Mulliken-Hush formula

The general features of the nonadiabatic coupling and its relation to molecular properties are surveyed. Some consequences of the equation of motion , formally expressing a smoothness of a given molecular property within the diabatic basis, are demonstrated. A particular emphasis is made on the relation between a smoothness of the electronic dipole moment and the generalized Mulliken-Hush formula for the diabatic electronic coupling. 

Mulliken-Hush formula for the diabatic electronic coupling. We suggest that the latter approach might be rather useful to thoroughly investigate multistate effects on the electronic diabatic coupling recently pursued by Cave and co-workers [66]. 

If the only change in the molecular charge distribution between the states a and b is the position of the transferred electron (i.e. if we assume that the other electrons are not affected) then rab is the transfer distance, that is, the separation between the donor and acceptor centers. Eq. (16.97) is known as the Mulliken-Hush formula. 

The other techniques can be divided into a few categories (see also Ref. [14c]). One of them goes back to the idea first coined by Mulliken [41], Hush [42] and Lichten [8] of using molecular properties to determine the diabatic basis and is actually based on the Werner-Meyer-Macfas-Riera formula [32,33] for the adiabatic-to-diabatic mixing angle in terms of electronic dipole moments. This... 

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