Journal - The Journal of chemical physics (United States )

Abstract :

Semiclassical instanton theory gives an approximate description of deep tunneling by means of periodic orbits on the inverted potential energy surface. There are two versions of the theory, one derived by taking a semiclassical limit of the exact flux-side time-correlation function and the other by starting from the "Im F" premise, in which the partition function is analytically continued into the complex plane. Here, we provide a derivation showing that the two versions of the theory are exactly equivalent. Unlike a previous derivation (which was restricted to a system-bath model), our derivation is completely general, and thus establishes that the "Im F" premise, which is behind such methods as quantum transition-state theory and ring polymer molecular dynamics rate-theory, is correct in the steepest-descent limit.

Journal - Science (New York, N.Y.)

Journal - The Journal of chemical physics (United States )

Abstract :

A recent approach [S. C. Althorpe, J. Chem. Phys. 124, 084105 (2006)] for interpreting geometric phase (GP) effects in a nuclear wave function confined to the lower of two conically intersecting potential energy surfaces is extended to treat coupled dynamics on both surfaces. The approach is exact, and uses simple topology to separate the wave function into contributions from Feynman paths that wind different numbers of times, and in different senses, around the conical intersection. We derive the approach first, by mapping the time-dependent wave packet describing the coupled dynamics onto a double space, and second, by classifying the Feynman paths within a time-ordered expansion of the path integral. The approach is demonstrated numerically for a simple Exe Jahn-Teller system and for a model of the (1)B(1)-S(0) intersection in pyrrole. The approach allows one to investigate and interpret the effect of the GP on population transfer between the surfaces, and also to extract contributions to the coupled nuclear wave function from different reaction paths.

Journal - The Journal of chemical physics (United States )

Abstract :

We describe a simple topological approach which was used recently to explain geometric phase (GP) effects in the hydrogen-exchange reaction [Juanes-Marcos et al., Science 309, 1227 (2005)]. The approach is general and applies to any reactive system in which the nuclear wave function encircles a conical intersection (CI) and is confined to one adiabatic surface. The only numerical work required is to add and subtract nuclear wave functions computed with normal and GP boundary conditions. This is equivalent to unwinding the nuclear wave function onto a double cover space, which separates out two components whose relative sign is changed by the GP. By referring to earlier work on the Aharanov-Bohm effect, we show that these two components contain all the Feynman paths that follow, respectively, an even and an odd number of loops around the CI. These two classes of path are essentially decoupled in the Feynman sum, because they belong to different homotopy classes (meaning that they cannot be continuously deformed into one another). Care must be taken in classifying the two types of path when the system can enter the encirclement region from several different start points. This applies to bimolecular reactions with identical reagents and products, for which our approach allows a symmetry argument developed by Mead [J. Chem. Phys. 72, 3839 (1980)] to be generalized from nonencircling to encircling systems. The approach can be extended in order to unwind the wave function completely onto a higher cover space, thus separating contributions from individual winding numbers. The scattering boundary conditions are ultimately what allow the wave function to be unwound from the CI, and hence a bound state wave function cannot be unwound. The GP therefore has a much stronger effect on the latter than on the wave function of a reactive system.

Journal - PNAS

Abstract :

We have measured differential cross sections (DCSs) for thevibrationally inelastic scattering process H + o-D2(v = 0, j= 0,2) H + o-D2(v' = 1–4, j' even). Several differentcollision energies and nearly the entire range of populatedproduct quantum states are studied. The products are dominantlyforward-scattered in all cases. This behavior is the oppositeof what is predicted by the conventional textbook mechanism,in which collisions at small impact parameters compress thebond and cause the products to recoil in the backward direction.Recent quasiclassical trajectory (QCT) calculations examiningonly the o-D2(v' = 3, j') products suggest that vibrationallyinelastic scattering is the result of a frustrated reactionin which the D—D bond is stretched, but not broken, duringthe collision. These QCT calculations provide a qualitativeexplanation for the observed forward-scattering, but they donot agree with experiments at the lowest values of j'. The presentwork shows that quantum mechanical calculations agree closelywith experiments and expands upon previous results to show thatforward-scattering is universally observed in vibrationallyinelastic H + D2 collisions over a broad range of conditions.1Present address: Department Chemie und Biochemie, Ludwig-Maximilians-UniversitätMünchen, Butenandtstrasse 5-13, Haus F, 81377 Munich, Germany. The authors declare no conflict of interest. This article is a PNAS Direct Submission. This article contains supporting information online at www.pnas.org/cgi/content/full/0807942105/DCSupplemental.© 2008 by The National Academy of Sciences of the USA