General explanation of geometric phase effects in reactive systems: Unwinding the nuclear wave function using simple topology

The Journal of Chemical Physics
Stuart C Althorpe

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 reagen...Continue Reading

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Citations

Feb 9, 2007·The Journal of Chemical Physics·Juan Carlos Juanes-MarcosEckart Wrede
Apr 2, 2008·The Journal of Chemical Physics·Foudhil BouaklineDaniel Peláez Ruiz
Nov 10, 2006·The Journal of Chemical Physics·Daniel PeláezJuan Soto
Oct 15, 2013·The Journal of Chemical Physics·Justin JankunasStuart C Althorpe
Dec 20, 2012·The Journal of Chemical Physics·Ali AbediE K U Gross
Apr 2, 2008·The Journal of Chemical Physics·Frantisek KarlickýFlorent Xavier Gadéa
Oct 2, 2009·The Journal of Chemical Physics·Amit Kumar PaulSatrajit Adhikari
Sep 1, 2015·The Journal of Physical Chemistry. a·Jisha HazraNaduvalath Balakrishnan
Jun 9, 2014·The Journal of Chemical Physics·Ilya G RyabinkinArtur F Izmaylov
Aug 1, 2015·Nature Communications·B K KendrickN Balakrishnan
Jun 8, 2015·The Journal of Chemical Physics·Xiao-Dong Cui, Yujun Zheng
Oct 27, 2016·The Journal of Chemical Physics·N Balakrishnan
Dec 31, 2016·The Journal of Physical Chemistry Letters·Loïc Joubert-DoriolArtur F Izmaylov
Apr 1, 2017·Journal of Chemical Theory and Computation·Changjian XieHua Guo
Feb 3, 2018·The Journal of Chemical Physics·Brian K Kendrick
Nov 10, 2015·Physical Review Letters·B K KendrickN Balakrishnan
Aug 24, 2017·The Journal of Chemical Physics·J F E CroftB K Kendrick
Jul 31, 2021·Physical Chemistry Chemical Physics : PCCP·Marwa H FaragPengfei Huo
Jan 23, 2018·Journal of the American Chemical Society·Changjian XieHua Guo
Jun 2, 2018·The Journal of Physical Chemistry. a·Guang-Shuang-Mu LinDaiqian Xie
Oct 28, 2019·The Journal of Physical Chemistry. a·Brian K Kendrick
Apr 13, 2018·The Journal of Physical Chemistry Letters·Foudhil Bouakline

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