Gradient-dependent exchange-correlation kernel for materials optical properties

We have developed an exchange-correlation kernel in the framework of time-dependent density-functional theory that remarkably accounts for the electron-hole interaction and the optical properties of semiconductors. This kernel, which we name JGM-G, generalizes the jellium-with-gap kernel of Trevisanutto et al. [Phys. Rev. B 87, 205143 (2013)] by considering the gradient of the density as a new ingredient. We have tested it on various materials, from low-band-gap to wide-band-gap semiconductors, and we have demonstrated that the JGM-G kernel yields an optical response that is close to experiment. These encouraging results indicate that the JGM-G kernel can become a low-cost and practical tool for the description of excitonic effects in semiconductors.