Electron correlation in the GK state of the hydrogen molecule

The second excited (1)Sigma(g)(+) state of the hydrogen molecule, the so-called GK state, has a potential energy curve with double minima. At the united atom limit it converges to the 1s3d configuration of He. At large internuclear distances R, it dissociates to two separated atoms, one in the ground state and another in the 2p excited state. Radial pair density calculations and natural orbital analyses reveal unusual effect of electron correlation around the K minimum of the potential energy curve. As R>2.0 a.u., a natural orbital of sigma(u) symmetry joins the two natural orbitals of sigma(g) symmetry at smaller R. The average interelectronic distance decreases as the internuclear distance increases from R=2.0 to 3.0 a.u. Around R=3.0 a.u. the singly peaked pair density curve splits into two peaks. The inner peak can be attributed to the formation of the ionic electron configuration (1s)(2), where both 1s electrons are on the same nucleus. As the two 1s electrons run into different nuclei, one of the two 1s electrons is promoted to the 2p state, which results in the outer peak in the pair density curve. The Rydberg 1s2p configuration persists as the nuclei stretch, and becomes dominant at large R where four natural orbitals, two of sigma(g) and two of sigma(u) symmetry, become responsible.