Semiclassical extension of the Landau-Teller theory of collisional energy transfer

Abstract

A semiclassical version of the quantum coupled-states approximation for the vibrational relaxation of diatomic molecules in collisions with monatomic bath gases is presented. It is based on the effective mass approximation and a recovery of the semiclassical Landau exponent from the classical Landau-Teller collision time. For an interaction with small anisotropy, the Landau exponent includes first order corrections with respect to the orientational dependence of the collision time and the effective mass. The relaxation N(2)(v=1)-->N(2)(v=0) in He is discussed as an example. Employing the available vibrationally elastic potential, the semiclassical approach describes the temperature dependence of the rate constant k(10)(T) over seven orders of magnitude across the temperature range of 70-3000 K in agreement with experimental data and quantum coupled-states calculations. For this system, the hierarchy of corrections to the Landau-Teller conventional treatment in the order of importance is the following: quantum effects in the energy release, dynamical contributions of the rotation of N(2) to the vibrational transition, and deviations of the interaction potential from a purely repulsive form. The described treatment provides significant simplifications over complete coupled-states calculations such that applications to more complex situations appear promising.

Interpretation of the vibrational relaxation of H2 in H2 within the semiclassical effective mass approach

“…Earlier calculations [20][21][22][23] of the rate of the inelastic process ͑1͒ either completely ignored the effect of rotation 20 or introduced, for a given potential surface, severe dynamical simplifications [21][22][23] which still required extensive numerical work. It appears therefore of interest to see whether an analytical SC approach within the EM method can provide a physically reasonable interpretation of the temperature dependence of the vibrational relaxation of H 2 in neat H 2 gas which was measured by different techniques [24][25][26][27] over a wide temperature range from 3000 down to 50 K. In this paper, similar to our earlier approach, 10 we consider only the direct mechanism of vibrational relaxation which proceeds without the formation of a transient complex formed as a result of the translation-rotational energy exchange. The reason for this is twofold: first, the complex formation is expected to be unimportant for the collision energies exceeding the depth of the interaction potential, and, second, for the complexassisted vibrational relaxation the temperature dependence of the rate coefficient shows upturn behavior which is not seen in the existing experimental data at lower temperatures.…”

Further insight into the tunneling contribution to the vibrational relaxation of NO in Ar

“…3 from Ref. 13). In the present work on NO relaxation in Ar, we have extended the LZCl theory to lower temperatures by using the WKB approach (LZWKB).…”

“…In our earlier study of the N 2 relaxation in He, we have extended the original, classical, LT theory (LTCl) to low temperatures by using the WKB approach (LTWKB). 13 At room temperature, the ratio LTWKB k 10 / LTCl k 10 amounts to more than a factor of 100 and markedly increases for still lower temperatures. This is in agreement with experimental data available over wide temperature ranges (see Fig.…”

“…13 The difference between 2.35 a −1 0 and 2 a −1 0 can be ascribed to the fact that the slope of the potentials along the reaction coordinate is slightly larger than along the radial coordinate. The slope ϕ f of υ f is noticeably larger than ϕ i .…”

“…8,9 As before, the potential energy surface (PES) of the forming quasi-bound collision complexes is of central importance. 10 When the collider finally is an inert rare gas atom, vibrational energy transfer still may be far more efficient than estimated on the basis of the Landau-Teller (LT) mechanism (transitions between vibrational states supported by uncoupled Born-Oppenheimer (BO) PESs as described in the original LT approach, 11 the Schwartz-Slawsky-Herzfeld (SSH) 12 treatment, or its semiclassical generalization 13 ). The reason for this enhancement of efficiency may again be found in the openelectronic shell character of NO.…”