Density functional theory methods time-dependent extension

The present review has been very selective, stressing the rationale behind density-functional methods above their applications and excluding many important topics (both theoretical and computational). The interested reader may refer to anyone of the many books [91-93] or review articles [94-101] on density-functional theory for more details. Of special importance is the extension of density-functional theory to time-dependent external potentials [102-105], as this enables the dynamical behavior of molecules, including electronic excitation, to be addressed in the context of DFT [106-108]. As they are particularly relevant to the present discussion, we cite several articles related to the formal foundations of density-functional theory [85,100,109-111], linear-scaling methods [63,112-116], exchange-correlation energy functionals [25, 117-122], and qualitative tools for describing chemical reactions [123-126,126-132]. 

The description of the photoionization process by means of a method based on the Density Functional Theory (DFT) is reviewed. The present approach is based on a basis set expansion in B-spline functions, which are particularly suited to deal with the boundary conditions of the continuum states. Both Kohn-Sham (KS) and its extension to the Time Dependent (TD-DFT) formalism are considered. The computational aspects of the method are described the implementations for atoms, for molecules in One Centre Expansion (OCE) and for molecules with the Linear Combination of Atomic Orbital (LCAO) scheme. The applications of the method are discussed, from atoms to large fullerenes, with comparison with available experimental data. 

DFTB is an excellent tool for structural optimization and total energy calculations, and it is very useful in molecular dynamics calculations involving a large number of atoms. An extension of the method to time-dependent density functional theory has given promising results [30, 31]. 

So electronic transitions of anisole [53] represents an example of the accuracy achievable when time-independent simulations of vibronic spectra are coupled to good-quality ab initio computations for geometries and force fields in both electronic states. For anisole, methods based on the density functional theory and its time-dependent extension for electronic excited states [B3LYP/6-311 +G(d,p) and TD-B3LYP/6-311 +G(d,p)] have been applied to perform geometry optimizations and harmonic frequency calculations, while the energy of the electronic transition has been refined by EOM-CCSD/CCSD//aug-cc-pVDZ computations. The remarkable... 

From a computational point of view there is a natural distinction between the molecular and the materials perspective which lies chiefly in the treatment of the surroundings a molecule is treated as a finite object in space, while spatial periodicity is imposed on the material description in order to describe its extensive nature. Today, so-called density functional theory (DFT) methods prevail for ground state calculations of both molecules and materials comprised of up to several hundred atoms. For example, bond lengths can typically be calculated with standard DFT methodologies to accuracies within a few hundredths of an angstrom. Excitations can also be calculated with significant accuracy using an extension of DFT known as time-dependent DFT (TD-DFT). Optical excitations, calculated at the TD-DFT level, often match experiments with an accuracy of ca 0.1 eV for well-behaved systems. 

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