Rotational energy exchange

E.E. Nikitin and D.V.Shalashilin, Quasiclassical model of vibrational-rotational energy exchange, Khim. Fiz. 11, 1471 (1992)... 

This relaxation proceeds without energy exchange between rotational and translational degrees of freedom and is supposed to be the same in EFA as in exact theory f = With this assumption we obtain a result identical to the ELIOS approximation [190] ... 

The physical meaning of and f L.., is obvious they govern the relaxation of rotational energy and angular momentum, respectively. The former is also an operator of the spectral exchange between the components of the isotropic Raman Q-branch. So, equality (7.94a) holds, as the probability conservation law. In contrast, the second one, Eq. (7.94b), is wrong, because, after substitution into the definition of the angular momentum correlation time... 

We recall that e, f are the vibration-rotation energies of the molecule in the anion and neutral molecule states, E denotes the kinetic energy carried away by the ejected electron, and the density of translational energy states of the ejected electron is p(E). Also recall that we use the short hand notation to symbolize the multidimensional derivative operators that arise in non BO couplings and that embody the momentum-exchange between the vibration/rotation and electronic degrees of fieedom ... 

The first term on the right corresponds to Raleigh scattering. The second term suggests an energy-exchange interaction that depends on the anisotropy of the polarizability and involves frequencies shifted from that of the incident radiation by an amount which depends on twice the rotational or vibrational frequency of the molecules in the sample. 

The difference of the translation and rotation energy is more or less the same among the compounds appearing at the left- and right-hand side of the exchange reaction equation, except for hydrogen, where rotation must be taken into account. This... 

This type of energy exchange in an autoionization process may correspond with the behavior of a kicked rotator in classical mechanics, which is known to exhibit chaos. It would be worthwhile to consider an autoionization process of a simple diatomic molecule in its Rydberg states to understand experimentally the essential dynamics of a quantum system, whose classical counterpart exhibits chaos. 

The importance of vibration-vibration exchange is now apparent in the results of the early experiments on HC1 and on hydroxyl (from H+03 - OHp+02) at pressures above 0.1 torr. These showed vibrational distributions that were nearly Boltzmann, but with shape parameters corresponding to temperatures of several thousand degrees, far greater than the translational temperatures. These distributions were samples taken after rotational relaxation and after the efficient vibration-vibration energy exchange... 

Formation of the complex is, however, associated with changes of the moments of inertia of the molecule. Consequently, part of the energy of total rotation is exchanged with that of vibration and internal rotation. In the case where the molecule is stretched in the complex, the overall rotational energy is decreased and hence +, IF( +) and the derived k( ) are enhanced. This is known as the centrifugal effect. The equation for the energy balance now has to be modified to... 

It appears, for example, that rotational energy is relatively easily transferred and that most collisions are in fact effective in the exchange of such energy. Frequencies associated with typical molecular rotations are of the order of 1011 or 1012 cycles, or rotations, per second. Alternatively, we say that it takes about 10-11 or 10"12 sec for one rotation of a molecule. We see, therefore, that in gases at pressures lower than 1 atm many rotations occur between collisions, and deactivation, but that in liquids the molecules generally will not be able to complete a rotation in the short time of 10"13 sec that exists on the average between collisions. We conclude, therefore, that in liquids the molecules are not free to rotate, and this conclusion is consistent with our observations that vibrational absorption bands generally show rotational fine structure only when the sample is a gas. 

Much of the work done prior to 1959 on the theory of energy exchange between translation and rotation has been reviewed by Herzfeld and Litovitz... 

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