First Excited Σg+1 State of the Hydrogen Molecule

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Abstract
A variation calculation on the first excited Σg+1 state of H2 has been carried out using an expansion in elliptical coordinates. All results are reported in Hartree atomic units. The potential function resulting from this calculation is characterized by having minima at R=1.9 and R=4.3 and a maximum at R=3.3. The energy obtained at R=1.9 using a 20-term, open-shell, covalent-type wave function was —0.7162 as compared with the ``experimental'' value of —0.7181. Due to convergence difficulties, many more configurations are required to improve this result significantly. At R=4.3, on the other hand, the best result was obtained with an open-shell wave function including nine ionic terms and nine atomic terms. This result of —0.7007 is below the reported ``experimental'' value of —0.6935 because the two lowest (2pσ)2Σg+1 vibrational levels have not been found experimentally. The energy at the top of the barrier was computed to be —0.6844 and probably is as low as —0.6884. The vibrational levels for this potential function have been computed by a numerical integration technique. The fact that these are in one-to-one correspondence with a combination of the experimental 1s2s and (2pσ)2 levels indicates that both of these sets of levels belong to the first excited state.

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