Intramolecular vibrational-rotational energy

Dynaniical theories of unimolecuiar decomposition deal with the properties of vibrational/rotational energy levels, state preparation and intramolecular vibrational energy redistribution (IVR). Thus, the presentation in this chapter draws extensively on the previous chapters 2 and 4. Unimolecuiar decomposition d)mamics can be treated using quantum and classical mechanics, and both perspectives are considered here. The role of nonadiabatic electronic transitions in unimolecuiar dynamics is also discussed. 

This is no longer the case when (iii) motion along the reaction patir occurs on a time scale comparable to other relaxation times of the solute or the solvent, i.e. the system is partially non-relaxed. In this situation dynamic effects have to be taken into account explicitly, such as solvent-assisted intramolecular vibrational energy redistribution (IVR) in the solute, solvent-induced electronic surface hopping, dephasing, solute-solvent energy transfer, dynamic caging, rotational relaxation, or solvent dielectric and momentum relaxation. 

The concept of corresponding states was based on kinetic molecular theory, which describes molecules as discrete, rapidly moving particles that together constitute a fluid or soHd. Therefore, the theory of corresponding states was a macroscopic concept based on empirical observations. In 1939, the theory of corresponding states was derived from an inverse sixth power molecular potential model (74). Four basic assumptions were made (/) classical statistical mechanics apply, (2) the molecules must be spherical either by actual shape or by virtue of rapid and free rotation, (3) the intramolecular vibrations are considered identical for molecules in either the gas or Hquid phases, and (4) the potential energy of a coUection of molecules is a function of only the various intermolecular distances. 

Electrons of still lower energy have been called subvibrational (Mozumder and Magee, 1967). These electrons are hot (epithermal) and must still lose energy to become thermal with energy (3/2)kBT — 0.0375 eV at T = 300 K. Subvibrational electrons are characterized not by forbiddenness of intramolecular vibrational excitation, but by their low cross section. Three avenues of energy loss of subvibrational electrons have been considered (1) elastic collision, (2) excitation of rotation (free or hindered), and (3) excitation of inter-molecular vibration (including, in crystals, lattice vibrations). 

Dynamics of intramolecular vibrational-energy redistribution (IVR). III. Role of molecular rotations, ibid, 2994-3010. 

The nuclear function %a(R) is usually expanded in terms of a wave function describing the vibrational motion of the nuclei, and a rotational wave function [36, 37]. Analysis of the vibrational part of the wave function usually assumes that the vibrational motion is harmonic, such that a normal mode analysis can be applied [36, 38]. The breakdown of this approximation leads to vibrational coupling, commonly termed intramolecular vibrational energy redistribution, IVR. The rotational basis is usually taken as the rigid rotor basis [36, 38 -0]. This separation between vibrational and rotational motions neglects centrifugal and Coriolis coupling of rotation and vibration [36, 38—401. Next, we will write the wave packet prepared by the pump laser in terms of the zeroth-order BO basis as... 

As discussed in Section III, TRPES is sensitive to vibrational and rotational dynamics, as well as electronic dynamics. In this section, we give examples of the use of TRPES to the study of intramolecular vibrational energy redistribution (IVR), and the use of time-resolved PAD measurements as a probe of rotational dynamics. 

This chapter is concerned with how energy deposited into a specific vibrational mode of a solute is dissipated into other modes of the solute-solvent system, and particularly with how to calculate the rates of such processes. For a polyatomic solute in a polyatomic solvent, there are many pathways for vibrational energy relaxation (VER), including intramolecular vibrational redistribution (IVR), where the energy flows solely into other vibrational modes of the solute, and those involving solvent-assisted processes, where the energy flows into vibrational, rotational, and/or translational modes of both the solute and the solvent. 

In this chapter we have reviewed the general theory of vibrational energy relaxation for a single oscillator coupled to a bath, and we have discussed the application of these results to three specific systems iodine in xenon, neat liquid oxygen, and W(CO)6 in ethane. In the first case the bath is the translations of the solute and solvent molecules, in the second case it is the translations and rotations of solute and solvent molecules, and in the third case it is the solute s other intramolecular vibrations and the translations of solute and solvent molecules. 

Figure 3.10 Vibrational deexcitation of a classical Morse oscillator as a function of the orientation angle fl0 (see text), according to Kelley [98], for the case mA + mB mc = 2 + 1 - 1. Rotational energy is acquired via intramolecular V—R transfer. AirT0T is the net internal energy lost by the molecule BC.

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. 

In the case of U and Cy, the question of accounting for the kinetic energy of the intramolecular degrees of freedom arises. Usually this is done by assuming that rotational degrees of freedom can be treated classically and that the intramolecular vibrational modes make no contribution. However, other assumptions have been made. This question is important when detailed agreement with an experiment is desired. The difference between the measured and calculated quantities can vary by 2-3 kcal/mol depending on the way in which the kinetic component is estimated. 

Once a potential energy function is chosen or determined for a molecule, there are three major components to a trajectory study the selection of initial conditions for the excited molecule, the numerical integration of the classical equations of motion, and the analysis of the trajectories and their final conditions. The last item may include the time at which the trajectory decomposed to products, the nature of the trajectory s intramolecular motion, i.e., regular or irregular, and the vibrational, rotational and translational energies of the reaction products. 

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