Relaxation energies

Rynbrandt J D and Rabinovitch B S 1971 Direct demonstration of nonrandomization of internal energy in reacting molecules. Rate of intramolecular energy relaxation J. Chem. Phys. 54 2275-6... 

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... 

Figure C3.5.5. Vibronic relaxation time constants for B- and C-state emitting sites of XeF in solid Ar for different vibrational quantum numbers v, from [25]. Vibronic energy relaxation is complicated by electronic crossings caused by energy transfer between sites.

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. 

Chapter 3 is devoted to pressure transformation of the unresolved isotropic Raman scattering spectrum which consists of a single Q-branch much narrower than other branches (shaded in Fig. 0.2(a)). Therefore rotational collapse of the Q-branch is accomplished much earlier than that of the IR spectrum as a whole (e.g. in the gas phase). Attention is concentrated on the isotropic Q-branch of N2, which is significantly narrowed before the broadening produced by weak vibrational dephasing becomes dominant. It is remarkable that isotropic Q-branch collapse is indifferent to orientational relaxation. It is affected solely by rotational energy relaxation. This is an exceptional case of pure frequency modulation similar to the Dicke effect in atomic spectroscopy [13]. The only difference is that the frequency in the Q-branch is quadratic in J whereas in the Doppler contour it is linear in translational velocity v. Consequently the rotational frequency modulation is not Gaussian but is still Markovian and therefore subject to the impact theory. The Keilson-... 

Here p is the radius of the effective cross-section, (v) is the average velocity of colliding particles, and p is their reduced mass. When rotational relaxation of heavy molecules in a solution of light particles is considered, the above criterion is well satisfied. In the opposite case the situation is quite different. Even if the relaxation is induced by collisions of similar particles (as in a one-component system), the fraction of molecules which remain adiabatically isolated from the heat reservoir is fairly large. For such molecules energy relaxation is much slower than that of angular momentum, i.e. xe/xj > 1. 

In the case of the isotropic spectrum it is useful to consider the functional dependence of Acoi/2 and 5gj on rE, since it is rotational energy relaxation that causes frequency modulation in this spectrum. Such a... 

Let us note that this definition of y breaks the limits of the Kielson-Storer model and can cause a few contradictions in interpretation of results. If the measured cross-section oj appears to be greater than oo, then, according to (3.45), the sought y does not exist. To be exact, this assertion is valid relative to the cross-section of the rotational energy relaxation oe = (1 — y2)oot since y2 is always positive. As to oj, taking into account the domain of negative values of y, corresponding to the anticorrelated case (see Chapter 2), formula (3.45) fails to define y when oj > 2co. 

If the. /-diffusion model is valid but only the energy relaxation time is known then Eq. (1.57) may be used to find the other ... 

With formulae (3.58), (3.59) and (3.66) Q-branch contours are calculated for CARS spectra of spherical rotators at various pressures and for various magnitudes of parameter y (Fig. 3.14). For comparison with experimental data, obtained in [162], the characteristic parameters of the spectra were extracted from these contours half-widths and shifts of the maximum subject to the density. They are plotted in Fig. 3.15 and Fig. 3.16. The corresponding experimental dependences for methane were plotted by one-parameter fitting. As a result, the cross-section for rotational energy relaxation oe is found ... 

Experimental verification of the universal wing shape (4.90) is not only an important way of checking the dominant role of spectral exchange but also an additional spectroscopic way to measure energy relaxation time even before collapse (in rare gases). Unfortunately it has not been done yet due to lack of accuracy far beyond the spectral edge. 

Eq. (5.8) formulates the same particle conservation law that was expected to hold for any f(0) in Eq. (4.65). The meaning of Eq. (5.9) becomes clear if one looks for rotational energy relaxation, which obeys the equation... 

Fig. 5.1. The semiclassical description of angular momentum distribution relaxation (a) and rotational energy relaxation at Ea — 0 (6).

Such a construction is not a result of perturbation theory in <5 , rather it appears from accounting for all relaxation channels in rotational spectra. Even at large <5 the factor j8 = B/kT < 1 makes 1/te substantially lower than a collision frequency in gas. This factor is of the same origin as the factor hco/kT < 1 in the energy relaxation rate of a harmonic oscillator, and contributes to the trend for increasing xE and zj with increasing temperature, which has been observed experimentally [81, 196]. 

It is commonly accepted [217, 218] that rotational energy relaxation to its equilibrium value (e) = kT proceeds roughly exponentially as in Eq. (5.29). A current value of rotational energy E = 2j jNj is obtained if the populations of any rotational levels Nj are measured. Such a... 

Fig. 5.8. (a) The weights of the eigenvalues of energy relaxation operator and (b) energy correlation function behaviour at short and long times (in inset) from [215]. 

Fig. 5.15. Theoretical dependences of HWHM on the rate of rotational energy relaxation perturbation theory asymptotics (1), classical weak-collision. /-diffusion model (2), quantum theory without (3) and with (4) adiabatic correction.

It was underlined twice in [251] that the use of fitting laws ties in with the validity of the impact theory, and the present results have to be interpreted cautiously . At high pressure nonlinear increase of rates of energy relaxation and vibrational dephasing with gas density must be... 

Strekalov M. L. Semiclassical theory of rotational energy relaxation in diffusion approximation, Khim. Fiz. 7, 1182-92 (1988). 

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