Nonadiabatic quantum Liouville and master equations in the adiabatic basis

A compact form of nonadiabatic molecular Hamiltonian in the basis of adiabatic electronic states and nuclear position states is presented. The Hamiltonian, which includes both the first and the second derivative couplings, is hermitian and thus leads to a standard expression for the quantum Liouville equation for the density operator. With the application of a projection operator technique, a quantum master equation for the diagonal components of the density operator is derived. Under the assumption that nuclear states are much more short ranged compared to electronic states and assuming no singularity, a semi-adiabatic approximation is invoked, which results in expressions for the nonadiabatic molecular Hamiltonian and the quantum Liouville equation that are much more amenable to advanced quantum dynamics calculation. The semi-adiabatic approximation is also applied to a resonance energy transfer system consisting of a donor and an acceptor interacting via Coulomb terms, and explicit detailed expressions for exciton-bath Hamiltonian including all the non-adiabatic terms are derived.