![]() Nevertheless the explicit form of E XC remains unknown. The first term T s, which accounts for a large portion of T, may now be calculated using KS orbitals as in Hartree–Fock calculations. Where T s is the kinetic energy of non-interacting electrons, J the classical electron-electron repulsion energy (Hartree energy), and E XC the exchange-correlation energy. When the density is treated this way, the total energy is written as Their approach attempts to describe the real electron density by way of non-interacting electrons that are described using a Slater determinant of molecular orbitals (MOs). A practical approach to this problem was proposed by Kohn and Sham (1965). To proceed, one needs to know how T and V ee are expressed as functionals of ρ( r). The variational principle and the Levy constrained-search formulation of DFT ( Levy, 1979) ensure that E can be determined by minimizing it with respect to some N-representable trial electron densities.ĭespite the fundamental importance of the Hohenberg–Kohn theorems, they do not provide explicit forms of the energy functionals in Equation 1 (except V ne). They also showed that the variational principle holds for the ground-state energy. In 1964, Hohenberg and Kohn proved that there is a one-to-one correspondence between the ground-state density and the external potential ( Hohenberg and Kohn, 1964). In stark contrast to the wave function Ψ that depends on 3 × N (space) + N (spin) = 4 N variables, ρ( r) contains only three spatial variables, implying that E may be obtained in a much more straightforward manner using ρ( r). Where x i collectively denote spatial ( r i) and spin ( s i) coordinates. In DFT, electronic energy E is expressed as a functional of electron density, viz., The availability of user-friendly software packages greatly assists in applying DFT calculations to individual specific problems. This feature is particularly useful when one intends to investigate large molecular systems, to which the application of accurate ab initio methods may be difficult or even impossible. DFT offers viable computational protocols with a good balance between accuracy and computational cost. Emphasis will be placed on our own work.ĭensity functional theory (DFT) has been playing increasingly important roles in many research activities of science and engineering in recent decades and has already become a mainstay for the quantum mechanical investigations of a broad range of complex molecular systems that are of interest in chemistry, biology, and physics ( Parr and Yang, 1989 Kohn et al., 1996 Baerends and Gritsenko, 1997 Kohn, 1999 Koch and Holthausen, 2001 Zhao and Truhlar, 2008 Perdew et al., 2009 Burke, 2012 Cohen et al., 2012). In this paper, we present a brief overview of several recent applications of DFT to iron-containing non-heme synthetic complexes, heme-type cytochrome P450 enzymes, and non-heme iron enzymes, all of which are of particular interest in the field of bioinorganic chemistry. From the viewpoint of chemistry, this is mainly because iron is abundant on earth, iron plays powerful (and often enigmatic) roles in enzyme catalysis, and iron thus has the great potential for biomimetic catalysis of chemically difficult transformations. Iron-containing molecules are particularly important targets of DFT calculations. Even for biological molecules such as proteins, DFT finds application in the form of, e.g., hybrid quantum mechanics and molecular mechanics (QM/MM), in which DFT may be used as a QM method to describe a higher prioritized region in the system, while a MM force field may be used to describe remaining atoms. Owing to its balanced accuracy and efficiency, DFT plays particularly useful roles in the theoretical investigation of large molecules. The past decades have seen an explosive growth in the application of density functional theory (DFT) methods to molecular systems that are of interest in a variety of scientific fields. Division of Chemistry and Biological Chemistry, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore.Hajime Hirao *, Nandun Thellamurege and Xi Zhang
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