Vibrational—Rotational Study of the Electronic Ground State of the Hydrogen Molecule

Abstract

The Schrödinger equation for nuclear motion in H₂, HD, and D₂ has been integrated numerically with accurate internuclear potential for numerous vibrational and rotational states. The theoretical dissociation energies are larger than the experimental results by 3.9, 4.7, and 3.6 cm⁻¹ for H₂, HD, and D₂, respectively. It is argued that this discrepancy exceeds the possible computational inaccuracies and is not due to the adiabatic approximation. The radiative corrections are also discussed and it is shown that the correction to the dissociation energy is definitely smaller in absolute value than 0.4 cm⁻¹. The computed vibrational quanta are larger than the observed ones by about 1 cm⁻¹ while the theoretical rotational quanta are in a very good agreement with experiment. The vibrational—rotational wavefunctions are used for averaging of some electronic expectation values. The computed quantities agree with experiment within the experimental errors.