Vibrational modes intramolecular

Furthemiore, IVR is not rapid between the C2H4 intramolecular modes and different excitation patterns of these modes result in different dissociation rates. As a result of these different timescales for dissociation, the relative populations of the vibrational modes of the C2H4 dimer change with time. 

Early studies showed tliat tire rates of ET are limited by solvation rates for certain barrierless electron transfer reactions. However, more recent studies showed tliat electron-transfer rates can far exceed tire rates of diffusional solvation, which indicate critical roles for intramolecular (high frequency) vibrational mode couplings and inertial solvation. The interiDlay between inter- and intramolecular degrees of freedom is particularly significant in tire Marcus inverted regime [45] (figure C3.2.12)). 

The thirty-two silent modes of Coo have been studied by various techniques [7], the most fruitful being higher-order Raman and infra-red spectroscopy. Because of the molecular nature of solid Cqq, the higher-order spectra are relatively sharp. Thus overtone and combination modes can be resolved, and with the help of a force constant model for the vibrational modes, various observed molecular frequencies can be identified with specific vibrational modes. Using this strategy, the 32 silent intramolecular modes of Ceo have been determined [101, 102]. 

The Raman and infrared spectra for C70 are much more complicated than for Cfio because of the lower symmetry and the large number of Raman-active modes (53) and infrared active modes (31) out of a total of 122 possible vibrational mode frequencies. Nevertheless, well-resolved infrared spectra [88, 103] and Raman spectra have been observed [95, 103, 104]. Using polarization studies and a force constant model calculation [103, 105], an attempt has been made to assign mode symmetries to all the intramolecular modes. Making use of a force constant model based on Ceo and a small perturbation to account for the weakening of the force constants for the belt atoms around the equator, reasonable consistency between the model calculation and the experimentally determined lattice modes [103, 105] has been achieved. 

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... 

Additional experimental, theoretical, and computational work is needed to acquire a complete understanding of the microscopic dynamics of gas-phase SN2 nucleophilic substitution reactions. Experimental measurements of the SN2 reaction rate versus excitation of specific vibrational modes of RY (equation 1) are needed, as are experimental studies of the dissociation and isomerization rates of the X--RY complex versus specific excitations of the complex s intermolecular and intramolecular modes. Experimental studies that probe the molecular dynamics of the [X-. r - Y]- central barrier region would also be extremely useful. 

Finally we shall derive the equation used by Bixon and Jortner. Suppose that an intramolecular vibrational mode, say Qi, plays a very important role in electron transfer. To this mode, we can apply the strong-coupling approximation (or the short-time approximation). From Eq. (3.40), we have... 

The above relations can easily be generalized to the case when each molecule has several vibrational modes, e.g., displays not only stretching but bending vibrations as well.123 To classify these intramolecular modes, introduce the... 

The partial solution of Eq.(27) for the configurational space can be conceived as a stepwise process. The fluctuations around the transient configuration X(n) = (Rs(n), Rm (n)) contain—pell-mell— vibrations driven by the intramolecular force field, librations and cage vibration modes of molecules as a whole. The transient configuration evolving in a different time scale contains diffusion terms for liquid environments. 

Despite the difficulty cited, the study of the vibrational spectrum of a liquid is useful to the extent that it is possible to separate intramolecular and inter-molecular modes of motion. It is now well established that the presence of disorder in a system can lead to localization of vibrational modes 28-34>, and that this localization is more pronounced the higher the vibrational frequency. It is also well established that there are low frequency coherent (phonon-like) excitations in a disordered material 35,36) These excitations are, however, heavily damped by virtue of the structural irregularities and the coupling between single molecule diffusive motion and collective motion of groups of atoms. 

In the examples smdied so far, the photoinduced short-time dynamics of a molecular system has been governed by a few high-frequency intramolecular vibrational modes that strongly couple to the electronic transition, a situation that... 

Figure 6. Comparison of SH (thin lines), MFT (dashed lines), and exact quantum (thick lines) calculations obtained for Model IVb describing ultrafast intramolecular electron transfer. Shown are the time-dependent population probabilities P t) and Pf i) of the initially prepared adiabatic (a) and diabatic (b) electronic state, respectively, as well as the mean momentum of a representative vibrational mode (c).

Next we consider Model IVb, which describes ultrafast intramolecular electron transfer driven by three strongly coupled vibrational modes. Figure 6... 

An intramolecular redistribution of energy among all the vibrational modes. For large molecules, this redistribution does not require collisions. 

However, the chromophoies used in SD experiments imdergo small changes in the solute intramolecular potential. Fmthermore, since they are large polyatomics with many intramolecular vibrational modes, vibrational energy relaxation is expected to be very rapid. Thus, AE = AE. In all theories and in most simulations of SD, with a few exceptions, the intramolecular contribution to AE is neglected. 

This way of expressing the overall modes for the pair of molecular units is only approximate, and it assumes that intramolecular coupling exceeds in-termolecular coupling. The frequency difference between the two antisymmetric modes arising in the pair of molecules jointly will depend on both the intra- and intermolecular interaction force constants. Obviously the algebraic details are a bit complicated, but the idea of intermolecular coupling subject to the symmetry restrictions based on the symmetry of the entire unit cell is a simple and powerful one. It is this symmetry-restricted intermolecular correlation of the molecular vibrational modes which causes the correlation field splittings. 

The changes in structure that must occur create a barrier to electron transfer. In order to understand the origin of the barrier and to treat it quantitatively, it is necessary to recall that the structural changes at each reactant can be resolved into a linear combination of its normal vibrational modes. The normal modes constitute a complete, orthonormal set of molecular motions into which any change in intramolecular structure can be resolved. 

The Fe111/11 case is particularly simple. For electron transfer reactions in general, several normal modes may contribute to the trapping of the exchanging electron at a particular site. In addition, intramolecular vibrational modes are of relatively high frequency, 200-4000 cm-1, and at room temperature the classical approximation is not valid since only the v = 0 level is appreciably populated. In order to treat the problem more generally, it is necessary to turn to the quantum mechanical results in a later section. 

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