Ab initio evaluation of the fine structure of the oxygen molecule

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Abstract
The electron spin dipole-dipole and spin-orbit contributions to the zero-field splitting in the O2 Σg−3 ground state are calculated using the correct microscopic Hamiltonians. The calculations are carried out using minimum, double-zeta, and double-zeta-plus polarization basis sets constructed from contracted Gaussian-lobe functions. Configuration-interaction wavefunctions are used for the ground state and all excited states that couple to the ground state via the spin-orbit Hamiltonian. Values of 1.790 and 1.928 cm−1 are obtained for the splitting parameter λ for the double-zeta and double-zeta-plus polarization bases, respectively, in good agreement with the accurate experimental value of 1.981 cm−1. The spin-orbit contribution which comes primarily from the low-lying excited Σg+1 state accounts for about 2/3 of the total splitting. It is observed that only states which are single excitations from the ground state have a significant spin-orbit contribution and that the over-all effect of electron correlation on the parameter λ is less than 10%. A value of λ1, λ1 = [R(dλ/dR)]Re, of 0.746 cm−1 was calculated in comparison to the experimental value of 0.7129±0.0012. The spin-spin and spin-orbit contributions to λ1 were, respectively, −1.478 and 2.224 cm−1.

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