Mulliken theory of charge transfer

The extent to which steric effects adversely affect the attainment of such intimate ion-pair structures would be reflected in an increase in the work term and concomitant diminution of the inner-sphere rate. This qualitative conclusion accords with the reactivity trend in Figure 16. However, Marcus theory does not provide a quantitative basis for evaluating the variation in the work term of such ion pairs. To obtain the latter we now turn to the Mulliken theory of charge transfer in which the energetics of ion-pair formation evolve directly, and provide quantitative informa-... 

According to the Mulliken theory of charge transfer complexes, the vertical electron affinity (VEa) of an acceptor and the vertical ionization potential (VIP) of a donor are related to the energy of maximum absorption of the complex (Ect) by the following equation ... 

In the same year as that of the proposal of the frontier-electron theory, the theory of charge-transfer force was developed by Mulliken with regard to the molecular complex formation between an electron donor and an acceptor 47>. In this connection he proposed the "overlap and orientation principle 48> in which only the overlap interaction between the HO MO of the donor and the LU MO of the acceptor is considered. 

The theory of charge transfer complexes relates the maximum in the absorption spectrum, the charge transfer energies Ect, and energies for complex formation AGct to the vertical ionization potential of the donor and the vertical electron affinities of the acceptor. The relationship uses constants related to the geometry of the complexes. Mulliken described the theory of charge transfer as follows ... 

A simple theoretical treatment of ET transitions in ferrous, cuprous and ferric phen complexes was given by Day and Sanders 90,119). This treatment is based on Murrell s one-electron system approximation 120) to Mulliken s theory of charge transfer complexes (727). To a zero order, ground and excited states wave functions are represented by the orbitals of the "donor and acceptor , respectively. For d-t-n, inverted ET, the transition energy is given by... 

Mulliken s theory of charge-transfer spectra predicts that for weak complexes the molar extinction coefficient of the charge-transfer band should be low. There have been many difficulties in demonstrating this expectation exper-... 

It is important to recognize that the intermolecular long-distance bonding with the participation of halogen derivatives represents a specific example of the broad general area of donor/acceptor interactions. Moreover, the complexes of molecular iodine, bromine and chlorine with aromatic donors represent classic examples of charge-transfer compounds [26-28] that are vital for the development of Mulliken theory of intermolecular association [29-31]. The latter thus provides the convenient framework for the... 

Some people argue that Lewis acids should be called electron-pair acceptors and the bases electron-pair donors. This may be concentrating the attention on electron pairs in chemistry more than they deserve M.O. theory suggests a much more nuanced view, and there is no sense in which exactly six electron pairs are involved in the bonding of CrFs" and IrFe according to spectroscopic observations (20). On the other hand, to call Lewis acids and bases simply acceptors and donors invite to confusion with Mulliken s t57pical charge-transfer complexes 37). 

The positive S.P. observed when gases are adsorbed on a metal surface has been atrributed to (a) polarization of the adsorbate by the electron field of the metal double layer 73) and (6) charge-transfer effects 103). The importance of charge-transfer forces has been stressed by Mulliken 87) in his general theory of donor-acceptor interaction. If, as suggested, these charge-transfer forces contribute to the van der Waals attraction, then they probably take part in the physical adsorption process. The complex M X resulting from the adsorption of an inert gas on a metal surface M has been described as essentially no-bond with a small contribution from the structure As seen in Table VI, the S.P., and hence... 

BHandHLYP density functional theory DFT calculations combined with the 6-31G(d) basis set have been used throughout this paper. The Mulliken charges partitioning scheme was used to quantify the amount of charge transfer between molecules. 

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). 

The discovery of charge-transfer bands in the UV spectra of diiodine complexes (Benesi and Hildebrand, 1949) [202] and the development of the underlying theory (Mulliken, 1952) [31] initiated a wealth of thermodynamic and spectroscopic measurements on diiodine complexes, mainly in the period 1949-1980. Complementary measurements by Berthelot, Guiheneuf, Laurence et al. (1970-2002) and Abboud et al. (1973-2004) enabled a homogeneous scale of diiodine basicity to be constructed. In addition, recommended values of diiodine affinity have been compiled from the literature (Laurence, 2006), for comparison with the SbCls, BF3 and 4-FC6H4OH affinity scales. UV and/or IR shifts upon complexation of the acids h, ICl and ICN have also been systematically measured by Berthelot, Laurence, Nicolet et al. (1981-1985). These thermodynamic and spectroscopic scales will allow the recent concept of a halogen bond to be treated quantitatively. They can be found in Chapter 5. 

The authors [33] have elucidated the linear dependence of Ao0 (z-dep) on E for the polyanions by a quantum chemical consideration. A model Hamiltonian approach to the charge transfer (CT) interaction between a polyanion and solvents has been made on the basis of the Mulliken s CT complex theory [34]. 

Electron-transfer mechanism for nucleophilic addition. In accord with Mulliken theory, irradiation of the charge-transfer band of [Py+, BMeT] directly affords the radical pair via one-electron transfer (equation 46). 

The UV-vis spectral analysis confirms the appearance of a new charge-transfer absorption band of the complexes of colorless a-donors (R3MH) and the n-acceptor (TCNE). In accord with Mulliken theory, the absorption maxima (Act) of the [R3MH, TCNE] complexes shift toward blue with increasing ionization potential of the metal hydrides (i.e., tin > germanium > silicon) as listed in Table 8. 

Electron transfer mechanism. In accord with the Mulliken theory, photoexcitation of the charge-transfer band effects the formation of a contact ion radical pair, which undergoes a rapid mesolytic scission of the M—H bond (equation 52). 

Similar vivid colorations are observed when other aromatic donors (such as methylbenzenes, naphthalenes and anthracenes) are exposed to 0s04.218 The quantitative effect of such dramatic colorations is illustrated in Fig. 13 by the systematic spectral shift in the new electronic absorption bands that parallels the decrease in the arene ionization potentials in the order benzene 9.23 eV, naphthalene 8.12 eV, anthracene 7.55 eV. The progressive bathochromic shift in the charge-transfer transitions (hvct) in Fig. 13 is in accord with the Mulliken theory for a related series of [D, A] complexes. 

The electron-transfer paradigm in Scheme 1 (equation 8) is subject to direct experimental verification. Thus, the deliberate photoactivation of the preequilibrium EDA complex via irradiation of the charge-transfer absorption band (/ vCT) generates the ion-radical pair, in accord with Mulliken theory (equation 98). 

Evaluation of the Work Term from Charge Transfer Spectral Data. The intermolecular interaction leading to the precursor complex in Scheme IV is reminiscent of the electron donor-acceptor or EDA complexes formed between electron donors and acceptors (21). The latter is characterized by the presence of a new absorption band in the electronic spectrum. According to the Mulliken charge transfer (CT) theory for weak EDA complexes, the absorption maximum hv rp corresponds to the vertical (Franck-Condon) transition from the neutral ground state to the polar excited state (22). 

According to Mulliken (1952a,b Mulliken and Person, 1969), the formation of the ion radical pair occurs upon the irradiation of the charge-transfer band of the EDA complex (2). The experimental proof of Mulliken theory is... 

---