Intramolecular vibrational energy redistribution, IVR

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. 

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... 

Another important effect on the Norrish type I/II ratio is the occurrence of intramolecular vibrational energy redistribution (IVR). For short timescale processes shorter than 10 ps (such as the Norrish type I reaction), IVR is yet far from completed as assumed by statistical theories such as RRKM. The opposite is true for Norrish type II reaction. The reaction only starts after 20 ps, pointing out that IVR seems to be necessary for the reaction. The longer the cai bon chain (the larger... 

Felker, P.M. and Zewail, A.H. (1985). Dynamics of intramolecular vibrational-energy redistribution (IVR). I. Coherence effects, J. Chem. Phys., 82, 2961-2974. 

Dynamics of intramolecular vibrational-energy redistribution (IVR). II. Excess energy dependence, ibid, 2975-2993. 

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. 

The fragment excited-state NO(A2S+) is a molecular 3r Rydberg state, and we shall refer to this as NO(A, 3s). The observed NO(A, 3.v) product state distributions supported the notion of a planar dissociation involving restricted intramolecular vibrational energy redistribution (IVR) [176]. A scheme for studying NO dimer photodissociation dynamics via TRPES is depicted in Fig. 25. The NO(A, 3.v) + NO(X) product elimination channel, its scalar and vector properties, and its evolution on the femtosecond time scale have been discussed in a number of recent publications (see Ref. [175] and references cited therein). 

In addition to the NHIMs with saddles, other kinds of NHIMs can also become important when intramolecular vibrational energy redistribution (IVR) comes into play. They are NHIMs with whiskered tori that are created by nonlinear resonances within the potential well [5]. In the network of nonlinear resonances, which is called the Arnold web [16,17], these NHIMs will be connected in an interwoven way with each other and also with NHIMs with saddles. 

The Arnold web is supposed to play an important role in intramolecular vibrational energy redistribution (IVR) [1]. However, in order to reveal its role for IVR, the following two problems must be investigated. 

Recently, however, experimental studies have cast a doubt on this assumption (see Ref. 1 for a review). For example, spectroscopic studies reveal hierarchical structures in the spectra of vibrationally highly excited molecules [2]. Such structures in the spectra imply the existence of bottlenecks to intramolecular vibrational energy redistribution (IVR). Reactions involving radicals also exhibit bottlenecks to IVR [3]. Moreover, time-resolved measurements of highly excited molecules in the liquid phase show that some reactions take place before the molecules relax to equilibrium [4]. Therefore, the assumption that local equilibrium exists prior to reaction should be questioned. We seek understanding of reaction processes where the assumption does not hold. 

In order to remove the need for explicit trajectory analysis, one makes the statistical approximation. This approximation can be formulated in a number of equivalent ways. In the microcanonical ensemble, all states are equally probable. Another formulation is that the lifetime of reactant (or intermediate) is random and follows an exponential decay rate. But perhaps the simplest statement is that intramolecular vibrational energy redistribution (IVR) is faster than the reaction rate. IVR implies that if a reactant is prepared with some excited vibrational mode or modes, this excess energy will randomize into all of the vibrational modes prior to converting to product. 

The fundamental assumption of RRKM theory is that the classical motion of the reactant is sufficiently chaotic so that a micro-canonical ensemble of states is maintained as the reactant decomposes [6,324]. This assumption is often referred to as one of a rapid intramolecular vibrational energy redistribution (IVR) [12]. By making this assumption, at any time k E) is given by Eq. (62). As a result of the fixed time-independent rate constant k(E), N(t) decays exponentially, i.e.. 

Vibrational predissociation (VP) of a van der Waals triatomic complex A..BC is an example of a unimolecular reaction the rate of which is controlled by the intramolecular vibrational energy redistribution (IVR) [1]. Within a rigorous quantum mechanical approach, the VP dynamics is completely characterized by the complex-valued energies E = - rT / 2 that lie above the dissociation threshold of A..BC into an atom A and... 

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