H+2 —A full three-body variational treatment

Abstract

The eigenstates of the hydrogen molecule ion have been determined by a variational calculation without resorting to the Born–Oppenheimer or adiabatic approximations. A Slater-type orbital basis in terms of perimetric coordinates was used and the eigenvalues were obtained by diagonalizing a 300×300 matrix. Computational techniques and numerical stability tests are described. Because of the relatively small basis and the large number of bound states, most of the eigenvalues were sensitive to the basis set. With a basis which favored the upper states, 18 bound states were obtained in a single diagonalization vs 20 bound states in the adiabatic approximation. With the best basis for the ground state, the eigenvalues of the six lowest levels were 1 to 3×10−6 a.u. lower than adiabatic calculations and the differences appear to increase with increasing vibrational quantum number.

Corrections to the Born-Oppenheimer approximation for a harmonic oscillator

“…On the other hand, the fit of the first three levels in Ref. [5] is exactly linear and in excellent agreement with the fit of Ref. [6].…”

“…We apply these corrections to the electronic and rotational ground state of H2+ and show that the diabatic energy corrections are linearly dependent on the vibrational quantum numbers as seen in recent variational calculations [D. A. Kohl and E. J. Shipsey, J. Chem. Phys.…”

“…Recently, Kohl and Shipsey [5] have shown from a variational treatment that the diabatic energy corrections to the H2 electronic ground states are linearly dependent on the vibrational quantum number n (at least up to n =2). This behavior is shown to be a direct result of our treatment and is seen in other variational studies as well [6 -8].…”

“…Only the erst three vibrational levels in Ref. [5] were used in the fit in Table I because the rapid deviation from linearity for n &2. On the other hand, the fit of the first three levels in Ref.…”

The Decoupling of Electronic and Nuclear Motions in the Isolated Molecule Schrödinger Hamiltonian

“…In this review he also considered its effects on the nature of the variational bounds. For diatomic one-electron systems this term has also been studied by Bishop and his coworkers [73] and from a slightly different point of view by Kohl and Shipsey [74] and also by Moss [75].…”