Optical spectra of solids obtained by time-dependent density functional theory with the jellium-with-gap-model exchange-correlation kernel

Abstract

Within the framework of ab initio Time Dependent-Density Functional Theory (TD-DFT), we propose a static approximation to the exchange-correlation kernel based on the jellium-with-gap model. This kernel accounts for electron-hole interactions and it is able to address both strongly bound excitons and weak excitonic effects. TD-DFT absorption spectra of several bulk materials (both semiconductor and insulators) are reproduced in very good agreement with the experiments and with a low computational cost.The theoretical description of the optical properties of materials by first principles calculations is one of the classical issues in solid state physics. After photon absorption, the excitonic effects, driven by the electron and hole (e-h) interactions, are principal actors, rendering the ab initio computational description demanding. The most successful approach is, so far, based on ManyBody Perturbation theory: the GW self energy accounts for electron-electron (e-e) many-body effects in the band structure calculations, whereas the Bethe-Salpeter Equation is solved to introduce e-h interactions [1]. This accurate method has a limited applicability to large systems due to its high computational cost.Time-Dependent Density-Functional Theory (TD-DFT) is another theory for the exact treatment of excited states. Similarly to ground state DFT, its main drawback is to properly approximate the unknown dynamic exchange-correlation (xc) kernel f xc , which should account for both e-e and e-h interactions. From the very first attempt, the Homogeneous Electron Gas (HEG) model system had been employed in construction of xc kernels [2,3], and one of the most used approach was derived from local density approximation (LDA) xc potential v xc in the static regime, Adiabatic LDA (ALDA) [2]. ALDA has been successfully applied to molecules and clusters, but it usually becomes inappropriate in solids where the improvements with respect to the Random Phase Approximation (RPA) (with the trivial f xc = 0) are negligible. The introduction of shortrange non-locality, like in a generalized-gradient approximation (GGA) [4] or in a non-LDA (NLDA) [5] approach, does not improve with respect to LDA or RPA optical spectra. Main reason for this failure resides in the missed ultra-long range behaviour, 1/|r−r ′ | or 1/q 2 in reciprocal space, absent in HEG and HEG-based kernels. On the other hand, the introduced empirical long range contribution (LRC) kernel, f xc = α/q 2 [6-8], with α found related to the screening, correctly reproduces e-h excitonic effects but it is limited to semiconductors and small gap insulators. Very recently, renewed interest in this issue has been boosted by two new approaches. In the first one, the Bootstrap kernel [9] extends the LRC kernel to a matricial form and proposes a heuristic form for the LRC weight in terms of the screening which has to be calculated self-consistently. This method has been successfully applied to a wide range of bulk materials. In the second work [10], starting from the meta-GGA xc functiona...

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

“…Specifically, both TDSRSH and BSE predict the first and largest excitation at 12.6 eV, very close to the experimental value at 12.75 eV, and the overall spectral shape is satisfying. Here too, then, SRSH and TDSRSH are shown to capture excitonic effects, even though the Si excitons are much more delocalized and weakly bound compared to the case of pentacene, and the LiF excitons are strongly-bound and known to be highly challenging for many of the TDDFT methods discussed in the introduction [20,26,28,39].…”

“…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.…”

Estimating Excitonic Effects in the Absorption Spectra of Solids: Problems and Insight from a Guided Iteration Scheme

“…[11][12][13][14][15][16], try to overcome this problem. A class of successful kernels has been derived from the BSE [17][18][19][20][21][22].…”

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

“…Moreover, the actual value of a determines how well excitonic effects are described (a is clearly system-dependent). [244] For silicon the TPSS functional (see Section 3.1.10) gives a510:0045, that is, with the wrong sign, whereas the VSXC functional (see Section 3.3.1) gives a520:104, which has the right sign, but it is about one half of the correct value. [142] …”