Exciton spectrum within the time-dependent density-functional theory in two models of one-dimensional periodic potential

In this paper, bound excitons are studied in the frame work of the time-dependent density-functional theory (TDDFT). Two 1D systems are considered: the Kronig-Penney model and a smooth periodic potential. Within the two-band approximation, we study the dependence of the number of bound excitons on the type of exchange-correlation kernels. Two simple approximations are used: the short-ranged contact xc kernel and the long-ranged (or `soft-Coulomb') one. As a result, one or two bound ecxitons are produced, depending on the system.