Interaction Potentials and matrix elements of Ground-State Molecular Hydrogen

In 1987 Schwartz & Le Roy [J.Mol.Spectrosc. 121, 420-439 (1987)] reported pointwise potentials for ground state of all 6 isotopologues of molecular hydrogen, based on the best ab initio results then available, which took account of relativistic and adiabatic Born-Oppenheimer breakdown corrections. Because of the mass-weighted adiabatic corrections, these potentials are slightly different for the different isotopomers.  However, because of how they were derived, when solving the radial Schrödinger equation with these ab initio isotopologue-specific effective adiabatic potentials, one technically should use the reduced masses of the nuclei, and that is done by the sample Program LEVEL input data sets associated with the potential functions reported here. However, this neglects the off-diagonal Born-Oppenheimer breakdown corrections to the kinetic operator, and a first-order approximate way to take account of such corrections seems be to use the reduced masses of the pairs of atoms, rather than of the nuclei (see [J.C.P. 49, 4312 (1968).   Program LEVEL input data files containing these pointwise potentials for the 6 isotopologues of ground state molecular hydrogen are automatically distributed (by e-mail) to those who fill in the following form: Download Diatomic Hydrogen Potentials .

As a Supplement to the above paper, University of Waterloo Chemical Physics Research Report CP-301R (1987) presents a full listing of the calculated nonadiabatic eigenvalues of all bound and quasibound levels of the six isotopologues of diatomic hydrogen, together with expectation values of six powers of r, of the nuclear kinetic energy, and of the polarizabiliy and polarizability anisotropy for perturbation by a static field, for all of those levels.

Matrix elements of the form < v',j'| xik |v,j>, where xi=(r-ro)/ro, are required for a variety of applications. For ro= 1.448739 bohr, diagonal and off-diagonal matrix elements of this type have been generated from these recommended potential energy curves for j'-j= -2,0,+2 and all possible combinations of v' and v < 5 and J≤ 8, for all six diatomic hydrogen isotopologues. For H2, D2 and T2 values are tabulated for k=0-5 while for HD, HT and DT they are tabulated for k=0-8. This tabulation, in the form of a plain ASCII file, will be automatically sent (by e-mail) to anyone who fill in the form: Download Diatomic Hydrogen Matrix Elements .


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This page was last updated on September 8, 2015