Mulliken theory

In Chapter 3, we studied the topic of population analysis. In population analysis, we attempt a rough-and-ready numerical division of the electron density into atom and bond regions. In Mulliken theory, the bond contributions are divided up equally between the contributing atoms, giving the net charges. The aim of the present section is to answer the questions Are there atoms in Molecules , and if so, How can they be defined . According to Bader and coworkers (Bader, 1990) the answers to both questions are affirmative, and the boundaries of these atoms are determined by a particular property of the electron density. 

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... 

The Mulliken theory of overlap and orientation principle (cf. Chap. 2) predicts that stabilization in the molecular complex formation should essentially be determined by the overlap of the donor HO and the acceptor LU. The iodine complex of trimethylamine will take the form... 

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). 

The energetics of electron transfer is quantitatively evaluated by Mulliken theory (AvCT = IP — EA + V). 

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 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... 

Different approaches have also been proposed. For instance, Painelli et al. [23] have expressed the frequency-dependent conductivity of dimerized and trimerized organic conductors on the base of vibronic adiabatic Mulliken theory. They have shown that the calculated spectrum is virtually identical to the one obtained from linear response theory. 

Explain the primary difference between the Heitler-London and Hund-Mulliken theories of covalent bonding. 

According to Mulliken theory [14-16], the energy gap ( ct) of the charge-transfer transition from the ground state to the excited ion-pair state determines the wavelength position of the CT absorption band (/Ict), i.e. E ct = hvci = hc/lci-This energy gap directly depends on the ionization potential IP) of the donor and the electron affinity [EA] of the acceptor, (Eq. 8) ... 

Most importantly, the organometallic donor-acceptor complexes and their electron-transfer activated reactions discussed in this review are ideal subjects to link together two independent theoretical approaches, viz. the charge-transfer concept derived from Mulliken theory [14-16] and the free-energy correlation of electron-transfer rates based on Marcus theory [7-9]. A unifying point of view of the inner-sphere-outer-sphere distinction applies to charge-transfer complexes as well as electron-transfer processes in organometallic chemistry. 

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