554018 Density Functional Theory

Programme for Autumn Term 2012 (15.–26.10.2012)

Mondays, Wednesdays, Fridays, 9:15–12:00 and 13:15–16:00, Chemicum

Latest update: October 29th, 2012

Brief Outline

This course (re)presents a comprehensive and up-to-date treatment of the de facto workhorse of quantum chemistry: density functional theory (DFT). Its foundations in quantum mechanics are covered in detail, and put immediately into practice by thoroughly discussing performance issues and practical use. Further, some contemporary trends are discussed.

Topics covered during the course include:

The course is highly recommended for graduate or advanced undergraduate students in chemistry or physics with preliminary knowledge of quantum mechanics and an interest in quantum chemistry. Also post-docs and researchers working in the field may deepen their knowledge of the fundamental basis and the applicability of commonly used DFT methods.

Lectures: 36 hours in total (including exercises), Mondays, Wednesdays, and Fridays, October 15–26, 2012, 9:15–16:00
Place: Rooms B143 (15.10, 17.10) and A121 (other days), Chemicum, Kumpula campus
Lecturers: Doc. Pekka Manninen (CSC) and Doc. Mikael Johansson (UdG)
Credits: 4 ECTS. A project work and compulsory exercises are required for the credits.
Language: English
Supporting Literature: Koch and Holthausen, A Chemist's Guide to Density Functional Theory
WebOodi link: weboodi.helsinki.fi (preregistration not compulsory but harmless)

Some Practical Details

Sketch of a Detailed Programme

Date Topics
15.10. Course intro; Introduction to electronic-structure theory; Computational intro
17.10. The Hohenberg–Kohn theorems and the Kohn–Sham approach; Approximate functionals
19.10. Basis sets; Intricacies of spin-DFT; Orbitals; Applications
22.10. Upwards the ladder; Different functionals; Applications
24.10. Non-covalent interactions; Which functional for what property
26.10. Implementation considerations; Project works; Summary

Project Works

The projects can be done in groups of one, two, or three. The extensiveness required of the work scales linearly with the size of the group. The projects are handed out in the order they are reserved.
  1. Approaches to use the ground-state density as the basic variable: Review, e.g., the Thomas–Fermi model and the Xα approach, their derivation and shortcomings. Discuss more recent advances in this area, especially for density functionals for the kinetic energy. (reserved, NG)

  2. The constrained-search approach: Discuss in detail the Levy constrained-search formalism for the minimization problem in DFT. Discuss also, whether we know the ground-state wave function or some related wave function in DFT. (reserved, JT&MM)

  3. Density functional theory for excited states (reserved, DD)

  4. How the random phase approximation differs from traditional functionals

  5. Exact-exchange Kohn–Sham DFT (reserved, MN)

  6. Linear scaling DFT: Review the vast literature on efforts for making the computational cost of the DFT method to scale linearly with respect to the size of the studied system.

  7. Weakly interacting systems: Perform an explicit study on the performance of contemporary DFT functionals for describing weak interactions, like van der Waals forces. Select a set of systems and try out various functionals, ranging from traditional ones to the highly parameterized Minnesota functionals, to DFT-D. Discuss the reliability of the approaches. (reserved, AA)

  8. Reaction energetics: Choose a reaction for which reliable experimental data are available. At DFT level, study its energetics, including the transition state and assess the reliability of the computational method.

  9. DFT for magnetic properties: Discuss the performance of standard DFT functionals for the evaluation of magnetic properties. Introduce the concept of, and compare to, current-DFT, discuss possible advantages of this approach. (reserved, AM)

  10. Tight-binding DFT: Discuss the idea behind, and the performance of the DFTB methods.

  11. Free title: Suggest your own topic.

Previous Incarnation