Understanding failures in electronic structure methods arising from the geometric phase effect

Abstract

The geometric phase effect arises from the dependence on the nuclear coordinates in the electronic Hamiltonian, leading to sign changes of the electronic wave functions upon traversal of certain paths in nuclear configuration space. The geometric phase effect can have important consequences for the electronic structure problem, but this fact has largely gone unnoticed. We show how the geometric phase effect can significantly impact the accuracy of approximate electronic structure methods. In particular, we prove that for paths that enclose a conical intersection, any component of the wave function (such as an approximation to it) must vanish exactly, unless the associated conical intersections of the component and the wave function coincide. This has implications for methods that employ intermediate normalization, where the contribution along a reference wave function is fixed. We demonstrate numerically that the failure to account for the phase effect leads to asymptotic discontinuities in the wave function parameters. This results in breakdowns in coupled cluster methods or perturbation theories converging to excited states rather than the ground state. The global nature of the geometric phase effect means that these failures can span extended regions of nuclear configuration space, including regions far away from any conical intersection.