Dielectric response electron oscillator model

Electrons in metals at the top of the energy distribution (near the Fermi level) can be excited into other energy and momentum states by photons with very small energies thus, they are essentially free electrons. The optical response of a collection of free electrons can be obtained from the Lorentz harmonic oscillator model by simply clipping the springs, that is, by setting the spring constant K in (9.3) equal to zero. Therefore, it follows from (9.7) with co0 = 0 that the dielectric function for free electrons is... 

Electron transfer processes, more generally transitions that involve charge reorganization in dielectric solvents, are thus shown to fall within the general category of shifted harmonic oscillator models for the thennal enviromnent that were discussed at length in Chapter 12. This is a result of linear dielectric response theory, which moreover implies that the dielectric response frequency a>s does not depend on the electronic charge distribution, namely on the electronic state. This rationalizes the result (16.59) of the dielectric theoiy of electron transfer, which is identical to the rate (12.69) obtained from what we now find to be an equivalent spin-boson model. 

Second, we note that the dynamical aspect of the dielectric response is still incomplete in the above treatment, since (1) no information was provided about the dielectric response frequency and (2) a harmonic oscillator model for the local dielectric response is oversimplified and a damped oscillator may provide a more complete description. These dynamical aspects are not important in equilibrium considerations such as our transition-state-theory level treatment, but become so in other limits such as solvent-control electron-transfer reactions discussed in Section 16.6. 

Simple Spectral Method [23] In the simple spectral method, a model dielectric response function is used. It combines a Debye relaxation term to describe the response at microwave frequencies with a sum of terms of classical form of Lorentz electron dispersion (corresponding to a damped harmonic oscillator model) for the frequencies from IR to UV ... 

From Eq, (1) it is clear that a model of crystal polarization that is adequate for the description of the piezoelectric and pyroelectric properties of the P-phase of PVDF must include an accurate description of both the dipole moment of the repeat unit and the unit cell volume as functions of temperature and applied mechanical stress or strain. The dipole moment of the repeat unit includes contributions from the intrinsic polarity of chemical bonds (primarily carbon-fluorine) owing to differences in electron affinity, induced dipole moments owing to atomic and electronic polarizability, and attenuation owing to the thermal oscillations of the dipole. Previous modeling efforts have emphasized the importance of one more of these effects electronic polarizability based on continuum dielectric theory" or Lorentz field sums of dipole lattices" static, atomic level modeling of the intrinsic bond polarity" atomic level modeling of bond polarity and electronic and atomic polarizability in the absence of thermal motion. " The unit cell volume is responsive to the effects of temperature and stress and therefore requires a model based on an expression of the free energy of the crystal. 

The induced dipole formulation is an example of the so-called polarizable embedding but it is not the only possible choice. There are in fact various alternatives schemes to simulate the polarization of the MM subsystem, such as the fluctuating charges [24, 25], the classical Drude oscillators [26], or the Electronic Response of the Surroundings (ESR) [27] which mixes a non-polarizable MM scheme with a polarizable continuum model characterized by a dielectric constant extrapolated at infinite frequency. 

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