On the inverse Born-Oppenheimer separation for high Rydberg states of molecules

The separation of radial electronic and nuclear motions is discussed with special reference to high Rydberg states of molecules. An inverse separation is obtained when the rapid nuclear motion instantaneously adjusts itself to the position of the Rydberg electron. The electron moves in the potential averaged over the position of the nuclei (and their valence electrons). This inverse separation is useful when ωn³ > 1, where ω is the spacing of nuclear energy states (in au) and n is the principal quantum number of the Rydberg electron whose orbital period increases as n³. The inverse Born-Oppenheimer separation can break down owing to the finite kinetic energy of the Rydberg electron. Like the Born-Oppenheimer separation, its inverse can also be formulated in an adiabatic or a diabatic basis. The diabatic inverse Born-Oppenheimer is practical both for interpretation of zero electron kinetic energy (ZEKE) spectra and for computations. Explicit results are given for a model system of an electron orbiting a vibrating dipole, identifying the relevant coupling constants. The discussion emphasizes the radial motion and the limits discussed here are not quite equivalent to the four (or, actually, five) Hund's coupling cases relevant to angular momentum coupling schemes.