Background: 1920s: Introduction of the Thomas-Fermi model.
1964: Hohenberg-Kohn paper proving existence of exact DF. 1965:
Kohn-Sham scheme introduced. 1970s and early 80s: LDA. DFT becomes
useful. 1985: Incorporation of DFT into molecular dynamics
(Car-Parrinello) 1988: Becke and LYP functional. DFT useful for
some chemistry. 1998: Nobel prize awarded to Walter Kohn in
chemistry for development of DFT.
Slide 4
Walter Kohn, Nobel Prize 1998 Chemistry
Slide 5
Hohenberg-Kohn theorem The total energy of an interacting
inhomogeneous electron gas in the presence of an external potential
V ext (r ) is a functional of the density
Slide 6
Density Functional Theory Density functional theory (DFT) is a
quantum mechanical modeling method used in physics and chemistry to
investigate the electronic structure (principally the ground state)
of many-body systems, in particular atoms, molecules, and the
condensed phases
Slide 7
Density functional theory is an exact reformulation of
many-body quantum mechanics in terms of the probability density
rather than the wave function The ground-state energy can be
obtained by minimization of the energy functional E[n]. All we know
about the functional is that it exists, however, its form is
unknown. Kohn-Sham reformulation in terms of single-particle
orbital helps in the development of approximations and is the form
used in current density functional calculations today
Slide 8
Density Functional Theory With this theory, the properties of a
many- electron system can be determined by using functional, i.e.
functions of another function, which in this case is the spatially
dependent electron density. Hence the name density functional
theory comes from the use of functional of the electron
density.
Slide 9
Density Functional Theory DFT is among the most popular and
versatile methods available in condensed-matter physics,
computational physics, and computational chemistry DFT has been
very popular for calculations in solid state physics since the
1970s. However, DFT was not considered accurate enough for
calculations in quantum chemistry until the 1990s, when the
approximations used in the theory were greatly refined to better
model the exchange and correlation interactions.
Slide 10
Density Functional Theory In many cases the results of DFT
calculations for solid-state systems agree quite satisfactorily
with experimental data. Computational costs are relatively low when
compared to traditional methods, such as Hartree-Fock theory
Slide 11
DFT-Properties Total energy Forces Structure determination
Charge density, dipole moments
Slide 12
DFT-FUNCTIONALS Some commonly used functionals in DFT are BLYP
B3LYP PBE0 (PBE1PBE) PW91 (PW91 PW91)
Slide 13
Applying DFT for computational purposes in Gauss 03
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
To observe Surface Charge Distribution From Gaussian 03W we
will open the.chk file of our work using the option (utilities)
from the scratch folder A DOS prompt will open and.chk file will be
converted to.fchk file
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Problems with DFT Despite recent improvements, there are still
difficulties in using density functional theory to properly
describe intermolecular interactions, especially van der Waals
forces (dispersion); charge transfer excitations; transition states
and some other strongly correlated systems.
Slide 30
Problems with DFT Its incomplete treatment of dispersion can
adversely affect the accuracy of DFT in the treatment of systems
which are dominated by dispersion (e.g. interacting noble gas
atoms) or where dispersion competes significantly with other
effects (e.g. in biomolecules).
Slide 31
NEW DFT METHODS: The development of new DFT methods designed to
overcome previously mentioned problem, by alterations to the
functional or by the inclusion of additive terms
Slide 32
Time-dependent density functional theory (TD DFT)
Time-dependent density functional theory (TDDFT) is a quantum
mechanical theory used in physics and chemistry to investigate the
properties and dynamics of many-body systems in the presence of
time-dependent potentials, such as electric or magnetic
fields.
Slide 33
Time-dependent density functional theory (TD DFT) The effect of
such fields on molecules and solids can be studied with TDDFT to
extract features like excitation energies, frequency- dependent
response properties, and photo absorption spectra.
Slide 34
Time-dependent density functional theory (TD DFT) TDDFT is an
extension of density functional theory(DFT), and the conceptual and
computational foundations are analogous to show that the (time-
dependent) wave function is equivalent to the (time- dependent)
electronic density, and then to derive the effective potential of a
fictitious non-interacting system which returns the same density as
any given interacting system
