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

A major obstacle for computing optical spectra of solids is the lack of reliable approximations for capturing excitonic effects within time-dependent density functional theory. We show that the accurate prediction of strongly bound electron-hole pairs within this framework using simple approximations is still a challenge and that available promising results have to be revisited. Deriving a set of analytical formulas we analyze and explain the difficulties. We deduce an alternative approximation from an iterative scheme guided by previously available knowledge, significantly improving the description of exciton binding energies. Finally, we show how one can “read” exciton binding energies from spectra determined in the random phase approximation, without any further calculation.

Figure 1

Real part of ${\epsilon }_M^{\mathrm{RPA}}(\omega )$ for Si, LiF, and Ar (black solid line). Its crossing with the red dashed [blue dot-dashed] horizontal lines gives the exciton binding energy ${\omega }_0$ from Eq. (7) [Eq. (11)]. The green vertical line indicates the quasiparticle gap.

Figure 2

Imaginary part of ${\epsilon }_M^{\mathrm{RPA}}(\omega )$ for Si, LiF, and Ar computed in various approximations. Experimental spectra are taken from Ref. [58] for Si, Ref. [55] for LiF, and Ref. [56] for Ar. The green vertical lines indicate the quasiparticle gap.