1/Rexpansion forH2+: Calculation of exponentially small terms and asymptotics

The energy of any bound state of the hydrogen molecule ion ${\mathrm{H}}_2$ ${\mathrm{}}^{+}$ has an expansion in inverse powers of the internuclear distance R of the form Rayleigh-Schrödinger perturbation theory (RSPT) gives the coefficients $E^{\left(N\right)}$ but is otherwise unable to treat the exponentially small series, which in part are characteristic of the double-well aspect of ${\mathrm{H}}_2$ ${\mathrm{}}^{+}$. (Here n denotes the hydrogenic principal quantum number.) We develop a quasisemiclassical method for solving the Schrödinger equation that gives all the exponentially small subseries.