)(u) and (1)Sigma(+)(g) states of H-2, which exhibit large variation in types of bonding, ranging from strongly ionic to covalent, are discussed. Both the excited (1)Sigma(+)(g) and (1)Sigma(+)(u) states have been interpreted as essentially consisting of (natural) orbital configurations with an inner electron in a contracted 1s sigma(g) orbital and an outer electron in a diffuse (united atom type, Rydberg) orbital. We show that nevertheless totally different correlation behavior is encountered in various states when comparing them at a common internuclear distance. Also when following one state along the internuclear distance coordinate, strong variation in correlation behavior is observed, as expected. Switches between ionic to covalent character of a state occur till very large distances (40 bohrs for states approaching the 1s3l asymptotic limit, and 282 bohrs for states approaching the 1s4l limit). (C) 2011 American Institute of Physics. [doi:10.1063/1.3624571]