Chemistry Reference
In-Depth Information
It was observed that, as in condensed matter physics, the density can be used as a
key variable. Systems should differ only by their potential energy. This would
provide a versatile, viable alternative. In 1964 Hohenber and Kohn show that all
many-body systems are a function of the ground state density and could be
determined. DFT subsequently became one of the most popular tools in the theory
of electronic structure. The genius of this work, involving this simple idea, was to
realize that it allowed the original many-body problem to be replaced by an
independent electron problem. This can be solved by requiring the ground state
density to be the same as the exact density. We can divide the Kohn-Sham
equations into one part for independent particles and another for the exchange-
correlational function. The energy is minimized and eigenvalues are approximated
to the energies. It is necessary to assume a form for the exchange correlation.
Density functionals have evolved through local spin density approximation,
gradient-expansion approximation, generalized gradient approximations (GGA),
Meta-GGAs, time dependent DFT (TD-DFT), hybrids, functionals to include (H-
bonding, longe-range corrections, thermochemistry, barrier heights, transition-
metal reaction energies, non-covalent interactions, valence and Rydberg electronic
excitations, non-local correlation, intermolecular interaction energies in DNA,
amino acid pairs and reaction energies in organometallic chemistry [653-712].
Recent developments in DFT includes (2012) the d-functional tight-binding
(DFTB) method based on the d.-functional theory as formulated by Hohenberg
and Kohn. The method introduces several approximations. First, the densities and
potentials are written as superpositions of atomic densities and potentials. Second,
many-center terms are summarized together with nuclear repulsion energy terms
in a way that they can be written as a sum of pairwise repulsive terms. The Kohn-
Sham orbitals are expanded in a set of localized atom-centered functions
(represented in a minimal basis of optimized atomic orbitals). These are obtained
self-consistently for spherical symmetrical spin unpolarized neutral atoms. The
Hamilton only contains one- and two-center contributions which can be calculated
and tabulated in advance as a function of the distance between atomic pairs. The
method addresses self-consistent charge extension, weak interactions and a linear
response scheme [656]. Using a Taylor expansion around the reference density the
protocol has been extended to first, second (modification of Coulomb scheme)
