Excited States from Time-Dependent Density Functional Theory

Excited States from Time-Dependent Density Functional Theory 

Peter Elliott/ Eilipp Eurche, and Kieron Burke S 

Reviews in Computational Chemistry, Volume 26 edited by Kenny B. Lipkowitz and Thomas R. Cundari Copyright 2009 John Wiley 6c Sons, Inc. 

Time-dependent density functional theory (TDDFT), in contrast, applies the same philosophy as ground-state DFT to time-dependent problems. Here, the complicated many-body time-dependent Schrodinger equation is replaced by a set of time-dependent single-particle equations whose orbitals yield the same time-dependent density. We can do this because the Runge-Gross theorem proves that, for a given initial wave function, particle statistics and interaction, a given time-dependent density can arise from, at most, one time-dependent external potential. This means that the time-dependent potential (and all other properties) is a functional of the time-dependent density. 

Armed with a formal theorem, we can then define time-dependent Kohn-Sham (TDKS) equations that describe noninteracting electrons that evolve in a time-dependent Kohn-Sham potential but produce the same density as that of the interacting system of interest. Thus, just as in the ground-state case, the demanding interacting time-dependent Schrodinger equation (TDSE) is replaced by a much simpler set of equations. The price of this enormous simplification is that the exchange-correlation piece of the Kohn-Sham potential has to be approximated. 

---

Elliott P, Furche F, Burke K (2009) Excited states from time-dependent density functional theory. In Reviews in computational chemistry, pp 91-165... 

Elliott, P., Furche, E, and Burke, K. (2008) Excited states from time-dependent density functional theory, in Reviews in Computational Chemistry, vol. 26 (ed. Lipkowitz, K. B., and Cundari, T. R.), John Wiley Sons, Hoboken, NJ, pp. 91-166. 

P. Elliott, F. Furche, and K. Burke, in Reviews in Computational Chemistry, K. B. Lipkowitz and D. B. Boyd (Eds.), Vol. 26, VCH Publishers, Inc., New York, 2009, pp. 91 -165, Excited States from Time-Dependent Density Functional Theory. 

---