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

Journal of Chemical Physics
 Pub Date:
 October 2002
 DOI:
 10.1063/1.1515768
 Bibcode:
 2002JChPh.117.7405B
 Keywords:

 BornOppenheimer Approximation;
 Eigenvalues;
 Eigenvectors;
 Electronic Structure;
 Group Theory;
 Hamiltonian Functions;
 Quantum Mechanics;
 Quantum Theory;
 Wave Functions;
 31.10.+z;
 03.65.Fd;
 03.65.Ta;
 02.20.Uw;
 Atomic and Molecular Physics;
 Theory of electronic structure electronic transitions and chemical binding;
 Algebraic methods;
 Foundations of quantum mechanics;
 measurement theory;
 Quantum groups