Thus, the problem of solving the many-body Schrödinger equation is bypassed, and now the objective becomes to minimize a density functional. Note, however, that although the

Hohenberg–Kohn theorems assure us that the density functional is a universal quantity; they do not specify Dasatinib molecular weight its form. In practice, the common current realization of DFT is through the Kohn–Sham (KS) approach (Kohn and Sham 1965a). The KS method is operationally a variant of the HF approach, on the basis of the construction of a noninteracting system yielding the same density as the original problem. Noninteracting systems are relatively easy to solve because the wavefunction can be exactly represented as a Slater determinant of orbitals, in this setting often referred to as a Kohn–Sham determinant. The form of the kinetic energy functional of such a system is known exactly and the only unknown term is the exchange–correlation functional. Here lies the major problem of DFT: the exact functionals for exchange and correlation are not known except for the free electron gas. However, many approximations exist which permit the calculation of

molecular properties at various levels of accuracy. The most fundamental and simplest approximation is the local-density approximation (LDA), in which the energy depends only on the density at the find more point where the functional is evaluated (Kohn and Sham 1965b). LDA, which in essence assumes that the density corresponds to that of an homogeneous

Rapamycin electron gas, proved to be an improvement over HF. While LDA remains a major workhorse in solid state physics, its success in chemistry is at best moderate due to its strong tendency for overbinding. The first real breakthrough came with the creation of functionals belonging to the so-called generalized gradient approximation (GGA) that incorporates a dependence not only on the electron density but also on its gradient, thus being able to CYT387 supplier better describe the inhomogeneous nature of molecular densities. GGA functionals such as BP86 (Becke 1988) or PBE (Perdew et al. 1996) can be implemented efficiently and yield good results, particularly for structural parameters, but are often less accurate for other properties. The next major step in the development of DFT was the introduction of hybrid functionals, which mix GGA with exact Hartree–Fock exchange (Becke 1993). Nowadays, hybrid DFT with the use of the B3LYP functional (Becke 1988; Lee et al. 1988) is the dominant choice for the treatment of transition metal containing molecules (Siegbahn 2003). This method has shown good performance for a truly wide variety of chemical systems and properties, although specific limitations and failures have also been identified.