Mulliken’s 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... 

Nothing in Mulliken s theory prevents a large value of p. 

Kochi and co-workers have recently identified and characterized the weak charge transfer complexes between tropylium ion and a series of substituted arenes in acetonitrile solution [74], Photoexcitation of these electron donor acceptor (EDA) complexes leads to an electron transfer from the arene donors to the tropylium ion in accord with Mulliken s theory [75]. Time resolved spectroscopic observation of the arene radical cations (formation within the 30 ps laser pulse) has confirmed their intermediacy. The subsequent decay of the photogenerated radical cation and the concomitant regeneration of the ground state EDA complex occurs with a rate constant, kBET > 4 x 1010 s 1 (Scheme 11). This fast back electron transfer... 

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). 

Figure 1 shows the linear correlation between F chemical shift and solvent donicity. No relationship exists between chemical shifts and dipole moments or polarizabilities of the solvent molecules. This result is particularly significant in that it shows that the functional approach can be successfully applied even to weak chemical interactions, for example, to interactions that are usually considered as being due to Van der Waals forces or intermolecular forces in the sense of Mulliken s theory. 

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-... 

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). 

According to Mulliken s theory [12, 13, 14] the charge-transfer complexes are resonance hybrides of non-polar (wave function Pq) polar or dative (wave function Wi) structures ... 

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] ... 

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]. 

In this chapter, we use the definitions of bond order and valence indices provided by Mayer [4-6] (for a historical account, see Ref. [6a] and for other types of bond indices, see Ref. [6b]). In terms of electronic structure theory, they represent an extension to Mulliken s population analysis. The bond order is defined as... 

Practitioners of quantum chemistry employed both the visual imagery of nineteenth-century theoretical chemists like Kekule and Crum Brown and the abstract symbolism of twentieth-century mathematical physicists like Dirac and Schrodinger. Pauling s Nature of the Chemical Bond abounded in pictures of hexagons, tetrahedrons, spheres, and dumbbells. Mulliken s 1948 memoir on the theory of molecular orbitals included a list of 120 entries for symbols and words having exact definitions and usages in the new mathematical language of quantum chemistry. 

In contrast, Bohr s use of the word "shells" and Langmuir s use of the term "sheaths" in place of "orbits" discarded the old gravitational analogy for electron energy levels and electron motions. Mulliken s invention of the word "orbital" self-consciously fit his theory within the old physical tradition going back to Newton but simultaneously asserted the discovery of a new theory to inaugurate a "Mulliken era" in chemistry. We have specifically... 

Mulliken also studied other band spectra of diatomic molecules. Only one such study will be mentioned here and that is his study of copper iodide (Mulliken 1925c), where he examined the copper isotope effect. Mulliken s pioneering work was followed by more papers on isotope effects on electronic spectra (visible and UV) which will not be detailed here. Many of these papers deal with diatomics since the theory of such spectra is much better understood than that for general polyatomic systems. Further discussion of isotope effects on spectra will be mainly restricted to their use in the discovery of less abundant isotopes. 

It should, however, be mentioned that Mulliken s study of the BO system has been followed over the years by many others, An extensive study by Jenkins and McKellar (1932) should be mentioned explicitly. This study involved the long wavelength band of BO. The same method as that used by both Jevons and Mulliken to produce the BO was used in this work. The new (present day) quantum mechanics was used in the theoretical interpretation. Both the vibrational and the rotational isotope effects were observed and agree with theory. One motivation for this work was to determine how well the isotopic ratio of the square roots of the two relevant isotopic masses (10B and nB) agrees with the ratio obtained from Aston s mass spectrometric measurements and hence how well isotopic mass ratios determined from band spectra compare with those obtained using Aston s mass spectrograph. 

IT Complexes may be described in terms of Mulliken s charge-transfer theory (23-25). This theory attributes the complex formation of stable aromatic molecules to an electron donor (D)-electron acceptor (A) interaction which is approximately represented by the combination of three wave functions ... 

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). 

Whereas many scientists shared Mulliken s initial skepticism regarding the practical role of theory in solving problems in chemistry and physics, the work of London (6) on dispersion forces in 1930 and Hbckel s 7t-electron theory in 1931 (7) continued to attract the interest of many, including a young scientist named Frank Westheimer who, drawing on the physics of internal motions as detailed by Pitzer (8), first applied the basic concepts of what is now called molecular mechanics to compute the rates of the racemization of ortho-dibromobiphenyls. The 1946 publication (9) of these results would lay the foundation for Westheimer s own systematic conformational analysis studies (10) as well as for many others, eg, Hendrickson s (11) and Allinger s (12). These scientists would utilize basic Newtonian mechanics coupled with concepts from spectroscopy (13,14) to develop nonquantum mechanical models of structures, energies, and reactivity. 

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