Electronic spectra, theoretical correlations

When the life-time of a radical is reduced by rapid intermolecular electron-exchange, all the lines in the spectrum are broadened. The theoretical correlation between line-widths and exchange rates has been discussed (Weissman, 1960 Ward and Weissman, 1957). These authors have determined the rates of electron transfer between naphthalene radical-anion and naphthalene in different solvents and when different metal ions are present. In addition, it is possible to distinguish between the simple exchange reaction, Np -t- Np = Np -j- Np (Np=naphthalene), and that involving the ion-pair, Np Na+ -f Np Np -1- Np Na+, since the e.s.r. spectrum of the ion-pair exhibits a splitting from the Na nucleus (Zandstra and Weissman, 1962). 

High-energy MES in the continuous electronic spectrum, especially those corresponding to the excitation of more than two electrons from the ground state, represent a rather exotic class of states, for which the available quantitative information as to their existence, their properties, and their role in processes, especially in molecules, is very limited. There are a number of theoretical and experimental reasons for this fact. The conventional wisdom that permeates the literature is that in order to understand the excitation by one photon of MES, one has to introduce electron correlation to high order. Indeed, this is the case if the determinants comprising the initial and the final wavefunctions consist of a single orthonormal basis set, as is normal in conventional methods. 

It is shown that the stabilities of solids can be related to Parr s physical hardness parameter for solids, and that this is proportional to Pearson s chemical hardness parameter for molecules. For sp-bonded metals, the bulk moduli correlate with the chemical hardness density (CffD), and for covalently bonded crystals, the octahedral shear moduli correlate with CHD. By analogy with molecules, the chemical hardness is related to the gap in the spectrum of bonding energies. This is verified for the Group IV elements and the isoelec-tronic III-V compounds. Since polarization requires excitation of the valence electrons, polarizability is related to band-gaps, and thence to chemical hardness and elastic moduli. Another measure of stability is indentation hardness, and it is shown that this correlates linearly with reciprocal polarizability. Finally, it is shown that theoretical values of critical transformation pressures correlate linearly with indentation hardness numbers, so the latter are a good measure of phase stability. 

In principle, refined and relatively reliable quantum-theoretical methods are available for the calculation of the energy change associated with the process of equation 2. They take into account the changes in geometry, in electron distribution and in electron correlation which accompany the transition M(1 fio) — M+ (2 P/-), and also vibronic interactions between the radical cation states. Such sophisticated treatments yield not only reliable predictions for the different ionization energies 7 , 77 or 7 , but also rather precise Franck-Condon envelopes for the individual bands in the PE spectrum. However, the computational expenditure of these methods still limits their application to smaller molecules. We shall mention them later in connection with examples where such treatments are required. 

In substituted benzenes, the symmetry is lowered and the transitions into the states that correlate to the B2u and B u states of benzene become allowed by IPA, 2PA, or both. However, when the substituents induce only a weak perturbation on the benzene yr-electron system, the IPA or 2PA spectra of the substituted compounds often closely resemble the spectrum of the unsubstituted parent molecule. Various theoretical models have been developed in an attempt to predict the type of change in the band intensity and characteristics in the 2PA spectra of substituted benzenes and, more generally, of alternant hydrocarbons [34-36]. It was found that the effect of a perturbation is quite different for IP and 2P allowed transitions. In particular, 2P transitions to the state correlated to the benzene B2u state (Lb) are affected more by vibronic coupling than transitions to the state correlated to the benzene Biu state (La, in Platt notation [31,32]). In contrast, inductive perturbations enhance the La band more than the Lb band. The effects of vibronic coupling and inductive substituents are reversed for IP transitions into these states. Experimental... 

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