Properties of the 1Σg+ State of H2 Calculated from an Accurate Adiabatic Potential

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Abstract
An accurate adiabatic potential for the X 1Σg+ state of H2 calculated by Kol/os and Wolniewicz has been used in direct numerical solutions for the radial Schrödinger equation. The bond dissociation energy lies at the lower bound of the present experimental uncertainty, namely 36112.7 cm−1. Vibrational and rotational term value separations are in excellent agreement with experiment, especially for low v and J states. Expectation values for 〈r−2〉 are also in very good accord with observed rotational constants. Hence, a primary conclusion of this work is that the adiabatic approximation gives a highly accurate representation of the ground state of molecular hydrogen. Also, the procedure used here affords a convenient means of generating accurate radial wavefunctions for a variety of practical purposes. Additional topics treated are the comparison of this approach with the nonadiabatic calculation of Kol/os and Wolniewicz, and the extent to which an analysis of the H2 data can be made in terms of the traditional approach used in diatomic spectroscopy of two‐point masses rotating and vibrating under the influence of a potential which is a single‐valued function of the internuclear distance. Specific results obtained are a reduction in the uncertainty of the zero‐point energy (with a slight adjustment in its most probable value) and a method for determining the force constant for this potential to five‐figure accuracy. In the absence of experimental data, the Kol/os and Wolniewicz potential appears to provide a better extimate of the term values and rotational constants for tritium‐containing isotopes of hydrogen than do isotopic relations applied to the ambiguous molecular constants for H2. Hence, a table of vibrational term values and rotational constants for the six hydrogen isotopic species is given as an appednix.