Time-dependent density functional theory exact exchange

Hirata S, Ivanov S, Bartlett RJ, Grabowski I (2005) Exact-exchange time-dependent density-functional theory for static and dynamic polarizabilities, Phys. Rev. A, 71 032507... 

The many-body ground and excited states of a many-electron system are unknown hence, the exact linear and quadratic density-response functions are difficult to calculate. In the framework of time-dependent density functional theory (TDDFT) [46], the exact density-response functions are obtained from the knowledge of their noninteracting counterparts and the exchange-correlation (xc) kernel /xcCf, which equals the second functional derivative of the unknown xc energy functional ExcL i]- In the so-called time-dependent Hartree approximation or RPA, the xc kernel is simply taken to be zero. 

Molecules by Time-Dependent Density Functional Theory Based on Effective Exact Exchange Kohn-Sham Potentials. 

Della Sala, R, and Gorling, A. (2003) Excitation energies of molecules by time-dependent density functional theory based on effective exact exchange Kohn-Sham potentials, IntJ. Quantum Chem., 91,131-138. 

Hessehnann A, Gorling A Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree—Fock, J Chem Phys 134 034120, 2011. 

A second distinct approximation to /xc is in terms of its (usually) dominant exchange contribution. A highly accurate approximation to the exact exchange-only equations of ground-state density functional theory (the optimized effective potential equations) was introduced by Krieger, Li, and lafrate. This approximation has been extended to the time-dependent case ... 

This chapter is devoted to orbital-dependent exchange-correlation (xc) functionals, a concept that has attracted more and more attention during the last ten years. After a few preliminary remarks, which clarify the scope of this review and introduce the basic notation, some motivation will be given why such implicit density functionals are of definite interest, in spite of the fact that one has to cope with additional complications (compared to the standard xc-functionals). The basic idea of orbital-dependent xc-functionals is then illustrated by the simplest and, at the same time, most important functional of this type, the exact exchange of density functional theory (DFT for a review see e.g. [1], or the chapter by J. Perdew and S. Kurth in this volume). 

With eqn (7) the time-dependent Kohn-Sham scheme is an exact many-body theory. But, as in the time-independent case, the exchange-correlation action functional is not known and has to be approximated. The most common approximation is the adiabatic local density approximation (ALDA). Here, the non-local (in time) exchange-correlation kernel, i.e., the action functional, is approximated by a time-independent kernel that is local in time. Thus, it is assumed that the variation of the total electron density in time is slow, and as a consequence it is possible to use a time-independent exchange-correlation potential from a ground-state calculation. Therefore, the functional is written as the integral over time of the exchange-... 

---