Experimental and calculational consequences of phases in molecules with multiple conical intersections

Abstract

ABSTRACT:We set up a theoretical model for treating several degeneracies between two adjacent potential energy surfaces in molecular systems, e.g., cases of four (or more) conically intersecting degeneracies, located in a plane formed by two-fold molecular displacement coordinates, in trigonal (or cubic) symmetry and twin conical intersections (CIs) for molecules with two-fold symmetries. When the system circles (in a time-variant manner) entirely inside or entirely outside these CIs, it picks up phases (the geometric phases) that are zero or 2N. Here, N is (to a good approximation) an integer whose value depends on the Hamiltonian for the system, on the distance of circling from the CI, and on the speed of circling. For the adiabatic (slow circling) limit, we develop a simple algebraic-graphical method that yields the value of N in each case. Even in this limit, the value of N is model dependent and is not uniquely given by the number of CIs that are circled. Further, we suggest an experiment (based on a pumpprobe method) for tracing the time development of a system that is subject to a periodically varying field carrying it around the CI. The experiment leads to relations between the spectroscopic transition strengths and state amplitudes, such that the (open-path) phases are fully given (including the additive 2N term and excluding the dynamic phase). Finally, we compare geometric phases that differ by integral multiples of 2 and, therefore, cannot be distinguished by phase interference. We show that the different cases have, nevertheless, observational correlates in the number of times that zero or unity occurs in a wave function component amplitude during circling. The rules of correspondence are given.

A study of conical intersections for the H3+ system

“…[10][11][12][13][14][15][16][17] In our present calculations, we used the flexibility of the DIM approach to eliminate unnecessary discrepancies with ab initio results. As we shall see, since the conical regions lie at infinite distances, they do not give rise to geometrical phases 7-9 since nuclear paths do not surround the seams.…”

The Berry phase revisited: application to Born–Oppenheimer molecular systems

“…For the Berry phases we got the value of 3π whereas we expected it to be π . It could very well be that these two phenomena may result from an as yet unexposed cause that eventually can be identified in the future (see discussion on this issue in [51]).…”

Fisher Information Perspective of Pauli’s Electron

“…The above statement is equivalent to taking a Clebsch representation of the velocity field but with α = β = 0. In that case, following Equation (20), one can describe the fluid mechanical system with the following Lagrangian density:…”

“…The Lagrangian L P has the same form as the Clebsch Lagrangian L given in Equation (20). However, there are some important differences.…”

“…This equation is based on a two-dimensional operator Hamiltonian matrix. The two-dimensional operator Hamiltonians matrices are currently abundant in the literature ( [9][10][11][12][13][14][15][16][17][18][19][20][21][22]) and describe many types of quantum systems. It is natural to inquire whether such a theory can be given a fluid dynamical interpretation.…”