The <i>E</i> <i>F</i>, <i>G</i> <i>K</i>, and <i>H</i> <i>H</i> 1Σ<i>g</i>+ states of hydrogen. Improved <i>ab initio</i> calculation of vibrational states in the adiabatic approximation

Abstract

Electronic energies and diagonal energy corrections for nuclear motion are calculated for the first three excited 1Σg+ states of H2 at some 70 internuclear separations in the interval R(a.u.) ∈{1,15}. More accurate electronic wave functions comprising, respectively, 129, 118, and 110 terms for the EF, GK, and HH̄ states, and a new method for the evaluation of the relevant integrals are used. The maximum values of the adiabatic energy corrections are found to be larger than the previously published values by 60 cm−1 (EF at R=3.2 a.u.), 55 cm−1 (GK at R=2.85 a.u.), and 38 cm−1 (HH̄ at R=2.95 a.u.), while the electronic energies at the same values of R are now lower by −6, −26, and −7 cm−1. The adiabatic ab initio vibrational energies of the EF, v=0, levels lie 1.9 (H2) and 1.4 cm−1 (HD and D2) above the experimental values. All higher vibrational levels of the three electronic states are appreciably affected by nonadiabatic energy shifts.