On the relation of dispersion to induction energies, and to their damping functions

Abstract

A simple, yet reliable, expression is suggested to represent the radial-dependent charge-overlap damping functions for the coefficients (C_n ) of the second-order induction and dispersion perturbation series expansions for arbitrary even n, and of the third-order charge-overlap induction damping functions for arbitrary odd n. By using a reduced coordinate of the form x = R/[λ + 2γ(<r ² _A >^1/2 + <r ² _B>^1/2)], where λ = 5·5 a ₀ and γ = 1.25, it is shown that the charge-overlap damping functions for the H(1s) … H⁺ second-order induction coefficients can be made consistent with those for the H(1s) … H(1s) second-order dispersion coefficients over a wide range of internuclear distances. Hence, in view of previous work, they are suggested to study other ion-atom interactions. Based on the damped induction energy, reliable analytic fits to the exact numerical Born-Oppenheimer curves for the X ²Σ _g ⁺ and 1 ²Σ _u ⁺ states of H⁺ ₂ are presented.