Adiabaticity, Ehrenfest

E. E. Nikitin, Pathways of vibrational relaxation of diatoms in collisions with atoms Manifestation of the Ehrenfest adiabatic principle, in Gas Phase Chemical Reaction Systems, Eds. J.Wolfrum et al, Berlin-Heidelberg, Springer, 1996, p 231... 

The exponential dependence of P on velocity is the manifestation of the Ehrenfest adiabatic principle [4], once tJilti is identified with the frequency ra of a perturbed system (the BC diatom) and In/h av with the characteristic time of the perturbing force t(E) for the exponential interaction. A representation... 

Adiabatic switching is based on the Ehrenfest adiabatic theorem [65-67], which states that classical actions and quantum numbers are preserved in adiabatic, slow processes. It is assumed that the actual Hamiltonian H may be written as a sum of a separable zero-order Hamiltonian H0 and a nonseparable part AH ... 

A solution of either (1.1) or (2.1) is impossible without in-, troducing some approximations even for the simplest chemical reactions. A great simplification of the problem is achieved on the basis of the EHRENFEST adiabatic principle, which states that a system remains in the same quantum state if a change in its surroundings occurs sufficiently slowly. Consequently, the electronic state will be not affected if the motions of nuclei are very slow compared with the motions of the electrons. This is usually the real situation, as first recognized in the molecular spectroscopy by BORN and OPPENHEIMER /22/ and, subsequently, in chemical dynamics by LONDON /23/ Therefore, in (la.I) T. ... 

P. Ehrenfest, Adiabatic Invariants and the Theory of Quanta, Philosophical Magazine, 33,500-513,1917, quoted from p. 501. 

Pathways of Vibrational Relaxation of Diatoms in Collisions with Atoms Manifestation of the Ehrenfest Adiabatic Principle... 

Different pathways of vibrational relaxation of diatoms in thermal collisions with atoms are discussed in the framework of the Ehrenfest adiabatic principle and generalized Landau-Teller model. Since the efficiency of different energy-transfer channels depend very strongly on the value of the Ehrenfest exponent, it is possible to assign, for given collision partners and the heat-bath temperature, the vibrational energy transfer events to VT, VRT or VR processes. 

The process of vibrational excitation and deexcitation of a diatom in a collision with an atom represents a simplest example from the host of processes which are relevant to gas-phase chemical kinetics. Experimental techniques available now allow one to measure directly state-to-state energy transfer rate coefficients. Theoretically, it is possible to accomplish completely ab initio calculation of these coefficients. One can therefore, regard the existing models of the vibrational relaxation from a new standpoint as a means for helping to understand more clearly the dynamics of the energy transfer provided that all the models are related to a single fundamental principle. This is the Ehrenfest adiabatic principle as formulated by Landau and Teller in the application to the collisional vibrational transitions of diatomic molecules. 

Landau and Teller demonstrated that the transfer of the vibrational energy of a diatomic molecule into translational energy of colliding partners (say, a diatomic molecule and an noble gas atom) is a very inefficient process, and this property of the collision is related to the Ehrenfest adiabatic principle [5] of mechanics. In its simplest version, the adiabatic principle asserts that the change 57, of the action variable 7, of a classical system under die influence of a slow external perturbation of... 

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