Artifacts in the adiabatic approximation

Generally, the adiabatic approximation is defined via a projection onto an adiabatically moving electronic base. The Hamiltonian then is separated into three constituents (‘‘adiabatic,’’ ‘‘diagonal-nonadiabatic,’’ ‘‘nondiagonal-nonadiabatic’’). A model system is considered for which the correct zero-order eigenfunctions are known. It is shown that with these any single of the three Hamiltonian constituents yields diverging expectation values; only their sum yields convergence. From this the conclusion seems stringent that any result pertaining to electronic transitions, which is based on the adiabatic approximation, is an artifact.