Parameter-Free Calculation of Response Functions in Time-Dependent Density-Functional Theory

Abstract

We have established and implemented a fully ab initio method which allows one to calculate optical absorption spectra, including excitonic effects, without solving the cumbersome Bethe-Salpeter equation, but obtaining results of the same precision. This breakthrough has been achieved in the framework of time-dependent density-functional theory, using new exchange-correlation kernels f(xc) that are free of any empirical parameter. We show that the same excitonic effects in the optical spectra can be reproduced through different f(xc)'s, ranging from frequency-dependent ones to a static one, by varying the kernel's spatial degrees of freedom. This indicates that the key quantity is not f(xc), but f(xc) combined with a response function. We present results for the optical absorption of bulk Si and SiC in good agreement with experiment, almost indistinguishable from those of the Bethe-Salpeter approach.

Efficientab initiocalculations of bound and continuum excitons in the absorption spectra of semiconductors and insulators

“…In the ab initio framework, such a complex spectrum is typically described by the solution of the four-point (electron-hole) Bethe-Salpeter equation (BSE) [2,14,15]. In Fig.1 we show the optical spectrum of solid argon calculated within the BSE approach, and within TDDFT both using TDLDA [18] and the MBPTderived kernel [7]. The agreement of the BSE curve with experiment (line-circles) [21] (and with previous BSE calculations [22]) is good, concerning both position and relative intensity of the first two peaks.…”

“…The widely used adiabatic local-density approximation [4,5] (TDLDA), with its static and short-ranged kernel, often yields good results in clusters but fails for absorption spectra of solids. Instead, more sophisticated approaches derived from Many-Body Perturbation Theory (MBPT) [6,7,8,9,10] have been able to reproduce, ab initio, the effect of the electron-hole interaction in extended systems, not least thanks to an explicit long-range contribution [6,11,12]. The latter strongly influences spectra like optical absorption or energy loss, especially for relatively small momentum transfer.…”

“…Instead, the first two peaks require less k-points and, as can be seen in the inset, are and TDDFT using kernel of Ref. [7] (solid) are compared (only the n ′ singlet exciton series) with experiment [21]. TDLDA is given by the points.…”

Solid-state optical absorption from optimally tuned time-dependent range-separated hybrid density functional theory

“…Several ingenious schemes for overcoming this deficiency have been suggested, including the use of an exchange-correlation kernel of the form f xc (r, r ) = −α/(4π|r − r |), where α is a system-dependent empirical parameter [24,25]; a static approximation to the exchangecorrelation kernel based on a jellium-with-gap model [26]; a "bootstrap" parameter-free kernel, achieved using selfconsistent iterations of the random phase approximation (RPA) dielectric function [20,27]; a related "guided iteration" RPA-bootstrap kernel [28]; and the Nanoquanta kernel [12,24,29,30], derived by constructing the exchangecorrelation kernel from an approximate solution to the BSE. Each correction provides a major step forward.…”

Analysis of the Vignale-Kohn current functional in the calculation of the optical spectra of semiconductors

“…4 However, when we consider transverse vector potentials, the natural Legendre conjugate is the current density. 16 Third, to describe nonlocal exchange-correlation effects in large systems, 15,17,18 it can be more convenient and more efficient to use a local functional of the current density instead of a nonlocal functional of the density. [19][20][21] Within TDDFT, one would need an exchange-correlation functional that is completely nonlocal to be able to take into account the charges that are induced at the surface of the system caused by the external field and that produce a counteracting field.…”