Time-dependent optimized effective potential

Petersilka, M., Gossmann, U. J., Gross, E. K. U., 1998, Time Dependent Optimized Effective Potential in the Linear Response Regime in Electronic Density Functional Theory. Recent Progress and New Directions, Dobson, J. F., Vignale, G., Das, M. P. (eds.), Plenum Press, New York. 

Time-dependent optimized effective potential in the linear response regime, M. Petersilka, U.J. Gossmann, and E.K.U. Gross, in Electronic Density Functional Theory Recent Progress and New Directions, eds. J.F. Dobson, G. Vignale, and M.P. Das (Plenum, NY, 1998). 

In this chapter, we discuss some new developments in TDDFT beyond the linear response regime for accurate and efficient nonperturbative treatment of multiphoton dynamics and very-high-order nonlinear optical processes of atomic and molecular systems in intense and superintense laser fields. In Section 2, we briefly describe the time-dependent optimized effective potential (OEP) method and its simplified version, i.e., the time-dependent Krieger-Li-Iafrate (KLI) approximation, along with self-interaction correction (SIC). In Section 3, we present the TDDFT approaches and the time-dependent generalized pseudospectral (TDGPS) methods for the accurate treatment of multiphoton processes in diatomic and triatomic molecules. In Section 4, we describe the Floquet formulation of TDDFT. This is followed by a conclusion in Section 5. Atomic units will be used throughout this chapter. 

Time-Dependent Optimized Effective Potential. Unfortunately, when trying to write v c as an explicit functional of the density, one encounters some... 

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 ... 

Prom such an action functional, one seeks to determine the local Kohn-Sham potential through a series of chain rules for functional derivatives. The procedure is called the optimized effective potential (OEP) or the optimized potential method (OPM) for historical reasons [15,16]. The derivation of the time-dependent version of the OEP equations is very similar to the ground-state case. Due to space limitations we will not present the derivation in this chapter. The interested reader is advised to consult the original paper [13], one of the more recent publications [17,18], or the chapter by E. Engel contained in this volume. The final form of the OEP equation that determines the EXX potential is... 

For this collision, the optimal effective mass varies from 7 to 10 atomic mass units depending on the interaction potentials adopted [27], while n is 19. This means that for this system 0 is about three times less (provided a) than 0. It implies in turn, that at room temperature / (r) is about two orders of magnitudes larger than k (T). A careful theoretical analysis of HCl + Ar collisions shows [27] that the experimental results on 1 0 transition within the... 

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