The electronic adiabatic-diabatic transformation matrix: A theoretical andnumerical study of a three-state system

Authors
Citation
A. Alijah et M. Baer, The electronic adiabatic-diabatic transformation matrix: A theoretical andnumerical study of a three-state system, J PHYS CH A, 104(2), 2000, pp. 389-396
Citations number
40
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physical Chemistry/Chemical Physics
Journal title
JOURNAL OF PHYSICAL CHEMISTRY A
ISSN journal
1089-5639 → ACNP
Volume
104
Issue
2
Year of publication
2000
Pages
389 - 396
Database
ISI
SICI code
1089-5639(20000120)104:2<389:TEATMA>2.0.ZU;2-Z
Abstract
In this work, we consider a diabatic 3 x 3 potential matrix which is used t o study the three adiabatic-diabatic transformation angles that form the co rresponding 3 x 3 adiabatic-diabatic transformation matrix. The three angle s are known to be solutions of three coupled first-order differential equat ions (Top, Z. H.; Baer, M. J. Chem. Phys. 1977, 66, 1363). These equations are solved here for the first time and are shown to be stable and to yield meaningful solutions. Since many sets of equations can be formed for this p urpose efforts were made to classify the various sets of equations, with th e aim of gaining more physical content for the calculated angles. The numer ical treatment was applied to a three-state diabatic potential matrix devis ed for the Nas excited states (Cocchini, F.; Upton, T. H.; Andreoni, W. J. Chem. Phys. 1988, 88, 6068). A comparison between two-state and three-state angles reveals that, in certain cases, the two-state angles contain inform ation regarding the interaction of the lower state with the upper states. H owever in general the two-state treatment may fail in yielding the correct topological features of the system. One of the main results of this study i s that the adiabatic-diabatic transformation matrix, upon completion of a c ycle, becomes diagonal again with the numbers ii in its diagonal.