Density functional theory other forms

Other Forms of Time-Dependent Density Functional Theory... 

Although dimethylberyllium is a coordination polymer in the solid state,27 it has long been known to be monomeric in the gas phase.28 It has also been found to be monomeric when synthesized from the co-condensation of laser-ablated beryllium atoms and a methane/argon mixture at 10 K.11 Formed in conjunction with several other species, including hydrides (see Section 2.02.2.4), (CH3)2Be was identified from its infrared absorption bands, which were compared to DFT-calculated frequencies (DFT = density functional theory). 

Density functional theory (DFT) is based on the Hohenberg-Kohn theorem, which states that there is a functional which gives the exact ground-state energy for the exact electron density. DFT models have become very popular because they are not more costly than Hartree-Fock models. The reason is that in the HF, Cl and MP models, a wavefunction for an N-electron system depends on 3N coordinates, whereas in the DFT approach, the electron density depends on only three coordinates, irrespective of the number of electrons. The problem is that the exact functional would be the Schrodinger equation itself Several approximate functionals have been developed by many authors (Becke, Parr, Perdew, and others) and different forms of the functional can yield slightly different results. Some of the most common DFT models are ... 

There are several problems in the physics of quantum systems whose importance is attested to by the time and effort that have been expended in search of their solutions. A class of such problems involves the treatment of interparticle correlations with the electron gas in an atom, a molecule (cluster) or a solid having attracted significant attention by quantum chemists and solid-state physicists. This has led to the development of a large number of theoretical frameworks with associated computational procedures for the study of this problem. Among others, one can mention the local-density approximation (LDA) to density functional theory (DFT) [1, 2, 3, 4, 5], the various forms of the Hartree-Fock (HF) approximation, 2, 6, 7], the so-called GW approximation, 9, 10], and methods based on the direct study of two-particle quantities[ll, 12, 13], such as two-particle reduced density matrices[14, 15, 16, 17, 18], and the closely related theory of geminals[17, 18, 19, 20], and configuration interactions (Cl s)[21]. These methods, and many of their generalizations and improvements[22, 23, 24] have been discussed in a number of review articles and textbooks[2, 3, 25, 26]. 

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