Intramolecular vibrations interactions

Kato, T. and Yamabe, T., Electron-intramolecular-vibration interactions in positively... 

Another important question deals with the intramolecular and unimolecular dynamics of the X-—RY and XR -Y- complexes. The interaction between the ion and molecule in these complexes is weak, similar to the intermolecular interactions for van der Waals molecules with hydrogen-bonding interactions like the hydrogen fluoride and water dimers.16 There are only small changes in the structure and vibrational frequencies of the RY and RX molecules when they form the ion-dipole complexes. In the complex, the vibrational frequencies of the intramolecular modes of the molecule are much higher than are the vibrational frequencies of the intermolecular modes, which are formed when the ion and molecule associate. This is illustrated in Table 1, where the vibrational frequencies for CH3C1 and the Cr-CHjCl complex are compared. Because of the disparity between the frequencies for the intermolecular and intramolecular modes, intramolecular vibrational energy redistribution (IVR) between these two types of modes may be slow in the ion-dipole complex.16... 

It is convenient to split this interaction into two parts the interaction with the intramolecular vibrations and with the nearest medium molecules, Vzv, and the interaction with the rest of the solvent, VzP, which may be described in terms of the inertial polarization per unit volume P(r) ... 

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 brief review of the newest results in the theory of elementary chemical processes in the condensed phase given in this chapter shows that great progress has been achieved in this field during recent years, concerning the description of both the interaction of electrons with the polar medium and with the intramolecular vibrations and the interaction of the intramolecular vibrations and other reactive modes with each other and with the dissipative subsystem (thermal bath). The rapid development of the theory of the adiabatic reactions of the transfer of heavy particles with due account of the fluctuational character of the motion of the medium in the framework of both dynamic and stochastic approaches should be mentioned. The stochastic approach is described only briefly in this chapter. The number of papers in this field is so great that their detailed review would require a separate article. 

This is the difference in interaction energy, for the solvent molecules in given positions, of the solvent with the reactant and product [31], In the simplest case of no geometric size changes accompanying the ET, AE will be exclusively determinated by the Coulombic interactions between the solute and the solvent molecules. We will assume this to be the case in all that follows. We make the further restriction that the solute intramolecular vibrations play no key role. 

Desorption can proceed via several mechanisms. For solids with a negative electron alSnity such as Ar [49,149-151] and N2 [153], the extended electron cloud around a metastable center will interact repulsively with the surrounding medium and metastables formed at the film-vacuum interface will be expelled into vacuum (the so-called cavity expulsion mechanism [161]). Also permitted in solids with positive electron affinities (e.g., CO) is the transfer of energy intramolecular vibration to the molecule-surface bond with the resulting desorption of a molecule in lower vibrational level [153,155,158-160]. Desorption of metastables via the excitation of dissociative molecular (or excimer) electronic states is also possible [49,149-151,154,156,157]. A concise review of the topic can be found in Ref. 162. 

For intramolecular vibrations, each site was considered independently. However, the reorganizations in the surrounding solvent are necessarily properties of both sites since some of the solvent molecules involved are shared between reactants. The critical motions in the solvent are reorientations of the solvent dipoles. These motions are closely related to rotations of molecules in the gas phase but are necessarily collective in nature because of molecule—molecule interactions in the condensed phase of the solution. They have been treated theoretically as vibrations by analogy with lattice vibrations of phonons which occur in the solid state.32,33... 

The symbol ( )n denotes one mole of domains of any spin state with n molecules in each domain. Interactions between the domains, irrespective of the spin state, are neglected. The total energy of an individual complex molecule is considered to be composed of electronic and intramolecular vibrational contributions. In terms of the partition functions for these contributions the equilibrium constant K = xhs/O-xhs) may be formulated as... 

First, we envisage the weak exciton-photon coupling (which allows an intuitive description of the phonon effects on the nature of the secondary emissions). Therefore we write the hamiltonian of the total system as sums of free photons (Hy), free excitons (He), and free phonons (Hp), with the appropriate interactions Hey (Section I) and Hep (see Sections II, A, B, C.), including intramolecular vibrations too. 

Another type of echo that is receiving much attention are fifth-order echoes, which are also based on Raman interactions (56-60). The majority of studies have looked at intermolecular interactions (11,43-54), but a few studies have looked at an intramolecular vibrational overtone (47,48). Compared to the Raman echo, the fifth-order echo replaces a pair of interactions by a single, double-quantum interaction. Although the fifth-order experiments are formally of lower order than the Raman echo, the doublequantum interaction is forbidden in the harmonic approximation. As a result, it is not clear that the signal from a fifth-order echo will be stronger than that from a seventh-order Raman echo. 

In organic conductors the electron-phonon couplings play a fundamental role. In general, the interaction of the electrons with intramolecular vibrations can be written in the form given by Rice [13] ... 

Another significant source of variations in the local site energies of molecular ions and excitons in condensed media is the modulation of these energies by the thermal vibrations either of the medium (e.g., acoustical phonons and librons) or of the molecular ion (exciton) itself (intramolecular vibrations). A model Hamiltonian which incorporates electronic interactions with... 

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-... 

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