Liquids energy relaxation

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... 

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... 

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],... 

Ultrafast vibrational spectroscopy offers a variety of techniques for unraveling the microsopic dynamics of hydrogen bonds occurring in the femto- to picosecond time domain. In particular, different vibrational couplings can be separated in nonlinear experiments by measuring vibrational dynamics in real-time. Both coherent vibrational polarizations and processes of population and energy relaxation have been studied for a number of hydrogen bonded systems in liquids [1],... 

Three-dimensional spectroscopy of vibrational energy relaxation in liquids. 

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... 

Aside from the difficulties at the upper and lower ends of the liquid s vibrational band, the INM ideas do seem to work and to work quantitatively. The ability of the liquid-mode concept to account for the absolute magnitude of the vibrational friction, including the factor of 2 difference between liquid and supercritical CO2 solvents, is worth noting (52). But does this success mean that vibrational energy relaxation is really a collective process To answer this question, we need to carry out precisely the kind of mechanistic investigation we discussed in Section II.C. 

That electrostatic forces could be crucial to vibrational energy relaxation was amply demonstrated by the liquid water simulations of Whitnell et al. (34). They noted that since the electrostatic portion of the force between their solvent and a dipolar solute was linear in the solute dipole moment, Equations (12) and (13) implied that the electrostatic part of the friction ought to scale as the dipole moment squared. When they then found that their entire relaxation rate scaled with the square of the solute dipole moment, it certainly seemed to be convincing evidence that electrostatics forces were indeed the primary ingredients generating ultrafast relaxation. Subsequent theoretical work on relaxation rates in such manifestly protic solvents as water and alcohols has largely served to reinforce this message (37,38,60,61). 

Chesnoy J, Gale GM. Vibrational energy relaxation in liquids. Ann Phys Fr 1984 9 893-949. 

Brueck SRJ, Osgood Jr. RM. Vibrational energy relaxation in liquid N2 — CO mixtures. Chem Phys Lett 1976 39 568-572. 

Deak JC, Iwaki LK, Dlott DD. Vibrational energy relaxation of polyatomic molecules in liquids acetonitrile. J Phys Chem 1998 102 8193-8201. 

Everitt KF, Egorov SA, Skinner JL. Vibrational energy relaxation in liquid oxygen. Chem Phys 1998 235 115-122. 

Laenen R, Rauscher C. Time-resolved infrared spectroscopy of ethanol monomers in liquid solution molecular reorientation and energy relaxation times. Chem Phys Lett 1997 274 63-70. 

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. 

Experiments using liquid rare gases may prove valuable in the study of simple solvent effects upon free radical reactions, in the study of energy relaxation phenomena where solvents of exceedingly high purity are required, or in the production of new reactive molecules of questionable chemical stability. The possible photodimerization of acetylene to cyclobutadiene is a good example of one kind of experiment which can be carried out at low temperatures in these inert solvents. 

II. ENERGY RELAXATION IN LIQUIDS A. Distribution Function Methods... 

Keeping the above considerations in mind it is relatively easy, starting from an a priori correlation function approach, to derive successive approximate expressions for binary and nonbinary terms in vibrational relaxation in liquids, to define the limits of validity of binary dynamics, and to obtain easily evaluated analytical expressions for energy relaxation rates that can be directly compared to experiment. 

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