Theory of Charge Transfer Complexes

The most satisfactory account of this phenomenon is due to Mulliken, according to whom a complex (D, A) is formed from a donor (D) species and an acceptor (A) species. This complex can exist in two energy states, the difference in energy between the two being equal to the energy of a quantum at the maximum of the absorption band. In the ground state of the complex the binding between foe components h chiefly due let the Van der Waais 

The wave-function, for the normal or ground state of a charge transfer complex may be expressed as a linear combination of the wave-functions for the no-bond structure (D, A) and the bonded (largely ionic) configuration 

In view1 of the electron-donating and accepting tendencies of D and A respectively, the contribution of the ionic structure (D — A+) may be neglected. The ratio b jcr determines the ionic contribution to the ground state of the complex. 

This representation of the ground state wave function IPn is quite analogous to the usual manner of representing resonance between covalent and ionic states. By extending the anology, the excited state of the complex may be represented similarly and the corresponding wave-function is given by 

Here the coefficients a and b which determine the ionic and no-bond cot .Lribttlions to the excited state of the complex are almost equal, respectively, to coefficients a and b in (2) which describe thd contributions of the oo-bond and ionic states to % for the complex in the ground state. Consequently, the excited state of the complex is almost completely ionic with a small contribution from the no-bond arrangement. 

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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 ... 

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 ... 

Any theory of charge transfer complexes should explain satisfactorily the following general features of the absorption spectra and energy changes associated with uch complex formation. 

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... 

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. 

Quite independently, of these fragmentary remarks, a distinctive role of HO (and later LU and SO, too) in unsaturated molecules was pointed out 43> in a general form and with substantiality (cf. Chap. 2). With respect to the molecular complex formation, the theory of charge-transfer force was proposed 47>. A clue tograsp the importance of HO—LU interaction was thus brought to light simultaneously both from the side of ionic reaction and from the side of molecular complex formation. 

The final part is devoted to a survey of molecular properties of special interest to the medicinal chemist. The Theory of Atoms in Molecules by R. F.W. Bader et al., presented in Chapter 7, enables the quantitative use of chemical concepts, for example those of the functional group in organic chemistry or molecular similarity in medicinal chemistry, for prediction and understanding of chemical processes. This contribution also discusses possible applications of the theory to QSAR. Another important property that can be derived by use of QC calculations is the molecular electrostatic potential. J.S. Murray and P. Politzer describe the use of this property for description of noncovalent interactions between ligand and receptor, and the design of new compounds with specific features (Chapter 8). In Chapter 9, H.D. and M. Holtje describe the use of QC methods to parameterize force-field parameters, and applications to a pharmacophore search of enzyme inhibitors. The authors also show the use of QC methods for investigation of charge-transfer complexes. 

Optical Spectra. The main (a) band in a variety of visual pigments exhibits absorption maxima in the range between 430 and 580 nm. It is this variability, as well as the basic bathochromic shift relative to a free PRSB in solution, which have provided the basis for most of the spectroscopic theories relevant to the structure of the chromophore and its environment in the binding site. Attempts to rationalize the shift in terms of charge-transfer complex formation between the (unprotonated) Schiff base and a protein functional group (200,210,212,228) have never... 

Attempts to extend the theory of charge transfer in polar media [106, 107] to ion transfer across a liquid-liquid interface were reviewed by Kunetsov and Kharkats [112]. The complexity of interfacial ion transfer follows from the fact that this is essentially a many-body problem, comprising motions of various components of the system interacting with each other which are difficult to separate. In particular, the... 

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-... 

Theory and Physico-Chemical Properties of Charge-Transfer Complexes... 

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... 

At shorter distances, particularly those characteristic of H-bonded and other charge-transfer complexes, the concepts of partial covalency, resonance, and chemical forces must be extended to intramolecular species. In such cases the distinction between, e.g., the covalent bond and the H-bond may become completely arbitrary. The concept of supramolecular clusters as fundamental chemical units presents challenges both to theory and to standard methods of structural characterization. Fortunately, the quantal theory of donor-acceptor interactions follows parallel lines for intramolecular and intermolecular cases, allowing seamless description of molecular and supramolecular bonding in a unified conceptual framework. In this sense, supramolecular aggregation under ambient thermal conditions should be considered a true chemical phenomenon. 

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