We solve the long-standing problem of the large overestimation of the static polarizability of conjugated polymers obtained using the local density approximation within density-functional theory. The local approximation is unable to describe the highly nonlocal exchange and correlation (xc) effects found in these quasi-one-dimensional systems. Time-dependent current-density-functional theory enables a local current description of ultranonlocal xc effects using the Vignale-Kohn functional [G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996)]. Except for the model hydrogen chain, our results are in excellent agreement with the best available correlated methods.

Time-dependent density-functional theory (TDDFT) is widely used in the study of linear response properties of finite systems. However, there are difficulties in properly describing excited states, which have double- and higher-excitation characters, which are particularly important in molecules with an open-shell ground state. These states would be described if the exact TDDFT kernel were used; however, within the adiabatic approximation to the exchange-correlation (xc) kernel, the calculated excitation energies have a strict single-excitation character and are fewer than the real ones. A frequency-dependent xc kernel could create extra poles in the response function, which would describe states with a multiple-excitation character. We introduce a frequency-dependent xc kernel, which can reproduce, within TDDFT, double excitations in finite systems. In order to achieve this, we use the Bethe-Salpeter equation with a dynamically screened Coulomb interaction W(omega), which can describe these excitations, and from this we obtain the xc kernel. Using a two-electron model system, we show that the frequency dependence of W does indeed introduce the double excitations that are instead absent in any static approximation of the electron-hole screening.

In this paper we present a new approach to calculate optical spectra, which for the first time uses a polarization dependent functional within current density functional theory (CDFT), which was proposed by Vignale and Kohn [Phys. Rev. Lett. 77, 2037 (1996)]. This polarization dependent functional includes exchange-correlation (xc) contributions in the effective macroscopic electric field. This functional is used to calculate the optical absorption spectrum of several common semiconductors. We achieved in all cases good agreement with experiment.