Theoretical Investigation of the Lowest Double-Minimum State E, F 1Σg+ of the Hydrogen Molecule

Accurate potential‐energy curve for the first excited ${}^1{\Sigma }_g^{+}$ state of the hydrogen molecule has been calculated for $\text{1\hspace{0.17em}≤\hspace{0.17em}R\hspace{0.17em}≤\hspace{0.17em}12}\mathrm{a.u}$ . The curve is known to have a double minimum, and for the outer minimum a significantly lower energy has been obtained than all previously reported results. The diagonal corrections for nuclear motion have also been computed and found to have a very sharp peak in the vicinity of the potential maximum. Vibrational and rotational levels have been calculated for all isotopes of the hydrogen molecule, and some results for H₂, D₂and T₂ are shown and compared with experimental data. For the outer minimum, two, three, and four vibrational levels for H₂, D₂, and T₂, respectively, are reported which lie below the lowest levels observed experimentally. For the observed levels good agreement with experimental data is obtained; however, the agreement is significantly worse when only the clamped nuclei potential without the diagonal corrections is used in the calculation of the vibrational energies. The wavefunction is analyzed in terms of some simple functions and appears to drastically change its character in the vicinity of the potential maximum.