554018 Density Functional Theory

Programme for Autumn Term 2009 (30.9.–9.12.2009)

Wednesdays 14:15–17:00, Chemicum, rooms A120 and A127

Latest update: January 20^th, 2010

Brief Outline

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

Topics covered during the course included:

Many-electron wave functions; electron distributions and densities
The Hohenberg–Kohn theorems and the Kohn–Sham approach
The Local Density Approximation (LDA)
The Generalized Gradient Approximation (GGA)
Hybrid functionals and the meta-GGA approaches
Implementations of density functional theory

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:	30 hours in total, Wednesdays, September 30–December 9, 2009, 14:15–17:00; no lecture on October 28^th
Place:	Rooms A120 (Sep 30–Oct 21) and A127 (Nov 4–Dec 9), Chemicum building, Kumpula campus
Lecturers:	Dr. Pekka Manninen and Dr. Mikael Johansson
Credits:	4 ECTS. A project work and compulsory exercises are required for the credits.
Language:	Finnish or English (audience dependent)
Supporting Literature:	Koch and Holthausen, A Chemist's Guide to Density Functional Theory

Contact

Questions can be sent to dft09@chem.helsinki.fi

Some Practical Details

The plan is to use NWChem 5.1.1 as the main computational suite during the course and exercises. Attendees are encouraged to have a glance at its usage before the third lecture. Naturally, other appropriate software packages can be used. For example, Gaussian09 features a nice variety of exchange-correlation functionals, and can be used as an alternative for the exercises and project works.
An example NWChem input file, for optimizing the water structure at B3LYP level, can be downloaded here:
- control.nw
To submit the NWChem job on Murska, use bsub < job-nwchem511-murska.job; The queuing system "job file" can be downloaded here:
- job-nwchem511-murska.job
An account at CSC could prove to be quite useful.

Sketch of a Detailed Programme

Date	Topic
30.9.	Many-electron quantum mechanics (PM)	Exercise 1 (PDF)
7.10.	The Hohenberg–Kohn theorems and the Kohn–Sham approach (PM)	Exercise 2 (PDF)
14.10.	Interpretation and reality of KS orbitals, intricacies of spin DFT, computational intro (MJ)	Exercise 3 (PDF)
21.10.	Approximate exchange-correlation functionals (PM)	Exercise 4 (PDF)
4.11.	Basis sets, applications (MJ)	Exercise 5 (PDF)
11.11.	Upwards the ladder (PM)	Exercise 6 (PDF)
18.11.	Different functionals, applications (non-covalent interactions, ...) (MJ)	Exercise 7 (PDF)
25.11.	Implementation considerations (PM)	Exercise 8 (PDF)
2.12.	Which functional for what property? (MJ)
9.12.	Summary, final remarks, project presentations (MJ)

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, being roughly 5×N pages. The projects are handed out in the order they are reserved. Reservation takes place by e-mail to dft09@chem.helsinki.fi. You were supposed to reserve a title on or before November 4.

A PDF of the topic list is available here.

Approaches to use the ground-state density as the basic variable: Review, e.g., the Thomas–Fermi model and the X_α approach, their derivation and shortcomings. Discuss more recent advances in this area, especially for density functionals for the kinetic energy.
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, TV)
Density functional theory for excited states
Exact-exchange Kohn–Sham DFT (reserved, EH)
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.
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.
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. (reserved, SK&HL)
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, ST&NÖ)
Tight-binding DFT: Discuss the idea behind, and the performance of the DFTB methods. (reserved, MB)
Free title: Suggest your own topic.