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
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:
- 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
- The Random Phase Approximation (RPA)
- 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.
||36 hours in total (including exercises),
Mondays, Wednesdays, and Fridays,
October 15–26, 2012, 9:15–16:00
||Rooms B143 (15.10, 17.10) and A121 (other days),
Chemicum, Kumpula campus
||Doc. Pekka Manninen (CSC)
and Doc. Mikael Johansson (UdG)
||4 ECTS. A project work
and compulsory exercises are required for the credits.
||Koch and Holthausen,
A Chemist's Guide to Density Functional Theory
weboodi.helsinki.fi (preregistration not compulsory but harmless)
Some Practical Details
- The plan is to use
NWChem as the main computational suite during
the course and exercises. Attendees are encouraged to have
a glance at its usage before the course commences. 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:
- To submit the NWChem job on Vuori, use sbatch job-nwchem611-vuori.job;
The queuing system "job file" can be downloaded here:
account at CSC could prove to be quite useful.
- A laptop for the practical application exercises would be handy as well.
Sketch of a Detailed Programme
||Course intro; Introduction to electronic-structure theory; Computational intro
||The Hohenberg–Kohn theorems and the Kohn–Sham approach; Approximate functionals
||Basis sets; Intricacies of spin-DFT; Orbitals; Applications
||Upwards the ladder; Different functionals; Applications
||Non-covalent interactions; Which functional for what property
||Implementation considerations; Project works; Summary
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
- 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
- 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.
- Density functional theory for excited states
- How the random phase approximation differs from
- Exact-exchange Kohn–Sham DFT
- 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
- 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.
- Tight-binding DFT: Discuss the idea behind,
and the performance of the DFTB methods.
- Free title: Suggest your own topic.