Multiphonon process

In diatomic VER, the frequency Q is often much greater than so VER requires a high-order multiphonon process (see example C3.5.6.1). Because polyatomic molecules have several vibrations ranging from higher to lower frequencies, only lower-order phonon processes are ordinarily needed [34]- The usual practice is to expand the interaction Hamiltonian > in equation (03.5.2) in powers of nonnal coordinates [34, 631,... 

Thus far we have discussed the direct mechanism of dissipation, when the reaction coordinate is coupled directly to the continuous spectrum of the bath degrees of freedom. For chemical reactions this situation is rather rare, since low-frequency acoustic phonon modes have much larger wavelengths than the size of the reaction complex, and so they cannot cause a considerable relative displacement of the reactants. The direct mechanism may play an essential role in long-distance electron transfer in dielectric media, when the reorganization energy is created by displacement of equilibrium positions of low-frequency polarization phonons. Another cause of friction may be anharmonicity of solids which leads to multiphonon processes. In particular, the Raman processes may provide small energy losses. 

Another conventional simplification is replacing the whole vibration spectrum by a single harmonic vibration with an effective frequency co. In doing so one has to leave the reversibility problem out of consideration. It is again the model of an active oscillator mentioned in section 2.2 and, in fact, it is friction in the active mode that renders the transition irreversible. Such an approach leads to the well known Kubo-Toyozawa problem [Kubo and Toyozava 1955], in which the Franck-Condon factor FC depends on two parameters, the order of multiphonon process N and the coupling parameter S... 

Description in Terms of a Radiationless Nonadiabatic Multiphonon Process. 93... 

It is thus evident that the experimental results considered in sect. 4 above are fully consistent with the interpretation based on absolute reaction rate theory. Alternatively, consistency is equally well established with the quantum mechanical treatment of Buhks et al. [117] which will be considered in Sect. 6. This treatment considers the spin-state conversion in terms of a radiationless non-adiabatic multiphonon process. Both approaches imply that the predominant geometric changes associated with the spin-state conversion involve a radial compression of the metal-ligand bonds (for the HS -> LS transformation). 

A quantum-mechanical description of spin-state equilibria has been proposed on the basis of a radiationless nonadiabatic multiphonon process [117]. Calculated rate constants of, e.g., k 10 s for iron(II) and iron(III) are in reasonable agreement with the observed values between 10 and 10 s . Here again the quantity of largest influence is the metal-ligand bond length change AR and the consequent variation of stretching vibrations. 

When considering the effect of temperature on multiphonon processes, one should take into account stimulated phonon-assisted transitions ([20,21]) and include thermally activated reversed transitions. Account of these factors gives... 

Diatomic molecules are the simplest condensed phase VER systems, for example, a dilute solution of a diatomic such as I2 or XeF in an atomic (e.g., Ar or Xe) liquid or crystal. Other simple systems include neat diatomic liquids or crystals, or a diatomic molecule bound to a surface. VER of a diatomic molecule can occur only by energy transfer to the collective vibrations of the bath, i.e., the phonons. Ordinarily VER is a high-order multiphonon process. Consequently there is an enormous variability in VER lifetimes, which may range from 56 s [liquid N2 (20)] to 1 ps [e.g., XeF in Ar (21)], and a high level of sensitivity to environment. Diatomic molecules have simple structures but complex VER mechanisms. 

Doorway vibration decay is particularly interesting because it is the one situation where polyatomic molecule VER looks just like diatomic molecule VER. The doorway vibrations of polyatomic molecules decay by exactly the same multiphonon mechanism as the VER of a diatomic molecule. Diatomic molecules have been extensively studied (7). One prediction for diatomic molecules is an exponential energy-gap law (2). As the vibrational frequency is increased, with everything else held constant, the number of emitted phonons increases (the order of the multiphonon process increases) and the VER rate should decrease exponentially with increasing vibrational frequency. 

Defect recombination is therefore primarily non-radiative. The standard theories of non-radiative transitions are based on the multiphonon processes described in Section 8.1.2. A temperature-independent capture cross-section of about 10 cm" is characteristic of a defect state with a strong electron-phonon coupling (see Fig. 8.6). 

Nonradiative transitions between the 4f levels of lanthanide ions are caused by multiphonon processes. In the case of band emissions, the quantum efficiency is commonly interpreted by the Mott s model. It should be noted that Struck and Fonger have shown that in fact an unified model can be used for these two types of emission. ... 

When the energy transfer occurs between the levels of a donor and an acceptor in which the mismatch of energy of several thousand cm-1, multiphonon phenomena must be considered. This was done by Miyakawa and Dexter (32). In their theoretical analysis of multiphonon processes, Miyakawa and Dexter derived a comparative relaxation analogue... 

Here g is the electron-lattice coupling constant, suffixes S and A are sensitizer and activator ions respectively, n is the number of phonons excited at the temperature of the system, hco is the phonon energy which contributes dominantly to these multiphonon processes and N is the number of phonons emitted in the processes, namely,... 

Ptutoyujum. (Am +). The energy level scheme and possible lasing transitions for Pu + are very similar to those of Np +. Prospective transitions include 6Hg/2+6H5/2, 9/2 7/2, and h7/2 Hc/2 For efficient fluorescence and laser action from either tne °Hg/2 or j/2 states, hosts should have low phonon frequencies to reduce nonradiative decay by multiphonon processes. Depending upon the host and the exact positions of higher-lying states, excited-state absorption may reduce or prevent net gain. 

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