Time-dependent current density functional theory

Berger JA, Snijders JG (2002) Ultranonlocality in time-dependent current-density-functional theory Application to conjugated polymers, Phys. Rev. Lett, 83 694-697... 

Since the current density in the bulk measures the surface charges, the time-dependent current-density functional theory (CDFT) appears to be a way to investigate this problem. At least the results presented by de Boeij et al. [171] for the bulk susceptibility and by van Faassen et al. [172] for the polarizability of linear chains are encouraging, although this may not be the case for second-and third-order effects. 

By the calculations of the time-dependent current density functional theory using this equation, accurate excitation energies are obtained for some n tt excitations (van Faassen and de Boeij 2004). Meanwhile, however, it has been found that quite poor excitation energies are produced for the excitations of some types of molecules. On the other hand, calculations of the adiabatic excitation energy benchmark set, containing 109 molecules, show that the vector potential correction hardly affects the calculated excitation energies (Bates and Furche 2012). 

TDCDFT Time-dependent current density functional theory... 

Lett., 88, 186401 (2002). Ultranonlocality in Time-Dependent Current-Density-Functional Theory Application to Conjugated Polymers. 

Sen and Chakrabarti have employed the CPHF, CPKS/B3LYP, TDDFT/ALDA, and TDCDFT/VK (time-dependent current density functional theory/Vignale Kohn) methods to calculate the polarizability in alkali-doped traws -polyacetylene chains as a function of chain length and as a function of the nature of the dopant. They have evidenced a minimum in the evolution of the average polarizability per unit cell and have attributed it to the charge transfer between the alkali and the chain. 

Time-dependent Current Density Functional Theory... 

The role of relativity in the optical response of gold within the time-dependent current-density-functional theory, P. Romaniello and P. L. de Boeij, J. Chem. Phys., 2005,122, 164303. 

Since RGI establishes that the external potential is a functional of the current density, one could choose to use the current density as the basic variable instead of the density. This is known as time-dependent cmrent density functional theory (TDCDFT) (See discussion below on solids.)... 

This equation defines the TDKS potentials Ajo implicitly in terms of the functionals A[j] and A,[j]. Clearly, Eq. (137) is rather complicated. The external-potential terms 5 and J are simple functionals of the density and the paramagnetic current density. The complexity of Eq. (137) arises from the fact that the density, Eq. (128), and the paramagnetic currents, Eqs. (129), (134), are complicated functionals of j. Hence a formulation directly in terms of the density and the paramagnetic current density would be desirable. For electrons in static electromagnetic fields, Vignale and Rasolt [61-63] have formulated a current-density functional theory in terms of the density and the paramagnetic current density which has been successfully applied to a variety of systems [63]. A time-dependent HKS formalism in terms of the density and the paramagnetic current density, however, has not been achieved so far. 

The time-dependent density functional theory [38] for electronic systems is usually implemented at adiabatic local density approximation (ALDA) when density and single-particle potential are supposed to vary slowly both in time and space. Last years, the current-dependent Kohn-Sham functionals with a current density as a basic variable were introduced to treat the collective motion beyond ALDA (see e.g. [13]). These functionals are robust for a time-dependent linear response problem where the ordinary density functionals become strongly nonlocal. The theory is reformulated in terms of a vector potential for exchange and correlations, depending on the induced current density. So, T-odd variables appear in electronic functionals as well. 

The frequency dependence of SHG at simple metal surface has been the focus of a recent theoretical study of Liebsch [100]. Time-dependent density functional theory was used in these calculations. The results suggest that the perpendicular surface contribution to the second harmonic current is found to be significantly larger than had been assumed previously. He also concludes that for 2 a> close to the threshold for electron emission, the self-consistently screened nonlinear electronic response becomes resonantly enhanced, analogous to local field enhancement in the linear response near the bulk plasma frequency. 

Gross, E.K.U., Dobson, J.F. and Petersilka, M. (1996). Density functional theory of time-dependent phenomena, in Density Functional Theory, ed. R.F. Nalewajski, Series Topics in Current Chemistry (Springer, Berlin). 

A totally different point of view is proposed by Time-Dependent Density Functional Theory [211-215] (TD-DFT). This important extension of DFT is based on the Runge-Gross theorem [216]. It extends the Hohenberg-Kohn theorem to time-dependent situations and states that there is a one to one map between the time-dependent external potential t>ea t(r, t) and the time-dependent charge density n(r, t) (provided we know the system wavefunction at t = —oo). Although it is linked to a stationary principle for the system action, its demonstration does not rely on any variational principle but on a step by step construction of the charge current. 

The treatment in terms of induced current is in the mainstream of modem development of the time-dependent density functional theory (TDDFT). Moreover, the current density formalism has been proposed [4] as a variant of TDDFT. The evolution of current density presents properly the response of electrons on an external field. In general words, such a strong basis is promising for a theoretical treatment of many aspects of ion interactions with atoms, molecules and solids. 

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