Accurate potentialhyphen;energy curve for the first excited1Sgr;gplus;state of the hydrogen molecule has been calculated for1thinsp;le;thinsp;Rthinsp;le;thinsp;12a.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 T2are 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.
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