First-principles calculations of nonlinear optical susceptibility of inorganic materials

Abstract

A method for calculations of the frequency-dependent nonlinear susceptibility of inorganic materials is implemented in the velocity gauge using a linear combination of atomic orbitals (LCAO) method within the framework of either the Hartree-Fock approximation or density functional theory. It is based on the standard time-dependent diagrammatic perturbation theory and has previously been applied successfully for atoms and molecules. For inorganic materials, it requires the eigenvalues and position operator matrix elements at several k points in the Brillouin zone. A quantitative assessment of the predictability of the method was made on cubic GaN for which the results of previous theoretical studies are available.

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.…”