Perspective on “Some recent developments in the theory of molecular energy levels”

Abstract

Conical intersections of two potential-energy surfaces have the obvious, but important, effect of facilitating radiationless decay of the excited state. They. also have a less obvious, but potentially more general, impact on single and multisurface dynamics through the geometric phase effect. The geometric phase effect, the subject of this perspective, requires that the adiabatic electronic wavefunction, real-valued and continuous with respect to nuclear coordinates, change sign when transported along a closed loop — a pseudorotation path — surrounding a single point of conical intersection. This was discovered by Longuet-Higgins in 1958 and carefully described in papers between 1958 and 1963. In the title article Longuet-Higgins demonstrates, in the context of a theoretical exposition of the dynamic Jahn—Teller (and Renner—Teller) effects, the connection between conical intersections and the geometric phase effect, and establishes the consequences of the geometric phase effect in nuclear dynamics. Since that time appreciation of the importance of the geometric phase effect has increased enormously aided in no small measure by Berry’s 1984 work that established the role of the geometric phase effect in general adiabatic processes. That work spurred research in areas well outside the realm of molecular spectroscopy/dynamics. However, recent work demonstrating the prevalence of conical intersections of two Born—Oppenheimer states of the same symmetry suggests that conical intersections and the geometric phase effect will be issues of significant importance in molecular/ chemical dynamics in the next century.