On the convergence rate of a cusp-corrected damped multipole expansion for the second-order H-H+ induction energy

The improvement in the convergence rate of the damped multipole expansion for the second order H-H⁺ induction energy due to the inclusion into the first-order function of a term satisfying the electron-proton cusp condition is quantitatively investigated. Following a technique suggested by Schwartz, the multipole contributions to the energy are put in the form of series ordered by inverse powers of the quantum number l. It is shown that, for high values of l, the dependence of the leading terms is raised from l ^-4 to l ^-6 by the cusp correction.