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
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.