## 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'| xi^{k} |v,j>, where
xi=(r-r_{o})/r_{o}, are required for a variety
of applications. For r_{o}= 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 H_{2}, D_{2} and T_{2}
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 .

**Site owned by R.J. Le Roy: leroy @ UWaterloo.ca
**
This page was last updated on September 8, 2015