Absorption Mulliken theory

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. 

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). 

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) ... 

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 ... 

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). 

This system (see Fig. 17) is unique in many aspects of the structure and dynamics and has historic roots for nearly 50 years since the seminal works by Hildebrand and Mulliken. Mixing of benzene and iodine results in a new color, a new absorption spectrum, and a new theory. 

No evidence was found from the picosecond absorption data for an excited state intermediate of the EDA complex. This formulation represente a confirmation of Mulliken s theory, in which CT band excitation of the quite nonpolar ground state produces an ion pair. Accordingly, indene and TCNE form ground state complexes which undergo fast electron transfer on irradition. However, back electron transfer occurs after relatively long time (ca. 500 ps) via a transient... 

It has been shown recently by Kapturkiewicz and co-workers [14] that the analysis of the CT absorption CT <— So and the radiative and radiationless charge recombination processes CT So (Figure 4) in selected D-A n-n interacting systems sterically hindered to coplanarity (such as 9-anthryl and 9-acridyl derivatives of aromatic amines [14a,b], carbazol-9-yl derivatives of aromatic nitriles [14c] and ketones [14d] and D-A derivatives of indoles [14e] or phenoxazines and phe-nothiazines [14f]) in terms of the theory of photoinduced ET processes in absorption [52, 53] and emission [53-55] and Mulliken and Murrell models of molecular CT complexes [56, 57] leads to the determination of the quantities relevant for the rate of the radiative ET processes (exemplified by the CT absorption and emission) and to the estimation of the electronic structure and molecular conformation of the states involved in the photoinduced ET. A similar approach can be applied to describe the properties of the fluorescent singlet CT states and phosphorescent triplet CT states [58]. It should be pointed out that the relatively large values of the electronic transition dipole moments of the CT fluorescence indicate a non-... 

Solutions of a mixture of an electron donor D, such as hexamethylbenzene (40), and an electron acceptor A, such as chloranil (41), often exhibit an absorption band that is not present in solutions of the pure components. This band has been assigned to an electron transfer from the donor to the acceptor and is therefore referred to as a donor-acceptor or a CT (charge transfer) transition. Mulliken (1952) has developed a theory of CT transitions which can be summarized as follows If the ground configuration and the polar configuration produced by electron transfer are described by wave functions and ,, i, respectively, the interaction of these two configurations... 

An extensive study has recently been made of [WgXgXg]2- clusters, comparing DF theory, Huckel MO results, an experimental luminescence and absorption bands [101]. Here we focus mainly on the NR vs R consequences. The Mulliken populations and net atomic charges of the [WgXgX ]2 clusters obtained from NR and R DV calculations are presented in Table VI. The symmetry type of the frontier orbitals and the gap between the HOMO and LUMO are summarized in Table VII experimental absorption edge and emission maxima are also included. The atomic orbital compositions of the HOMO and LUMO from the two calculations differ primarily in their W 5d content, in the order NR> R as expected. 

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 ... 

The theory for Mulliken charge transfer complexes is essentially the same as the Marcus theory applied to excited state electron transfer (ET). Typical for the absorption spectrum of a Mulliken charge transfer complex is additional absorption at quite low energy, absorption that does not exist in the pure substances (Figure 18.5). 

PMDA is a well-known low molecular weight strong electron acceptor in a large number of studies on CTCs. Fig. 2 shows the plot of the peak wavenumber in CT absorption bands (Ami) vs the values 7p [11 -15] of the donor components in the PMD A-aromatic hydrocarbon systems reported in the literature [ 10,16-26]. A good linear relationship was observed according to Mulliken s theory for weak CTCs [27-29] ... 

A nearly universal feature of EDA complexation is the presence of new absorption bands in the electronic spectrum of the complex that are not found in the spectrum of uncomplexed donor or acceptor [137-140]. These spectral bands are observed even in cases where no other evidence of complexation exists, i.e., where Keda is too small to measure. The charge-transfer resonance theory of Mulliken [141] was originally formulated to account for these striking spectral features. According to Mulliken, the ground-state wave function for the complex can be formulated as... 

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