Microscopic dielectric function

Electronic Stopping and Momentum Density of Diamond from First-Principles Treatment of the Microscopic Dielectric Function... 

I he notation 0e indicates that this is the dielectric function at frequencies low i ompared with electronic excitation frequencies. We have also replaced co0 with l (, the frequency of the transverse optical mode in an ionic crystal microscopic theory shows that only this type of traveling wave will be readily excited bv a photon. Note that co2 in (9.20) corresponds to 01 e2/me0 for the lattice vibrations (ionic oscillators) rather than for the electrons. The mass of an electron is some thousands of times less than that of an ion thus, the plasma liequency for lattice vibrations is correspondingly reduced compared with that lor electrons. 

The separation of the field components, and the expression of anisotropic adsorbate dielectrics ( e x, e y, e z ) becomes useful when e is expressed in terms of meaningful microscopic quantities (eg. The dynamic charge of the adsorbate mode), and the Lorentzian oscillator [53] parameterisation of an adsorbate layer has proved useful [34] for this purpose. For any particular vibrational mode, the effective dielectric function 8(co) is given by ... 

The work summarized in these lecture notes is based on extensive use of the Density Functional method, and a local expression selected for the exchange-correlation operator is the only essential approximation. The DF theory, originally thought as method for evaluation of total energy, turned out to be equally efficient for determination of forces acting on atoms, macroscopic stresses and, most recently, of details of the microscopic dielectric response. 

Having estabUshed the connection between conductivity and dielectric function, we will next express the conductivity in terms of microscopic properties of the solid (the electronic wavefunctions and their energies and occupation numbers) as a final step, we will use the eonnection between conductivity and dielectric function to obtain an expression of the latter in terms of the microscopic properties of the solid. This will provide the direct link between the electronic structure at the microscopic level and the experimentally measured dielectric function, which captures the macroscopic response of the solid to an external electromagnetic field. 

Compare the expression for the dielectric function due to intraband transitions, Eq. (5.49), to the Drude result, Eq. (5.39), and identify the constants in the latter in terms of fundamental constants and the microscopic properties of the solid. Provide a physical interpretation for the constants in the Drude expression. 

These results are useful in making the connection between the dielectric function and the conductivity from microscopic considerations, as discussed in chapter 5. 

X. Cartoixa, L.W. Wang, Microscopic dielectric response functions in semiconducUn-quantum dots. Phys. Rev. Lett. 94(23), 236804 (2005)... 

In a contrary to the DFT studies of isolated molecules, where there is a strong link between applications to biological systems and general developments in the theory of density functionals, approaches used for modeling properties of chemical molecules embedded in the biological microscopic environment combine developments in many fields. These fields include DFT, statistical physics, dielectric theory, and the theory of liquids. 

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