Geometric Phase Effects in Chemical Reaction Dynamics and Molecular Spectra

Abstract

The theoretical methodology for including the effects of the geometric phase in quantum reactive scattering and bound-state calculations is reviewed. Two approaches are discussed: one approach is based on solving the standard Born−Oppenheimer equation but with double-valued boundary conditions, and the second approach is based on solving a generalized Born−Oppenheimer equation with single-valued boundary conditions. The generalized Born−Oppenheimer equation contains a vector potential which is mathematically equivalent to that of a magnetic solenoid. The recently developed numerical methodology for solving the generalized Born−Oppenheimer equation is reviewed, and several applications of this methodology in chemical reaction dynamics and molecular spectra are discussed. New results from accurate six dimensional quantum reactive scattering calculations for the D + H2(v, j) → HD(v ‘, j ‘) + H and H + H2(v, j) → H2(v ‘, j ‘) + H reactions are presented. These calculations are performed both with and without the geometric phase. The geometric phase calculations are done using both the double-valued basis set approach and vector potential approach. The effects of the geometric phase in the reaction probabilities, integral, and differential cross sections are investigated as a function of scattering energy and total angular momentum J.

New, unexpected, and dominant mechanisms in the hydrogen exchange reaction

“…Experimental agreement with quantum mechanical ͑QM͒ calculations is now so good that it is generally accepted that this prototype reaction is fully understood. [8][9][10][11] The results from different QM approaches, i.e., different time independent and different time dependent codes, have also converged to agreement. 12,13 While QM can fully reproduce experimental findings, it only has a limited ability to explain the motion of the nuclei during the reactive encounter.…”

Perspective: Ultracold molecules and the dawn of cold controlled chemistry

“…[263][264][265] The geometric phase, also known as the Berry phase, 266 results from a sign change of the adiabatic electronic wave function (typically the ground state) when the nuclei follow a closed path around a conical intersection (CI) between two electronic PESs. To keep the total wave function single-valued, a corresponding sign change must also occur on the nuclear motion wavefunction.…”

“…271,272 The H + H 2 reaction and its isotopologues have long served as benchmark systems for experimental verification of the GP effect in chemical reactions. [263][264][265][271][272][273][274][275] All of these experiments that probe GP effects involve molecules in low initial vibrational quantum numbers (mostly the v = 0 vibrational level) and high kinetic energies for the relative motion. At these high kinetic energies, a large number of partial waves or impact parameters contribute to the reaction.…”

Molecular collisions in ultracold atomic gases

“…Collisions of atoms and molecules in non-spin-stretched states will be particularly challenging, because they will involve doublet surfaces as well as quartet surfaces, and for alkali metal trimers the doublet surfaces exhibit conical intersections and geometric phase effects [100,101] that considerably complicate the dynamics.…”