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Lecture

Density Functional Theory: Foundations and Applications

In course

CH-353: Introduction to electronic structure methods

Repetition of the basic concepts of quantum mechanics and main numerical algorithms used for practical implementions. Basic principles of electronic structure methods:Hartree-Fock, many body perturbation theory, configuration interaction, coupled-cluster t ...

Description

This lecture covers the theoretical foundations and practical applications of Density Functional Theory (DFT). Starting with the Hohenberg-Kohn theorems, it explains how DFT provides an alternative approach to solving the electronic Schrodinger equation by focusing on the electron density. The lecture discusses the popularity of DFT due to its computational efficiency and accuracy in predicting various chemical properties. It also delves into the functionals and functional derivatives used in DFT calculations, along with the Thomas-Fermi model and the challenges in expressing the kinetic energy as a functional of the density. The presentation concludes with a quiz on total energy expressions and the limitations of DFT methods.

Instructor

Ursula Röthlisberger

U. Röthlisberger was born in Solothurn (Switzerland). In 1988 she made her diploma in Physical Chemistry in the group of Prof. Ernst Schumacher at the University of Berne (Switzerland). Her Ph.D. thesis was done in collaboration with Dr. Wanda Andreoni at the IBM Zurich Research Laboratory in Rüschlikon. After finishing her Ph.D in 1991 she spent some time as a postdoctoral research assistant at the IBM Research Lab. From 1992-1995 she was a postdoctoral research assistant in the group of Prof. Michael L. Klein at the University of Pennsylvania in Philadelphia (USA). In 1994 she was awarded an advanced researcher fellowship (Profil 2) from the Swiss National Science Foundation. Before starting her Profile 2-fellowship she spent another year as postdoctoral research assistant in the group of Prof. Michele Parrinello at the Max-Planck-Institute for Solid State Physics in Stuttgart, Germany. In 1996 she moved as Profile 2-fellow to the ETH in Zurich, hosted by the group of Prof. Wilfred F. van Gunsteren. In 1997 she became Assistant Professor of Computer-Aided Inorganic Chemistry at the ETH Zurich.

Official source

Related concepts (31)

Density functional theory

Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density.

Quantum chemistry

Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions to physical and chemical properties of molecules, materials, and solutions at the atomic level. These calculations include systematically applied approximations intended to make calculations computationally feasible while still capturing as much information about important contributions to the computed wave functions as well as to observable properties such as structures, spectra, and thermodynamic properties.

Electron density

Electron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial variables and is typically denoted as either or . The density is determined, through definition, by the normalised -electron wavefunction which itself depends upon variables ( spatial and spin coordinates). Conversely, the density determines the wave function modulo up to a phase factor, providing the formal foundation of density functional theory.

Electronic band structure

In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called band gaps or forbidden bands). Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules.

Theoretical chemistry

Theoretical chemistry is the branch of chemistry which develops theoretical generalizations that are part of the theoretical arsenal of modern chemistry: for example, the concepts of chemical bonding, chemical reaction, valence, the surface of potential energy, molecular orbitals, orbital interactions, and molecule activation. Theoretical chemistry unites principles and concepts common to all branches of chemistry. Within the framework of theoretical chemistry, there is a systematization of chemical laws, principles and rules, their refinement and detailing, the construction of a hierarchy.

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