Intramolecular vibrational density

Figure 1. Intramolecular vibrational density redistribution IVR of Na3

Note that in the reference model all the interactions of the electron with the medium polarization VeP are included in Eqs. (8) determining the electron states. The dependence of A and B on the polarization and intramolecular vibrations was entirely neglected in most calculations of the transition probability [the approximation of constant electron density (ACED)]. This approximation, together with Eqs. (4)-(7), resulted in the parabolic shape of the diabatic PES Ut and Uf. The latter differed only by the shift... 

The effects of modulation of the electron density by the intramolecular vibrations on the process of inner-sphere activation... 

Let us assume that all the nuclear subsystems may be separated into several subsystems (R, q9 Q, s,...) characterized by different times of motion, for example, low-frequency vibrations of the polarization or the density of the medium (q), intramolecular vibrations, etc. Let (r) be the fastest classical subsystem, for which the concept of the transition probability per unit time Wlf(q, Q,s) at fixed values of the coordinates of slower subsystems q, Q, s) may be introduced. 

The shape of the minimum in the surface is experimentally probed by vibrational spectroscopy. It is here that the computations can make direct coimection with experimental information. Formation of the H-bond from a pair of isolated molecules converts three translational and three rotational degrees of freedom of the formerly free pair of molecules into six new vibrations within the complex. The frequencies of these modes are indicative of the functional dependence of the energy upon the corresponding geometrical distortions. But rather than consisting of a simple motion, for example, H-bond stretch, the normal modes are composed of a mixture of symmetry-related atomic motions, complicating their analysis in terms of the simpler motions. In addition to these new intermoleeular modes, the intramolecular vibrations within each of the subunits are perturbed by the formation of the H-bond. The nature of each perturbation opens a window into the effects of the H-bond upon the molecules involved. The intensities of the various vibrations carry valuable information about the electron density within the complex and the perturbations induced by the formation of the H-bond. 

Infrared and Raman spectra have long been used to probe the structure and strength of interactions in liquid water. The vibrational density of states, components of which are probed by both these forms of spectroscopy, can be divided into three components. At the lowest frequencies, usually below about 100 cm , the most important vibrations are associated with translational motions in which the molecular centers of mass are moving with respect to each other. Between 100 cm and 1000 cm" the vibrational density of states is dominated by intermolec-ular rotational and librational motions. Near 1600 cm there is a fairly broad band arising from intramolecular HOH bending modes. Then, between 3100 cm" and 3400 cm" the intramolecular vibrations become important. There are quite impor-... 

An important achievement of the early theories was the derivation of the exact quantum mechanical expression for the ET rate in the Fermi Golden Rule limit in the linear response regime by Kubo and Toyozawa [4b], Levich and co-workers [20a] and by Ovchinnikov and Ovchinnikova [21], in terms of the dielectric spectral density of the solvent and intramolecular vibrational modes of donor and acceptor complexes. The solvent model was improved to take into account time and space correlation of the polarization fluctuations [20,21]. The importance of high-frequency intramolecular vibrations was fully recognized by Dogonadze and Kuznetsov [22], Efrima and Bixon [23], and by Jortner and co-workers [24,25] and Ulstrup [26]. It was shown that the main role of quantum modes is to effectively reduce the activation energy and thus to increase the reaction rate in the inverted... 

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