Born–Oppenheimer invariants along nuclear configuration paths

摘要: Whenever a quantum chemist extracts the eigenstate of an electronic Hamiltonian, he makes, consciously or not, decision concerning phase wave function. This is done for each calculated state at nuclear position. Thus defines Born–Oppenheimer (BO) frame reference. There no absolute just as there position time in mechanics. leads naturally to question: What are quantities which do not depend on arbitrary phases, i.e., what BO invariants? In this article we identify invariants with respect path configuration space. We invariant states along these paths and their Aharonov–Anandan geometric phases. For closed loops passing through energy degeneracies adiabatic functions phases Berry The results establish rigorous relations between full nonadiabatic couplings matrix