Temperature dependence librational state

We now consider hydrogen transfer reactions between the excited impurity molecules and the neighboring host molecules in crystals. Prass et al. [1988, 1989] and Steidl et al. [1988] studied the abstraction of an hydrogen atom from fluorene by an impurity acridine molecule in its lowest triplet state. The fluorene molecule is oriented in a favorable position for the transfer (Figure 6.18). The radical pair thus formed is deactivated by the reverse transition. H atom abstraction by acridine molecules competes with the radiative deactivation (phosphorescence) of the 3T state, and the temperature dependence of transfer rate constant is inferred from the kinetic measurements in the range 33-143 K. Below 72 K, k(T) is described by Eq. (2.30) with n = 1, while at T>70K the Arrhenius law holds with the apparent activation energy of 0.33 kcal/mol (120 cm-1). The value of a corresponds to the thermal excitation of the symmetric vibration that is observed in the Raman spectrum of the host crystal. The shift in its frequency after deuteration shows that this is a libration i.e., the tunneling is enhanced by hindered molecular rotation in crystal. 

Tn denotes the dephasing time of the optical transition, T the lifetime of the excited state (fluorescence hfetime) and the pure dephasing time. At low temperatures T is essentially independent on temperature while shows a strong dependence on temperature. The actual value of at a given temperature depends on the excitation of low frequency modes (phonons, librations) that couple to the electronic transition of the chromophore. In crystalline matrices at low temperatures (T <2 K) Tl approaches infinity as host phonons and local modes are essentially quenched and the linewidth is solely determined by the lifetime contribution. 

We have also shown that some originally proposed (e.g., in GT2) properties of the hat potential turn out to be excessively abstract, so that we disregarded them. We mean here (i) absence of free rotors, performing circular motion, since in the water/ice structure there is no place for such a motion, and (ii) nonexistence of precessors, since, as it appears, the libration of dipoles in a diametric cross section of the hat-like potential well dominates. On the other hand, the well s curvature is important for modeling the spectra, since, unlike the well depth, this curvature strongly depends on temperature and fluid phase state. 

Distinct characters of the static structure enter the specification of this more complex motion. Same as for librational oscillations, the symmetry of tumbling reorientations proceeds from both the symmetry of the intermolecular torques and the symmetry of the molecules themselves through the values of their distinct molecular moments of inertia. The most prominent role of inertial factors, and more recently that of torques too, have been made especially clear by W.A. Steele (1). Apart from these molecular and local factors, collective properties of the liquid enter the dynamics through the rate of reorientation. This rate itself is a combination of two factors, generally undistin-guishable in the observed mean value these are the velocity of the angular rotation and the rate of occurence of elementary rotations. Hereafter in section V we will come back to experimental approaches specifying the rate of occurence dependence upon the liquid equation of state (i.e. its temperature and density dependence). ... 

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