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

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.