Density Functional Theory

Recommended Prerequisites

Quantum Mechanics, Atomic and Molecular Physics, Condensed Matter Physics.

Teaching Methods

The subject matter will be presented in the theoretical classes. These presentations will be complemented with practical and theoretical problems given as homework and discussed afterwards in the tutorial classes.

Learning Outcomes

Upon completion of this curricular unit the student should:
i) know density-functional theory (DFT), understand its limitations and recognise to which problems it can be applied
ii) know and understand Kohn-Sham's method
iii) understand the physical significance of exchange and correlation energy and know and understand the limitations of the various exchange and correlation functional families'
iv) know time-dependent density functional theory (TDDFT) and recognise to which problems it can be applied
v) be able to identify and justify the differences between density-functional methods and other many-body methods
vi) know how to use computer programs based on (TD)DFT
vii) be able to interpret the results obtained with the codes mentioned in vi)

The following competences will also be developed:
- Analysis and synthesis;
- Problem solving;
- Critical reasoning;
- Autonomous learning;
- Research.

Work Placement(s)

No

Syllabus

Many-body systems: representations with fixed and variable number of particles, Hartree-Fock theory, field quantisation

Single- and two-particle density matrices and density operators

Thomas-Fermi theory

Foundations of density-functional theory: Hohenberg-Kohn theorem, degenerate ground states, variational equation, interacting v-representability, fractional particle numbers, derivative discontinuity, current density-functional theory

Kohn-Sham equations: noninteracting v-representability, degenerate Kohn-Sham ground states, Janak’s theorem, interpretation of Kohn-Sham eigenvalues

Exchange and correlation energy functionals: local density approximation, generalised gradient approximation, meta-GGA, self-interaction corrections, orbital-dependent functionals, optimised potential method, exact exchange, hybrid functionals

Time-dependent density-functional theory: Runge-Gross theorem, time-dependent Kohn-Sham equations, adiabatic approximations, linear response.

Head Lecturer(s)

Fernando Manuel Silva Nogueira

Assessment Methods

Assessment
Synthesis work: 20.0%
Project: 30.0%
Resolution Problems: 50.0%

Bibliography

Density Functional Theory: An Advanced Course
Eberhard Engel and Reiner M. Dreizler
Springer (2011)

A Primer in Density Functional Theory
C. Fiolhais, F. Nogueira, M. Marques (Eds)
Springer (2003)

Density Functional Theory: An Approach to the Quantum Many-Body Problem
Reiner M. Dreizler and Eberhard K. U. Gross
Springer (1990)

Density-Functional Theory of Atoms and Molecules
Robert G. Parr and Weitao Yang
Oxford University Press (1989)

Fundamentals of Time-Dependent Density Functional Theory
M. Marques, N. Maitra, F. Nogueira, E. K. U. Gross, A. Rubio (Eds)
Springer (2012)

Time-Dependent Density-Functional Theory: Concepts and Applications
Carsten Ullrich
Oxford University Press (2012)

The Fundamentals of Density Functional Theory
Helmut Eschrig
B. G. Teubner (1996)

A Chemist's Guide to Density Functional Theory
Wolfram Koch and Max C. Holthausen
Wiley (2001)