Accurate Calculation of the Vibrational Force Constant of the Hydrogen Molecule by Variation–Perturbation Theory

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Abstract
By using the Parr and White perturbation scheme for the diatomic potential energy as a function of internuclear distance, the quadratic force constant ke of the ground state of the hydrogen molecule is calculated by solving a perturbation equation in which the electronic kinetic energy is the perturbation. The first‐ and second‐order energies in the force‐constant expression are calculated by a second perturbation expansion with electron correlation as perturbation. The zeroth‐order uncorrelated wavefunction is determined from the Distorted Atoms in Molecule Model. The first‐ and second‐order perturbation equations involving kinetic‐energy perturbations are solved exactly. By applying accessible correlation expressions, all of the perturbation energies are evaluated without explicit determination of the correlation wavefunctions. The value of ke found is 0.35–0.37 a.u., in good agreement with the experimental value 0.368 a.u.