Time-dependent density functional theory. See

An alternative theory is the popular time-dependent density functional theory [44], in which transition energies are obtained from the poles of dynamic linear response properties. There are several excellent reviews on time-dependent density functional theory. See, for instance, Ref. [45]. 

Roewer G, Herzog U, Trommer K, Muller E, Friihauf S (2002) Silicon Carbide - A Survey of Synthetic Approaches, Properties and Applications 101 59-136 Rosa A, Ricciardi G, Gritsenko O, Baerends EJ (2004) Excitation Energies of Metal Complexes with Time-dependent Density Functional Theory 112 49-116 Rosokha SV, Kochi JK (2007) X-ray Structures and Electronic Spectra of the n-Halogen Complexes between Halogen Donors and Acceptors with jc-Receptors. 126 137-160 Rudolf P, see Golden MS (2004) 109 201-229... 

Rosa A, Ricciardi G, Gritsenko O, Baerends EJ (2004) Excitation Energies of Metal Complexes with Time-dependent Density Functional Theory 112 49-116 Rudolf P, see Golden MS (2004) 109 201-229... 

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. 

TDDFT see time-dependent density functional theory... 

As the basis sets developed for glycine produced excellent results for fhat amino acid (see Table 5.1 of Ref. [31] for details), we chose to use the same basis also for fhe presenf calculations [68]. Preliminary calculations were also carried out at the level of time-dependent density functional theory (TD-DFT) using the PBE functional [56]. However, the results differed by less fhan 1% from fhe RPA result and are thus not reported here. 

Regarding excited states, time-dependent density functional theory " (TDDFT) is considered a relatively accurate method (see, for example, reference 79) for the study of the low-lying excited states, with results by far superior to the simple virtual-occupied DFT energy difference. The most recent formulations of the GW formalism, originally proposed about 20 years... 

Another important method to calculate transition energies and intensities is time-dependent density functional theory (TDDFT) (see Chapter 2.40). 

Time-dependent density functional theory (TDDFT) is the extension of density functional theory (DFT) (see Chapter 2.39) to time-dependent problems. It has become popular in chemistry since formulations have appeared that allow excitation energies and other important properties to be easily implemented in standard DFT software packages, including Gaussian, ADF, Turbomole, CADPAC, Q-Chem, and several others. 

Instead, the time-dependent density-functional theory, first formulated by Runge and Gross (see also refs. 86 and 87), provides a mathematically exact scheme with which excitation energies can be calculated within density-functional theory. We shall here briefly describe its main foundations and subsequently give a few recent examples of its applications. Although the theory was formulated almost two decades ago, it is only within the last few years that it has become of practical use for a larger class of systems. 

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