Meade

Mead R D, Stevens A E and Lineberger W C 1984 Photodetachment in negative ion beams Gas Phase Ion Chemistry ed M T Bowers (New York Academic)... 

Mead C A and Truhlar D G 1982 Conditions for the definition of a strictly diabatic electronic basis for molecular systems J. Chem. Rhys. 77 6090... 

Mead C A and Truhlar D G 1979 On the determination of Born-Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei J. Chem. Phys. 70 2284... 

Joannopoulos J D, Meade R D and Wnn J N 1995 Photonic Orystais (Princeton, NJ Princeton University Press)... 

The next significant development in the history of the geomebic phase is due to Mead and Truhlar [10]. The early workers [1-3] concenbated mainly on the specboscopic consequences of localized non-adiabatic coupling between the upper and lower adiabatic elecbonic eigenstates, while one now speaks... 

More general situations have also been considered. For example. Mead [21] considers cases involving degeneracy between two Kramers doublets involving four electronic components a), a ), P), and P ). Equations (4) and (5), coupled with antisymmetry under lead to the following identities between the various matrix elements... 

While the presence of sign changes in the adiabatic eigenstates at a conical intersection was well known in the early Jahn-Teller literature, much of the discussion centered on solutions of the coupled equations arising from non-adiabatic coupling between the two or mom nuclear components of the wave function in a spectroscopic context. Mead and Truhlar [10] were the first to... 

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... 

We now consider the connection between the preceding equations and the theory of Aharonov et al. [18] [see Eqs. (51)-(60)]. The tempting similarity between the structures of Eqs. (56) and (90), hides a fundamental difference in the roles of the vector operator A in Eq. (56) and the vector potential a in Eq. (90). The fomrer is defined, in the adiabatic partitioning scheme, as a stiictly off-diagonal operator, with elements (m A n) = (m P n), thereby ensuring that (P — A) is diagonal. By contiast, the Mead-Truhlar vector potential a arises from the influence of nonzero diagonal elements, (n P /i) on the nuclear equation for v), an aspect of the problem not addressed by Arahonov et al. [18]. Suppose, however, that Eq. (56) was contracted between (n and n) v) in order to handle the adiabatic nuclear dynamics within the Aharonov scheme. The result becomes... 

The upshot is that Eq. (95) goes over precisely to the kinetic energy part of Eq. (90). Despite some phrases in the introduction to Aharonov et al. [18] there is therefore no fundamental contradiction with Mead and Truhlai [10]. 

It is beyond the scope of these introductory notes to treat individual problems in fine detail, but it is interesting to close the discussion by considering certain, geometric phase related, symmetry effects associated with systems of identical particles. The following account summarizes results from Mead and Truhlar [10] for three such particles. We know, for example, that the fermion statistics for H atoms require that the vibrational-rotational states on the ground electronic energy surface of NH3 must be antisymmetric with respect to binary exchange... 

Note that Mead and Truhlar [10] employ the symbol 0 in place of the present [Pg.29]

Mead and Truhlai [10] further demonstrate that the real adiahatic eigenstates close to S = 0 behave in the AB representation as... 

Finally, following Mead and Truhlar [10], it may be seen that an interchange of A and B is equivalent to a sign reversal of <() followed by a rotation perpendicular to the AB bond, under the latter of which Aab) is invariant and Fab) changes sign. The net effect is therefore to induce the tiansitions... 

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