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We have formulated a methodology to derive a generalized nanoquanta (nanoquanta+) TDDFT exchange-correlation (XC) kernel that is capable of describing excitonic properties of extended systems. Compared to the standard nanoquanta XC kernel, the generalized one takes into account screening effects more accurately through the usage of exact (beyond one-loop) electron susceptibility in the formalism. As we demonstrate for the example of monolayer WS₂, such an improved XC kernel allows one to reproduce accurately the experimentally-observed nonhydrogenic Rydberg series in the excitonic spectrum, [1] which has so far not been possible with other familiar kernels. We also calculate the effective electron-hole potential that enters the TDDFT eigen-energy equation of excitons, and demonstrate that the reason for the nonhydrogen Rydberg energy series is a non-Coulomb structure of the potential. We discuss the general properties of the nanoquanta+ kernel and compare them to that of other XC kernels employed for extracting properties of excitons.

[1] A. Chernikov et. al, Phys. Rev. Lett. 113, 076802 (2014).