Classification of topological effects in molecular systems

This article discusses two subjects which are shown to be closely connected. The first subject concerns the existence of pure diabatic states and the derivation of an adiabatic-to-diabatic matrix within a sub-Hilbert space. If certain requirements are fulfilled this sub-space behaves, for all practical purposes, like a full Hilbert space. The second concerns the necessary condition for having uniquely defined diabatic potentials. Fulfillment of this condition has led to the introduction of a matrix – the Topological matrix – which was found to contain the topological features of a given system. In the present Letter, the study of the topological matrix is extended to reveal new features.