Time‐Independent Excited‐State Density Functional Theory

Abstract

We review the current status of time‐independent density‐functional theory for an individual excited‐state. The theory is built upon generalized constrained‐search formulation that maps a given excited‐state density to the corresponding many‐body wavefunction. This process obtains the wavefunction as a bi‐functional of the excited‐state desnity and the ground‐state density However, the important issues in excited‐state density‐functional theory are whether an accurate exchange‐correlation functional can be constructed to get excited‐state energy and whether a unique Kohn‐Sham system can be constructed for a given excited‐state. In this paper we show that the answer to both the questions is in the affirmative. The existence of excited‐state Kohn‐Sham system is demonstrated by constructing it for the excited‐states of some members of Boron isoelectronic series. In connection with the excited‐state functional, we present recently constructed exchnage energy fucntional for excited‐states within the local‐density‐approximation. Accuracy of the functional is demonstrated by applying it to a large number of excited‐states of atoms and by calculating accurate band gaps of a range of semiconductors.