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7.2 Density Functional Theory
Density functional theory (DFT) is primarily a theory of the electronic structure of
atoms, molecules, and solids in their ground states, in which the electronic density
distribution n(r) plays the central role. It is one of the standard computational
tools in the condensed matter, chemistry, and biochemistry in both academia and
industry [40]. Up to now, the DFT is presently the most successful and also the most
promising approach to compute the electronic structure of materials. It provides
the description of electronic structure (i.e., structure prediction) and enables to
calculate the optical properties, total energies (thermodynamics and kinetics), and
forces of materials under very general conditions [41]. The theory was extensively
applicable for atoms, molecules, solids, nuclei, and quantum as well as classical
fluids [42]. In its original formulation, the DFT provides the electron density
which plays a key role in describing the ground state properties of a material.
Later on in the field of chemistry, the DFT is employed to predict a great variety
of molecular properties including molecular structures, vibrational frequencies,
atomization energies, ionization energies, electric and magnetic properties, reaction
paths, etc. [43]. The original DFT has been generalized to deal with many different
situations: spin-polarized systems, multicomponent systems such as nuclei and
electron-hole droplets, free energy at finite temperatures, superconductors with
electronic pairing mechanisms, relativistic electrons, time-dependent phenomena
and excited states, bosons, molecular dynamics, etc. [44]. For example, the energies
of the functional group and the interaction of carbon dioxide were investigated by
DFT calculations with the use of the DMol 3 code [45] and selection of generalized
gradient approximation (GGA-PBE) by Perdew, Burke, and Ernzerhof (PBE) [46].
The atomic orbital was described using double numeric polarization (DNP) basis
set, which is comparable to 6-31G (d,p). The van der Waals correction was further
taken into account [47]. The type of core processing is set up using a DFT half-core
pseudopots (DSPP) specifically designed for DMol 3 calculations [48]. The realspace orbital global cutoff radius is 3.7 Å. The convergence threshold parameters
for the optimization are 10 −5 Hartree (energy), 2 × 10 −3 Hartree (gradient), and
5 × 10 −3 Hartree (displacement) [49].
Since the 1960s, the DFT was introduced in two seminal papers by the authors
Hohenberg-Kohn and Kohn-Sham, and its citation is soon up to ∼4000 (1964)
∼9000 (1965). The annual paper collections dealing with the DFT application
are shown in Fig. 7.1 [50]. Note that the relatively small number of publications
before 1990 by no means implies that important work was not being carried out.
It was a very well-established computational technique, and “density functional”
or other designations are named in many applications. Remarkably, the number
of publications per year (1975–2014) on topics (“density functional” or “DFT”) is
listed, according to the Web of Science Core Collection (February 2015). The inset
shows data near 1990 on an expanded scale [51]. Obviously, it shows the dramatic
increase in the number of publications on the topics “density functional” and density
functional theory “(DFT)” in recent years. DFT was promptly incorporated into
P. Veerakumar et al.
7.2 Density Functional Theory
Density functional theory (DFT) is primarily a theory of the electronic structure of
atoms, molecules, and solids in their ground states, in which the electronic density
distribution n(r) plays the central role. It is one of the standard computational
tools in the condensed matter, chemistry, and biochemistry in both academia and
industry [40]. Up to now, the DFT is presently the most successful and also the most
promising approach to compute the electronic structure of materials. It provides
the description of electronic structure (i.e., structure prediction) and enables to
calculate the optical properties, total energies (thermodynamics and kinetics), and
forces of materials under very general conditions [41]. The theory was extensively
applicable for atoms, molecules, solids, nuclei, and quantum as well as classical
fluids [42]. In its original formulation, the DFT provides the electron density
which plays a key role in describing the ground state properties of a material.
Later on in the field of chemistry, the DFT is employed to predict a great variety
of molecular properties including molecular structures, vibrational frequencies,
atomization energies, ionization energies, electric and magnetic properties, reaction
paths, etc. [43]. The original DFT has been generalized to deal with many different
situations: spin-polarized systems, multicomponent systems such as nuclei and
electron-hole droplets, free energy at finite temperatures, superconductors with
electronic pairing mechanisms, relativistic electrons, time-dependent phenomena
and excited states, bosons, molecular dynamics, etc. [44]. For example, the energies
of the functional group and the interaction of carbon dioxide were investigated by
DFT calculations with the use of the DMol 3 code [45] and selection of generalized
gradient approximation (GGA-PBE) by Perdew, Burke, and Ernzerhof (PBE) [46].
The atomic orbital was described using double numeric polarization (DNP) basis
set, which is comparable to 6-31G (d,p). The van der Waals correction was further
taken into account [47]. The type of core processing is set up using a DFT half-core
pseudopots (DSPP) specifically designed for DMol 3 calculations [48]. The realspace orbital global cutoff radius is 3.7 Å. The convergence threshold parameters
for the optimization are 10 −5 Hartree (energy), 2 × 10 −3 Hartree (gradient), and
5 × 10 −3 Hartree (displacement) [49].
Since the 1960s, the DFT was introduced in two seminal papers by the authors
Hohenberg-Kohn and Kohn-Sham, and its citation is soon up to ∼4000 (1964)
∼9000 (1965). The annual paper collections dealing with the DFT application
are shown in Fig. 7.1 [50]. Note that the relatively small number of publications
before 1990 by no means implies that important work was not being carried out.
It was a very well-established computational technique, and “density functional”
or other designations are named in many applications. Remarkably, the number
of publications per year (1975–2014) on topics (“density functional” or “DFT”) is
listed, according to the Web of Science Core Collection (February 2015). The inset
shows data near 1990 on an expanded scale [51]. Obviously, it shows the dramatic
increase in the number of publications on the topics “density functional” and density
functional theory “(DFT)” in recent years. DFT was promptly incorporated into