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An optimal adiabatic-to-diabatic transformation of the 1 2A[prime] and 2 2A[prime] states of H3

Abrol, Ravinder and Kuppermann, Aron (2002) An optimal adiabatic-to-diabatic transformation of the 1 2A[prime] and 2 2A[prime] states of H3. Journal of Chemical Physics, 116 (3). pp. 1035-1062. ISSN 0021-9606. http://resolver.caltech.edu/CaltechAUTHORS:ABRjcp02

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Abstract

Molecular reaction dynamics in the adiabatic representation is complicated by the existence of conical intersections and the associated geometric phase effect. The first-derivative coupling vector between the corresponding electronically adiabatic states can, in general, be decomposed into longitudinal (removable) and transverse (nonremovable) parts. At intersection geometries, the longitudinal part is singular, whereas the transverse part is not. In a two-electronic-state Born–Huang expansion, an adiabatic-to-diabatic transformation completely eliminates the contribution of the longitudinal part to the nuclear motion Schrödinger equation, leaving however the transverse part contribution. We report here the results of an accurate calculation of this transverse part for the 1 2A[prime] and 2 2A[prime] electronic states of H3 obtained by solving a three-dimensional Poisson equation over the entire domain [sans-serif U] of internal nuclear configuration space [script Q] of importance to reactive scattering. In addition to requiring a knowledge of the first-derivative coupling vector everywhere in [sans-serif U], the solution depends on an arbitrary choice of boundary conditions. These have been picked so as to minimize the average value over [sans-serif U] of the magnitude of the transverse part, resulting in an optimal diabatization angle. The dynamical importance of the transverse term in the diabatic nuclear motion Schrödinger equation is discussed on the basis of its magnitude not only in the vicinity of the conical intersection, but also over all of the energetically accessible regions of the full [sans-serif U] domain. We also present and discuss the diabatic potential energy surfaces obtained by this optimal diabatization procedure.


Item Type:Article
Additional Information:©2002 American Institute of Physics. (Received 31 July 2001; accepted 1 October 2001) This work was supported in part by NSF Grant No. CHE 9810050. The authors thank Mr. Prashant Purohit for suggesting the derivation given in the Appendix.
Subject Keywords:hydrogen neutral molecules; molecular electronic states; Schrodinger equation; Poisson equation; potential energy surfaces
Record Number:CaltechAUTHORS:ABRjcp02.pdf
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:ABRjcp02
Alternative URL:http://dx.doi.org/10.1063/1.1419257
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1139
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:22 Dec 2005
Last Modified:26 Dec 2012 08:42

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