Vibrational energy relaxation

Develop crack or wrinkles, their holy wills 

Rocks rot, and towers topple, even the shrines And images of the gods grow very tired. 

Develop crack or wrinkles, their holy wills Unable to extend their fated term, 

Lucretius (c.99-c.55 BCEj The way things are translated by Rolfe Humphries, Indiana University Press, 1968 

---

Meagher J F, Chao K J, Barker J R and Rabinovitch B S 1974 Intramolecular vibrational energy relaxation. Decomposition of a series of chemically activated fluoroalkyl cyclopropanes J. Phys. Chem. 78 2535 3... 

As an illustrative example, consider the vibrational energy relaxation of the cyanide ion in water [45], The mechanisms for relaxation are particularly difficult to assess when the solute is strongly coupled to the solvent, and the solvent itself is an associating liquid. Therefore, precise experimental measurements are extremely usefiil. By using a diatomic solute molecule, this system is free from complications due to coupling... 

Chesnoy J and Gale G M 1984 Vibrational energy relaxation in liquids Ann. Phys., Pahs 9 893-949... 

IS] Brueok S R J and Osgood R M Jr 1976 Vibrational energy relaxation in liquid N2-CO mixtures Chem. Phys. Lett. 39 568-72... 

Heilweil E J, Casassa M P, Cavanagh R R and Stephenson J C 1984 Piooseoond vibrational energy relaxation of surfaoe hydroxyl groups on oolloidal silioa J. Chem. Phys. 81 2856-8... 

Deak J C, Iwaki L K and DIott D D 1998 Vibrational energy relaxation of polyatomio moleoules in liquids aoetonitrile J. Phys. Chem. 102 8193-201... 

Everitt K F, Egorov S A and Skinner J L 1998 Vibrational energy relaxation in liquid oxygen Chem. Phys. 235 115-22... 

Velsko S and Oxtoby D W 1980 Vibrational energy relaxation in liquids J. Chem. Phys. 72 2260-3... 

A review of vibrational energy relaxation of small molecules in solution. 

Vibrational spectroscopy can help us escape from this predicament due to the exquisite sensitivity of vibrational frequencies, particularly of the OH stretch, to local molecular environments. Thus, very roughly, one can think of the infrared or Raman spectrum of liquid water as reflecting the distribution of vibrational frequencies sampled by the ensemble of molecules, which reflects the distribution of local molecular environments. This picture is oversimplified, in part as a result of the phenomenon of motional narrowing The vibrational frequencies fluctuate in time (as local molecular environments rearrange), which causes the line shape to be narrower than the distribution of frequencies [3]. Thus in principle, in addition to information about liquid structure, one can obtain information about molecular dynamics from vibrational line shapes. In practice, however, it is often hard to extract this information. Recent and important advances in ultrafast vibrational spectroscopy provide much more useful methods for probing dynamic frequency fluctuations, a process often referred to as spectral diffusion. Ultrafast vibrational spectroscopy of water has also been used to probe molecular rotation and vibrational energy relaxation. The latter process, while fundamental and important, will not be discussed in this chapter, but instead will be covered in a separate review [4],... 

Fully classical approaches do, however, have three significant advantages. First, they are simple to implement second, it is no more difficult to model H2O, where OH stretches are coupled, than it is to model HOD/D2O (whereas in the approaches to follow this is most certainly not the case ) and third, vibrational energy relaxation is automatically included (see below). Results from several of these classical approaches have appeared in the literature [79, 87 91]. 

First, as the molecule on which the chromophore sits rotates, this projection will change. Second, the magnitude of the transition dipole may depend on bath coordinates, which in analogy with gas-phase spectroscopy is called a non-Condon effect For water, as we will see, this latter dependence is very important [13, 14]. In principle there are off-diagonal terms in the Hamiltonian in this truncated two-state Hilbert space, which depend on the bath coordinates and which lead to vibrational energy relaxation [4]. In practice it is usually too difficult to treat both the spectral diffusion and vibrational relaxation problems at the same time, and so one usually adds the effects of this relaxation phenomenologically, and the lifetime 7j can either be calculated separately or determined from experiment. Within this approach the line shape can be written as [92 94]... 

To conclude, even if there exist several processes that affect the vibrational line shape it seems probable that when most of them have been sorted out and with the good agreement between theory and experiment, the lifetime broadening for a chemisorbed CO molecule is of the order of a few cm, corresponding to a lifetime of a few ps. The main vibrational energy relaxation mechanism is creation of electron-hole pairs caused by the local charge oscillations between the metal and the 2n molecular resonance crossing the Fermi level. 

In principle, fluorescence spectra from shortlived upper metalloporphyrin states in solution can be shifted in the longwave direction with vibrational energy relaxation at the cost of short-wave excitation (7). However, in our case the energy difference of annihilatTng and direct excitation was slight ( <... 

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. 

Three-dimensional spectroscopy of vibrational energy relaxation in liquids. 

The VET rate constants kvET = 11 Wet of benzene in scC02 as presented in Fig. 5 for various reduced densities pred = p/pcrit show the same S-shaped density dependence as previously observed for the vibrational energy relaxation of azulene in supercritical fluids... 

The observations of vibrational coherence in optically initiated reactions described above clearly show that the standard assumption of condensed-phase rate theories—that there is a clear time scale separation between vibrational dephasing and the nonadiabatic transition—is clearly violated in these cases. The observation of vibrational beats has generally been taken to imply that vibrational energy relaxation is slow. This viewpoint is based on the optical Bloch equations applied to two-level systems. In this model, the total dephasing rate is given by... 

A many-atom system excited by light or by collisions, such as occurs in the photo-excitation of a molecule adsorbed on a surface or in photosynthesis and vision, leads to energy dissipation on different time scales. A fast dissipation typically occurs due to electronic energy relaxation in the medium, while a slow (delayed) dissipation arises from vibrational energy relaxation. Here we concentrate on localized phenomena where a relatively small number... 

In contrast to the subsystem representation, the adiabatic basis depends on the environmental coordinates. As such, one obtains a physically intuitive description in terms of classical trajectories along Born-Oppenheimer surfaces. A variety of systems have been studied using QCL dynamics in this basis. These include the reaction rate and the kinetic isotope effect of proton transfer in a polar condensed phase solvent and a cluster [29-33], vibrational energy relaxation of a hydrogen bonded complex in a polar liquid [34], photodissociation of F2 [35], dynamical analysis of vibrational frequency shifts in a Xe fluid [36], and the spin-boson model [37,38], which is of particular importance as exact quantum results are available for comparison. 

G. Hanna and E. Geva. Vibrational energy relaxation of a hydrogen-bonded complex dissolved in a polar liquid via the mixed quantum-classical lionville method. J. Phys. Chem. B, 112(13) 4048-4058, APR 3 2008. 

Vibrational Energy Relaxation in Liquids and Supercritical Fluids... 

Heilweil EJ, Casassa MP, Cavanagh RR, Stephenson JC. Vibrational energy relaxation of surface hydroxyl groups on colloidal silica. J Chem Phys 1984 81 2856-2859. 

---