Mulliken-Hush theory

In a recent study, Curtis and coworkers (34) developed an analysis of electronic coupling in mixed-valence complexes that combines electrochemical results with an extension of Mulliken s theory of donor-acceptor interactions. The approach was applied to class II and near class III complexes. It was found that the degree of electronic coupling in these systems is at least three times that which would be predicted based solely on spectroscopic measurements (Eq. 15 of the Hush model). However, the electronic coupling determined for complexes that were very close to, if not of, class III character was significantly smaller than that predicted by Eq. (16). 

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. 

Hush applied Mulliken s theories of the transition dipole moment of charge transfer bands to the specific question of IT bands in mixed-valence complexes. By equating theoretical and experimental expressions for /, where / is the oscillator strength of the intervalence band, it is possible to derive an expression for metal-metal coupling (//ad). 

Several approaches are available in the literature to generate and evaluate Hamiltonian matrix elements with wavefunctions of charge-localized, diabatic states. They differ in the level of theory used in the calculation and in the way localized electronic structures are created [15, 25, 26, 29-31]. When wavefunction-based quantum-chemical methods are employed, the framework of the generalized Mulliken-Hush method (GMH) [29, 32-34], is particularly successful. So far, it has been used in conjunction with accurate electronic structure methods for small and medium sized systems [35-37]. As an alternative to GMH and other derived methods [38, 39], additional methods have been explored for their applicability in larger systems such as constrained density functional method (CDFT) [25, 37, 40, 41], and fragmentation approaches [42-47], which also include the frozen density embedding (FDE) method [48, 49]. 

The theory of photoinduced electron transfer is based on the classical work of Marcus, Hush, Mulliken, Murrell and many others and it has been extensively reviewed in Chapter 1 of Part 1. The study of isolated, ultra-cold systems provides an opportunity to check some of the basic assumptions of these theories. In particular, one can easily discriminate between different structural isomers of a given system... 

Since V b plays a central role in the theory, its determination in the largest possible series of compounds is of great interest. In a two-state model, a simple evaluation of the transition moment, using Mulliken s approach of donor acceptor systems, yields Hush s (1967) equation [38bj ... 

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