Einstein oscillator force constant

Figure 2. A schematic of the free energy density of an aperiodic lattice as a function of the effective Einstein oscillator force constant a (a is also an inverse square of the locahzation length used as input in the density functional of the liquid). Specifically, the curves shown characterize the system near the dynamical transition at Ta, when a secondary, metastable minimum in F a) begins to appear as the temperature is lowered. Taken from Ref. [47] with permission.

Consider now one of these variable and its contribution to the potential energy, z(r) = 27rg 2(7Xz(r)2. This is the potential energy of a three-dimensional isotropic harmonic oscillator. The total potential energy, Eq. (16.82) is essentially a sum over such contributions. This additive form indicates that these oscillators are independent of each other. Furthermore, all oscillators are characterized by the same force constant. We now also assume that all masses associated with these oscillators are the same, namely we postulate the existence of a single frequency Ms., sometimes referred to as the Einstein frequency of the solvent polarization fluctuations, and Ws are related as usual by the force constant... 

The transition dipole moment characterizes the strengfli of the electronic transition (its square is, up to constants, the rate constant for file transition known as the Einstein B coefficient). In the semiclassical limit we can think of the transition dipole moment as a dipole oscillating at the frequency of the transition, rather like the antenna of a radio transmitter. The dispersion force is due to the fluctuating field around the atom (or molecule). While the dipole averages out to zero, its interaction energy with anoflier molecule does not. 

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