Ab initio calculation of dynamic polarizability and dielectric constant of carbon and silicon cubic crystals

Abstract

Valence and conduction bands of carbon silicon cubic systems are first obtained by a process called linear combination of atomic orbitals Ž . Ž . self-consistent field LCAO-SCF , both at the Hartree-Fock HF and local density Ž . approximation LDA levels. Then, the crystalline orbitals are used in a sum-Ž . over-states SOS method to calculate the corresponding dielectric constants related to electronic polarizabilities. This method allows parallel computations with large granularity of the optical properties and leads to uncoupled HF and LDA results.

First-principles study of the structural, electronic, and optical properties ofGa2O3in its monoclinic and hexagonal phases

“…The sum over states ͑SOS͒ method is used to calculate the real and imaginary parts of the mean dynamic polarizabilty ͓␣͔͑͒ as a function of the electric field frequency ͑͒. 41 The polarizability can be expressed as follows:…”

First-principles study of the optical properties of BeO in its ambient and high-pressure phases

“…After determining the equilibrium structural and electronic properties, the static optical properties were calculated using the finite-field (FF) method [15]. The dynamic optical properties were obtained using a ''sum over states'' (SOS) method [16]. This method has been applied successfully to determine accurately the index of refraction, real and imaginary parts of dielectric function and energy-loss spectra of wide-band-gap systems, such as Ga 2 O 3 [17], BN, GaN and MgO [18].…”

Ab initio electron energy‐loss spectra and depolarization effects: Application to carbon nanotubes

“…The SOS method derived from the linear response theory calculates the mean dynamic polarizability [α(ω)] as a function of the electric field frequency (ω)8, 9 and the dielectric constant ε(ω) is deduced from $\varepsilon (\omega ) = 1 + 4\pi N\alpha (\omega )$ where N is the number of moieties per volume unit. The unit cell volume is not well defined for slabs or nanotubes.…”

“…Another approach to calculate the ELF function is based on the “sum over states” (SOS) calculation of static and dynamic polarizability using the one‐electron eigenfunctions and eigenvalues provided by the periodic code CRYSTAL097. This method8, 9 allows the calculation of the dielectric constant as a function of real or imaginary frequencies10–14 and nonlinear susceptibilities of periodic systems15. Note that these approaches based on the independent‐particle approximation are not sufficient for full interpretation of the experiments, especially for the 2D (surfaces) or 1D (nanotubes) periodic systems.…”