Landau-Teller expression

Landau-Teller expression oc exp(—2 zA / Ctv) for a head-on collision. Here... 

Landau-Teller expression P °c exp(-2M /ft v) for a head-on collision. Here V is the collision velocity and a is the logarithmic derivative of the repulsive exponential potential [3],... 

In order to ascertain whether the 3-regime behavior observed in the experimental vibrational lifetimes is indeed a result of local density enhancements, Goodyear and Tucker [12] computed both vibrational lifetimes and local density enhancements from molecular dynamics simulation for a model solute-solvent SCF solution. These authors considered a diatomic solute in a 2-dimensional supercritical Lennard-Jones fluid of 1150 atoms (Fig. 1). In this model, each of the solute atoms was designated as a Lennard-Jones site, and the Lennard-Jones parameters between solute and solvent atoms were taken to be the same as those between solvent atoms. The vibrational lifetimes were computed using the standard, classical Landau-Teller expression [69,70,72,73,78], i.e. 

It is now interesting to consider the classical (h 0) limits of these two expressions. Actually, in the first instance it is inappropriate to take this limit, since just the opposite limit (/fftkuio 1) is invoked in truncating the state space to two levels. However, in the second instance, one can smoothly take the classical limit, and one finds that in this case Ti is given by the usual classical Landau-Teller result ... 

The temperature dependence for the probability of VT relaxation for anharmonic oscillators (2-178) is similar to that of harmonic oscillators (2-172), (2-173), and corresponds to the Landau-Teller formula. The exponential parameter 5vx can be expressed for anharmonic oscillators as... 

The Landau-Teller model considers a linear collision of a structureless particle A with a harmonic oscillator BC within an approach which by now is known as a semiclassical method the relative particle-oscillator motion (coordinate R) is described classically and the vibrational motion of the oscillator (coordinate x) by quantum mechanics the interaction between incoming particle A and the nearest end B of the oscillator BC is taken to be exponential, I/(/ g) c exp(-aR g). The expression for the transition probability in the near-adiabatic limit was found [4] to have the following generic form ... 

A simple well-known extension of a collinear Landau-Teller model is provided by the breathing sphere (BSP) model of Schwartz, Slawsky and Herzfeld [13] which fully retains the Landau-Teller exponential factor. More consistent treatment, which approximately takes into account the anisotropic character of the atom-molecule interaction, is based on the so-called infinite order sudden approximation (lOSA) [14] with respect to rotational transitions that accompany the vibrational transition. Within this approximation the rotation of the relaxing molecule plays the role of a spectator, which insignificantly modifies the exponent in Eq. (8) through quite unimportant redefinition of a. If, in addition, the quasiclassical correction to the semiclassical Landau-Teller exponent is small and the effect of the attractive part of the potential is weak, one can write the following simple expression for the deactivation rate constant within BSP or lOSA approximation ... 

If one follows the approach of Landau and Teller [11], who in dealing with vibrational relaxation developed an expression by averaging a transition probability based on the relative molecular velocity over the Maxwellian distribution, one can obtain the following expression for the recombination rate constant [6] ... 

The Jahn-Teller theorem has a footnote this is always true with the only exception of linear molecules. So the amusing story of the Jahn-Teller effect is that I first worked with my student, Renner, on a paper that presented the only general exception to the Jahn-Teller effect. It really should be the Landau-Jahn-Teller theorem because Landau was the first one who expressed it, unfortunately using the only exception where it was not valid. 

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