Download Density Functional Theory And Time Dependent Density Functional

(DFT & TDFT)
PRESENTED BY:
MALEEHA QASIM
MUHAMMAD ZAIN AKRAM
Background:
 1920s: Introduction of the Thomas-Fermi model.
 1964: Hohenberg-Kohn paper proving existence of exact
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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.
Walter Kohn, Nobel Prize 1998
Chemistry
Hohenberg-Kohn theorem
The total energy of an interacting
inhomogeneous electron gas in the presence of
an external potential Vext(r ) is a functional of
the density 

 
E   Vext ( r )  ( r )dr  F [  ]
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
 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
Density Functional Theory
With this theory, the properties of a manyelectron 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.
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.
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
DFT-Properties
• Total energy
• Forces
• Structure determination
• Charge density, dipole moments
DFT-FUNCTIONALS
Some commonly used functionals in DFT are
 BLYP
 B3LYP
 PBE0 (PBE1PBE)
 PW91 (PW91 PW91)
Applying DFT for computational
purposes in Gauss 03
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
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.
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).
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
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.
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, frequencydependent response properties, and photo
absorption spectra.
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 (timedependent) wave function is equivalent to the (timedependent) 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
TD DFT-Properties
 Excitation energies
 Frequency-dependent response properties
And
 Photo absorption spectra.