Vibrational quantum transfers

Spears K G, Wen X and Zhang R 1996 Electron transfer rates from vibrational quantum states J. Phys. Chem. 100 10 206-9... 

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.

Section 4.04.1.2.1). The spectroscopic and the diffraction results refer to molecules in different vibrational quantum states. In neither case are the- distances those of the hypothetical minimum of the potential function (the optimized geometry). Nevertheless, the experimental evidence appears to be strong enough to lead to the conclusion that the electron redistribution, which takes place upon transfer of a molecule from the gas phase to the crystalline phase, results in experimentally observable changes in bond lengths. 

Fig. 2. Surface temperature dependence of the vibrational excitation of NO(v = 0 — 1) in collisions with a clean Ag(lll) surface. The observed thermal activation was attributed to hot electron-hole-pair recombination transferring energy to NO vibration. This work provided some of the first strong evidence that metal electrons can interact with an adsorbate molecule strongly enough to change its vibrational quantum numbers. (See Ref. 24.)...

The vibrational overlap integrals play a key role in electron transfer. A region of vibrational overlap defines values of the normal coordinate where a finite probability exists for finding coordinates appropriate for both reactants and products. The greater the overlap, the greater the transition rate. The vibrational overlap integrals can be evaluated explicitly for harmonic oscillator wavefunctions. An example is shown in equation (26) for the overlap between an initial level with vibrational quantum number v = 0 to a level v = v where the frequency (and force constant) are taken to be the same before and after electron transfer. 

The reaction Ne + (N2,Ne)N (Table III) is the only exoergic charge-transfer process for which the Cross section has been observed to increase with increasing vibrational quantum number of the neutral reactant.128 A probable rationale for this phenomenon is that both criteria of efficient charge transfer, namely, energy resonance and favorable Franck-Condon overlap, are satisfied if the reaction entails formation of a quartet N2+ state from the (v=2) vibrational level of N2 in the ground electronic state. 

The slowest process will be the vibration-translation activation to the (v = 1) level, which will be rate-determining, and the subsequent vibration-vibration transfers will occur at increasingly fast rates with increasing vibrational quantum number. (For harmonic oscillators 1 = n(m+ l) 1 .) Shock-tube experi-... 

Quantum mechanical methods do not suffer these difficulties, and they have been widely applied to predissociative vibrational energy transfer in dimers (see, e.g., Balint-Kurti 1990 Chu 1984 Clary 1989, 1991 Hutson 1990 LeRoy 1984 Tucker and Truhlar 1988 Zhang and Zhang 1993), but they become impractical for larger ones. 

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