Time-dependent density functional theory effective potential

S. Yoo, F. Zahariev, S. Sok, M.S. Gordon, Solvent effects on optical properties of molecules A combined time-dependent density functional theory/effective fragment potential approach, J. Chem. Phys. 129 (2008) 144112. 

Yoo, S., Zahariev, R, Sok, S., Gordon, M. S. (2008). Solvent Effects on Optical Properties of Molecules A Combined Time-Dependent Density Functional Theory/Effective Fragment Potential Approach, /. Chem. Phys., 129,144112-8. 

Phenylperoxy radical has similarly been a topic of experimental and theoretical interest. Tokmakov et al. " calculated a potential energy surface for phenyl radical and O2 using ab initio G2(MP2) calculations. Weisman and Head-Gordon used time-dependent density functional theory (TD-DFT) calculations to examine the effect of substituents on the phenylperoxy radical s UV-vis absorption spectrum. " Lin and Mebel used ab initio methods to study the phenoxy radical -f O-atom reaction. "... 

Time-dependent density functional theory (TDDFT) as a complete formalism [7] is a more recent development, although the historical roots date back to the time-dependent Thomas-Fermi model proposed by Bloch [8] as early as 1933. The first and rather successful steps towards a time-dependent Kohn-Sham (TDKS) scheme were taken by Peuckert [9] and by Zangwill and Soven [10]. These authors treated the linear density response of rare-gas atoms to a time-dependent external potential as the response of non-interacting electrons to an effective time-dependent potential. In analogy to stationary KS theory, this effective potential was assumed to contain an exchange-correlation (xc) part, r,c(r, t), in addition to the time-dependent external and Hartree terms ... 

SOCI spin-orbit configuration interaction SOFT second-order perturbation theory SOREP spin-orbit relativistic effective potential TD-DFT time dependent density functional theory ZORA zero-order regular approximation... 

The most promising approaches for efficient electronic structure calculations on large molecules are generally based on density functional theory with Kohn-Sham orbitals [32-35]. The most efficient such method for CE-BEs is based on Koopmans theorem, but this approach has quite limited accuracy [36-39]. Better accuracy can be obtained from calculations based on an effective core potential [40-45], an equivalent core approximation [46-48], a fractionally occupied transition state [49-52], or with a ASCF approach [29, 31, 53-57]. Time-dependent density functional theory is also widely used for CEBE calculation [58-62], wherein the best results are usually given with functionals having a long-range correction [63, 64]. 

Time-dependent density-functional theory (TDDFT) extends the basic ideas of ground-state density-functional theory (DFT) to the treatment of excitations and of more general time-dependent phenomena. TDDFT can be viewed as an alternative formulation of time-dependent quantum mechanics but, in contrast to the normal approach that relies on wave-functions and on the many-body Schrodinger equation, its basic variable is the one-body electron density, n(r,t). The advantages are clear The many-body wave-function, a function in a 3A-dimensional space (where N is the number of electrons in the system), is a very complex mathematical object, while the density is a simple function that depends solely on the 3-dimensional vector r. The standard way to obtain n r,t) is with the help of a fictitious system of noninteracting electrons, the Kohn-Sham system. The final equations are simple to tackle numerically, and are routinely solved for systems with a large number of atoms. These electrons feel an effective potential, the time-dependent Kohn-Sham potential. The exact form of this potential is unknown, and has therefore to be approximated. 

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. 

On top of this effective ground-state description a time-dependent extension has been proposed by Niehaus and co-workers, which is usually referred to as a time-dependent density-functional response theory tight-binding (TD-DFRT-TB) scheme. It corresponds to the formulation of Casida s linear-response theory that has been discussed before. The coupling matrix giving the response of the potential with respect to a change in the electron density has to be built as stated in eqn (19), and we use again the adiabatic approximation. 

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. 

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 ... 

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). 

The second approach is used by Baerends and co-workers. They use linear response theory, but instead of calculating the full linear response function they use the response function of the noninteracting Kohn-Sham system together with an effective potential. This response function can be calculated from the Kohn-Sham orbitals and energies and the occupation numbers. They use the adiabatic local density approximation (ALDA), and so their exchange correlation kernel, /xc (which is the functional derivative of the exchange correlation potential, Vxc, with respect to the time-dependent density) is local in space and in time. They report frequency dependent polarizabilities for rare gas atoms, and static polarizabilities for molecules. 

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