More general description of the
research area.

### A. Methods for calculating rates and long time scale dynamics

The group has developed several methods for calculating rates of slow transitions, such as chemical reactions and diffusion. The methods are based on transition state theory (TST), with or without the harmonic approximation. Within the harmonic approximation, the challenge is to find the relevant saddle point(s) on the energy surface, as well as the harmonic frequencies at the saddle point and at the initial state. In some cases only the initial state is known. Then the
'Minimum-mode following' method
is a powerful tool for finding both the mechanism of likely transitions as well as the activation energy. We have, for example, used this to simulate
long time scale dynamics
in solids. When both the initial and final states are known, the
CI-NEB
method is the most powerful one we know of. A
review sumary
of various methods was recently published. We have in particular applied these methods to calculations of
crystal growth.
Within full TST, the challenge is to find the optimal dividing surface with dimensionality D-1 (where D is the number of degrees of freedom in the system). The optimal surface corresponds to the dividing surface with maximum free energy on the way from the initial state to final state. This represents the tightest bottle neck for the transition. We have developed a method, called
OH-TST
for finding an optimal hyperplanar dividing surface in a systematic way and a
mosaic of several hyperplanes
enclosing the intial state. In both the harmonic and full TST calculations, the challenge is to navigate in a high dimensional space. The group has also developed an extension of classical TST to
quantum TST,
where tunneling can become an important transition mechanism.
Here is a more complete list of
publications
on these topics.

### B. Density functional theory calculations

The group mainly uses plane wave based DFT to calculate the interaction between atoms in condensed systems. While a parallel DFT program
was developed in the group in the early 90s, the rapid development of the methodology and maturity of the field has made it more practical to adopt some of the sophisticated packages now available such as the
DACAPO
code and the
VASP
code. Methods for calculating rates (see above) and
analysis of electron density
developed by the group have been implemented within these packages, see in particular
VASP implementations
(maintained by former graduate student, Prof. Graeme Henkelman at UT). A particular focus of the DFT calculations in the group is the testing and development of DFT methods for calculating properties of excited states, such as
self-trapped excitons in solids,
catalysis, and
surface diffusion and island formation
The development and implementation of orbital dependent functionals in DFT is an ongoing effort in the group.