A first principle effective Hamiltonian for including nonadiabatic effects for H[sub 2][sup +] and HD[sup +].

We compute nonadiabatic corrections for all bound and long-lived quasi-bound vibrational levels of H[sub 2][sup +] and HD[sup +] for selected rotational levels. This is done using the Bunker and Moss formalism with the correction factors computed from ab initio wave functions. The electronic wave functions are expanded in terms of nuclear centered Gaussian basis functions. The agreement with accurate calculations is very good: for H[sub 2][sup +], the root-mean-square error in the computed dissociation energies is 0.0006 cm-1, and, furthermore, most transition frequencies are predicted to within about 0.0001 cm-1. For HD[sup +], the results are not quite as good due to the uncertainties in the adiabatic correction. This paves the way for using these techniques to accurately predict the nonadiabatic effects for more complicated molecules. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]