Geometric phase effect

Kuppermann A and Wu Y S M 1993 The geometric phase effect shows up in chemical reactions Chem. 

Mead and Truhlar [10] broke new ground by showing how geometric phase effects can be systematically accommodated in scattering as well as bound state problems. The assumptions are that the adiabatic Hamiltonian is real and that there is a single isolated degeneracy hence the eigenstates n(q-, Q) of Eq. (83) may be taken in the form... 

Figure 1. Quasiclassical cross-sections for the reaction D -I- H2 (w — 1,2 — 1) DH (v — 1, /) -f H at 1.8-eV total energy as a function of/. The solid line indicates results obtained without including the geometric phase effect. Boxes show the results with the geometric phase included using either 9o = 0 (dashed) or 9o = 11.5 " (dotted).

As demonstrated in [53] it is convenient to incorporate the geometrical phase effect by adding the vector potential in hyperspherical coordinates. Thus we found that the vector potential gave three terms, the first of which was zero, the second is just a potential term... 

In order to incorporate the geometric phase effect in a formulation based on an expansion in G-H basis functions we need to consider the operation of the momentum operator on a basis function, that is, to evaluate terms as... 

Since the geometric phase effect is related to the angle 4> we express as... 

Note that in this TDGH-DVR formulation of quantum dynamics, the inclusion of the geometric phase effects through the addition of a vector potential is veiy simple and the calculations can be carried out with about the same effort as what is involved in the ordinary scattering case. 

Figure 3 shows the results with and without including the geometric phase effect for the D + H2 reaction. The basis set is taken as 1,1,1,15,15,15, that is. 

The phase-change nale, also known as the Ben phase [101], the geometric phase effect [102,103] or the molecular Aharonov-Bohm effect [104-106], was used by several authors to verify that two near-by surfaces actually cross, and are not repelled apart. This point is of particular relevance for states of the same symmetry. The total electronic wave function and the total nuclear wave function of both the upper and the lower states change their phases upon being bansported in a closed loop around a point of conical intersection. Any one of them may be used in the search for degeneracies. 

C. Dynamical Jahn-Teller and Geometric Phase Effects... 

Vibronic Species of the Vibrational States of Li3 with Consideration of Geometric Phase Effect ... 

Figure 9. Vibrational levels of the first-excited state Lis calculated without consideration (NGP) and with consideration (GP) of geometric phase effect [12].

This relation will be used to study geometrical phase effects within the diabatic framework for the FI3 system and its two isotopic analogues. What is meant by... 

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