Spectroscopic effective-medium theory

The radius thus calculated from the theory of Smith and Symons does not correspond to any known property of halide ions. However, when the acceptable physical model of Franck and Platzman is combined with the concept of a variable radius, as proposed by Smith and Symons, both absolute value and environmental effects can be accounted for. This was done in the theory of Stein and Treinin (18, 19, 47), using an improved energetic cycle to obtain absolute values of r, the spectroscopically effective radius of the cavity containing the X ion. These values were then found to correspond to the known partial ionic radii in solution, as did values of dr/dT to values obtained from other experiments. The specific effects of temperature, solvents, and added salts could be used to differentiate between internal and such CTTS transitions where the electron interacts in the excited state strongly with the medium. These spectroscopic aspects of the theory were examined later in detail and compared with experiment by Treinin and his co-workers (3, 4, 32, 33, 42,48). 

The topic of interactions between Lewis acids and bases could benefit from systematic ab initio quantum chemical calculations of gas phase (two molecule) studies, for which there is a substantial body of experimental data available for comparison. Similar computations could be carried out in the presence of a dielectric medium. In addition, assemblages of molecules, for example a test acid in the presence of many solvent molecules, could be carried out with semiempirical quantum mechanics using, for example, a commercial package. This type of neutral molecule interaction study could then be enlarged in scope to determine the effects of ion-molecule interactions by way of quantum mechanical computations in a dielectric medium in solutions of low ionic strength. This approach could bring considerable order and a more convincing picture of Lewis acid base theory than the mixed spectroscopic (molecular) parameters in interactive media and the purely macroscopic (thermodynamic and kinetic) parameters in different and varied media or perturbation theory applied to the semiempirical molecular orbital or valence bond approach [11 and references therein]. 

An e1ementary but complete introduction to the Raman effect appears in a text by Guillory (2) which also discusses several other molecular spectroscopic structural probes. More rigorous treatments of the subject may be found in works dealing primarily with vibrational spectroscopic methods (3)-(6). A brief introduction to the theory of Raman spectroscopy follows and is based on the inelastic scatter ng of light by a nonabsorbing medium. 

In this chapter we will focus instead on another approach, the vibrational second-order perturbation theory (VPT2) [93-98], which provides closed expressions for most of the spectroscopic parameters required for the analysis of the experimental frequencies. VPT2 has been shown to be very effective for the study of semirigid polyatomic molecules of medium size [38-41, 99, 100] at relatively low computational cost. This level of theory requires quadratic, cubic, and semi-diagonal quartic force constants. Starting from analytical Hessians, the needed cubic i4>rst) and quartic constants can be computed by one-dimensional... 

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