Density Functional Theory And Time Dependent Density Functional Theory

1. Density Functional TheoryAnd Time Dependent Density Functional Theory (DFT & TDFT)

2. PRESENTED TO: DR.IRFAN PRESENTED BY: MALEEHA QASIM MUHAMMAD ZAIN AKRAM

3. 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.

4. Walter Kohn, Nobel Prize 1998 Chemistry

5. 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 

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

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

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.

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.

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

11. DFT-Properties • Total energy • Forces • Structure determination • Charge density, dipole moments

12. DFT-FUNCTIONALS Some commonly used functionals in DFT are • BLYP • B3LYP • PBE0 (PBE1PBE) • PW91 (PW91 PW91)

13. Applying DFT for computational purposes in Gauss 03

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

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.

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).

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

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.

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.

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

35. TD DFT-Properties • Excitation energies • Frequency-dependent response properties And • Photo absorption spectra.

36. Thank You