Induced dipole corresponding states

Molecules initially in the J = 0 state encounter intense, monochromatic radiation of wavenumber v. Provided the energy hcv does not correspond to the difference in energy between J = 0 and any other state (electronic, vibrational or rotational) of the molecule it is not absorbed but produces an induced dipole in the molecule, as expressed by Equation (5.43). The molecule is said to be in a virtual state which, in the case shown in Figure 5.16, is Vq. When scattering occurs the molecule may return, according to the selection mles, to J = 0 (Rayleigh) or J = 2 (Stokes). Similarly a molecule initially in the J = 2 state goes to... 

Principle of corresponding states. Intermolecular potentials, like the induced dipole surfaces, are functionals of the intermolecular interactions. The signatures of electron exchange, dispersion and multipole induction are clearly exhibited in both they have much in common. 

Turning our attention to the induced dipole function, one wonders if the principle of corresponding states might have any validity for the latter. The question arises whether, or to what extent, the induced dipole function may be written as a universal function with a small number of adjustable scaling parameters. If such a function existed, it would clearly be of interest to workers in the field of collision-induced absorption. 

The question raised above was is the principle of corresponding states applied to induced dipole surfaces (perhaps approximately) valid If the dipoles were well represented by an exponential function, like Eq. 4.1, the principle would of course be valid. However, it is quite clear that the dispersion part cannot be neglected in the induced dipole models. Moreover, for the best dipole models presently available, we need nonvanishing values b, Eq. 4.30, see p. 162. In other words, the induced dipole surfaces of rare gas pairs seem to require four-parameter functions, like Eq. 4.30, and it is not at all clear how these four parameters may be reduced to but two. The principle, therefore, seems at present to be of little practical value (if it were valid at all). 

The first two terms in Eq. 5.15 provide a difference of the polarization energy of the QM/EFP system in the excited and ground electronic states, while the last term is the leading correction to the interaction of the ground-state-optimized induced dipoles with the excited state wave function. The perturbative treatment of the response of the polarizable environment as in Eqs. 5.14 and 5.15 corresponds to the "method 2 from Ref. [56]. This approach has been used for calculations discussed in Section 5.6. 

While a neutral molecule has an entirely symmetrical electron distribntion when considered as an average over a period of time, when it is considered at an instant, the state is different. At any instant of time, the electrons will have a definite distribution, which is most unlikely to be symmetrical, so that the molecule will have an instantaneous dipole moment. This instantaneous dipole can induce a corresponding dipole moment in another adjacent molecule. So, there will be an interaction between these two molecules, which will result in forces of attraction between them. The dispersion force is then this instantaneous force of attraction averaged over all the instantaneous configurations of the electrons in the first molecule. 

The effects of a dc electric field on a single polar molecule are shown in Figure 12.6, and they amount to (1) a split in the (27+ l)-fold degeneracy in the rotor spectrum, and (b) aligning the molecule along the direction of the field. The latter corresponds to inducing a finite dipole moment in each rotational state. For weak fields p = dEic/B 1, the state (1)7,a/) and its associated induced dipole moment approximately read... 

Normal Raman spectroscopy probes the variations of the polarizability tensor with respect to the degrees of freedom, in the ground electronic state. When an electrical field is applied to a system the electron distribution is modified and the sample acquires an induced dipole moment as the barycenters of the charges are displaced. The polarizability tensor [a] defines the correspondence between the incident electrical field E and the induced dipole moment M = [a]E. The polarizability tensor can be expanded in a Taylor series analogous to Equation (8.8) ... 

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