  We derive an electron-vibration model Hamiltonian in a quantum chemical
framework, and explore the extent to which such a Hamiltonian can capture key
effects of nonadiabatic dynamics. The model Hamiltonian is a simple two-body
operator, and we make preliminary steps at applying standard quantum chemical
methods to evaluating its properties, including mean-field theory, linear
response, and a primitive correlated model. The Hamiltonian can be compared to
standard vibronic Hamiltonians, but is constructed without reference to
potential energy surfaces, through direct differentiation of the one- and
two-electron integrals at a single reference geometry. The nature of the model
Hamiltonian in the harmonic and linear-coupling regime is investigated for
pyrazine, where a simple time-dependent calculation including
electron-vibration correlation is demonstrated to exhibit the well-studied
population transfer between the S$_2$ and S$_1$ excited states.
