Polarizability pure vibrational

In the Bishop and Kirtman (BK) perturbation treatment [17-19] two basic additional assumptions are made. First, when K> is an intermediate excited electronic state it is assumed that, under ordinary non-resonant conditions, one may ignore the optical frequency term zr j. /2- -w in the corresponding energy denominator as compared to the electronic excitation energy. Then, after summing over all intermediate states other than K = 0, one is left with die pure vibrational (hyper)polarizability, P". The latter may be expressed compactly in terms of so-called square bracket quantities. Thus,... 

Since the occurrence of the Raman effect depends on the change in polarizability as vibration occurs, the selection rules are different for the Raman effect than they are for the infrared spectrum. In particular, in molecules with a center of symmetry the totally symmetric vibration is Raman-active, but is forbidden in the infrared since it produces no change in dipole moment. Thus the homonuclear diatomic molecules, H2, O2, N2, show the Raman effect but do not absorb in the infrared. There is also a purely rotational Raman eff ect in these molecules. However, in this case the selection rule is A J = 2. Thus we have for the rotational Stokes lines... 

We shall review the electronic and the pure vibrational contributions to the hyperpolarizabilities of pyrrole [50]. The original article involved also dipole moment and polarizabilities. The molecule is placed on the yz plane (Fig. 5.2). The computations have been performed at the Hartree-Fock level, employing the Pol basis set [45]. 

We note that the evaluation of CARS requires largely the same quantity as is needed for conventional Raman spectroscopy as well as ROA, namely the polarizability gradient. If the nonresonant contributions are also wanted, then the electronic second hyperpolarizability is also needed, as well as the off-resonant pure vibrational contributions [292]. Ab initio studies of CARS have to date been very limited [292, 293]. 

The conventional approach used to describe the response of a molecule to a static electric field is either to perform pure electronic BO calculations or to perform calculations where the BO values are corrected for vibrational and rotational (thermal) motion of the nuclei. The vibrationally corrected polarizabilities usually do an excellent job of correcting the errors inherent in the pure electronic BO values. Bishop has written several excellent reviews on this topic [78-80]. 

PEC, are in general in better agreement with the CAS results than the pure SOPPA results. This applies to the equilibrium geometry results as well as to the vibrational averaged results. This shows that SOPPA(CCSD) performs better in the calculation of polarizabilities for LiH than SOPPA as might have been expected [36,41]. 

SOPPA(CCSD) calculations with the CCSD or MCSCF PEC are also larger. In general the differences in the ZPVC are larger between the different PEC than between the different linear response methods. The SOPPA(CCSD) results for the equilibrium geometry as well as the vibrationally averaged polarizabilities are in both molecules in better agreement with the MCSCF results than the pure SOPPA values. 

We saw that homonuclear diatomic molecules exhibit no pure-rotation or vibration-rotation spectra, because they have zero electric dipole moment for all internuclear separations. The Raman effect depends on the polarizability and not the electric dipole moment homonuclear diatomic molecules do have a nonzero polarizability which varies with varying internuclear separation. Hence they exhibit pure-rotation and vibration-rotation Raman spectra. Raman spectroscopy provides information on the vibrational and rotational constants of homonuclear diatomic molecules. 

Therefore, HREELS is capable, like SIMS, of disclosing molecular, long-range information on the polymer surface. However, at this stage, it is fair enough to address our ignorance of the influence of the substrate on the vibrational response of a polymer thin film What are the effects of substrate quality - pure metal or with native oxide -, roughness on the atomic scale, and polarizability Authors (8.11) do feel these external parameters must be controlled and taken into account. 

In this book we are concerned only with that part of the spectrum dependent on pure rotations and translations of molecules. No further discussion of the vibrational Raman scattering is given. Thus Eq. (3.3.3) is used, but always with the rigid-frame polarizabilities. We refer to this type of scattering as Rayleigh-Brillouin" scattering.11... 

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