Mulliken-Hush

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. 

SMOOTHNESS OF THE ELECTRONIC DIPOLE MOMENT AND THE GENERALIZED MULLIKEN-HUSH APPROACH... 

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]. 

R. J. Cave and M. D. Newton, Generalization of the Mulliken-Hush treatment for the calculation of electron transfer matrix elements, Chem. Phys. Lett., 249 (1996) 15-19. 

H.-C. Chen and C.-P. Hsu, Ab initio characterization of electron transfer coupling in photoin-duced systems generalized Mulliken-Hush with configuration-interaction singles, J. Phys. Chem. A, 109 (2005) 11989-11995. 

Equations [140]-[143] provide a connection between the preexponential factor entering the nonadiabatic ET rate and the spectroscopically measured adiabatic transition dipole mu- It turns out that the Mulliken-Hush matrix element, commonly considered as an approximation valid for m b = 0, enters exactly the rate constant preexponent as long as the non-Condon solvent effects are accurately taken into account. Equation [142] stresses the importance of the orientation of the adiabatic transition dipole relative to the direction of ET set up by the difference diabatic dipole Am. The value of is zero when the vectors mi2 and Am are perpendicular. 

Comparison of Thermal and Optical Processes The Mulliken-Hush model... 

The generalized Mulliken-Hush model and formulation of diabatic states... 

The Mulliken-Hush expression is a particular form of the more general equation... 

We note that, for CT transitions, the expression for /fab is not needed if the Mulliken-Hush approach is used to calculate H h from experimental quantities as discussed in Section 1.3.4. Also, the generalized Mulliken-Hush treatment [32, 33] allows the calculation of //ab from the adiabatic wavefunctions and the complete Hamiltonian the extension of Eq. 56 to include more than two states is then used to obtain Hub-... 

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 resonance integral in equation (23) can be obtained from experimental data using the Mulliken-Hush relation... 

Equations (23) and (24) presume a knowledge of the relevant electronic states, either the charge-localized diabatic states (pA and b or the adiabatic states Fi and 4 2 (equation 8). Typically, diabatic states are natural for studying electron transfer, whereas the adiabatic states are used for optical transitions. The generalized Mulliken-Hush approximation adopts the definition of diabatic states that are diagonal with respect to the component of the dipole moment operator along... 

Wul-6 (In contrast to Marcus-Hush which refers to the theory of electron transfer activation, the Mulliken-Hush equation describes the preexponential factor of the rate constant. We spell out Mulliken-Hush each place it occurs in this chapter and use the acronym MH to refer to only Marcus-Hush.) In practice, however, FCWD(O) cannot be extracted from experimental spectra, and one needs a theoretical model to calculate FCWD(O) from experimental band shapes measured at the frequencies of the corresponding electronic transitions. This purpose is achieved by a band shape analysis of optical lines. 

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