A Brief Compendium of Time-Dependent Density Functional Theory

Abstract

Time-dependent density-functional theory (TDDFT) is a formally exact approach to the timedependent electronic many-body problem which is widely used for calculating excitation energies. We present a survey of the fundamental framework, practical aspects, and applications of TDDFT. This paper is mainly intended for non-experts (students or researchers in other areas) who would like to learn about the present state of TDDFT without going too deeply into formal details. I. PREFACEThis paper presents an introduction to and a survey of time-dependent density-functional theory (TDDFT). The purpose of the paper is to explain in a nutshell what TDDFT is and what it can do. We will discuss the basics of the formal framework of TDDFT as well as the current state of the art, skipping over details of the proofs, and highlight some of the most important applications. Readers who would like a more detailed treatment and more literature references are encouraged to consult recent books [1, 2] and review articles [3][4][5].TDDFT is a theoretical approach to the dynamical quantum many-body problem; it can be used to describe quantum systems that are not stationary. As a consequence, TDDFT provides formally exact and practically convenient methods to calculate electronic excitation energies. By contrast, density-functional theory (DFT) is a ground-state theory: in other words, it is used to find the ground state of a quantum system and calculate related quantities of interest, such as the ground-state energy. In many, if not most, situations of practical interest, we have to determine the ground state of the system before we can study its dynamics or calculate its excitations.The beginnings of ground-state DFT date back to the years 1964/65 when the famous papers by Hohenberg and Kohn [6] and Kohn and Sham [7] were published. Since then, DFT has developed into a dominating method for electronic structure calculations in physics, chemistry, materials science, and many other areas (see Ref.[8] for a recent up-to-date account of DFT). Although TDDFT is of much more recent origin [9], it now has reached a similar status for calculating electronic excitations.TDDFT uses many familiar concepts from DFT, most prominently, the Kohn-Sham idea of replacing the real interacting many-body system by a noninteracting system that reproduces the same density. But there are also many concepts that are unique to the time-dependent case, such as memory and initial-state dependence. To gain a thorough understanding of TDDFT it is hence advisable to begin with a study of the basic concepts of DFT. We refer the reader to the very nice introductions to DFT by Capelle [10] and by Burke and Wagner [11]. There exist a number of books on DFT, some of which are very accessible to newcomers in the field [12,13], others are more advanced [14].

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