Dr. Andreas Götz: Projects

Development of new approaches for the simulation of properties of biomacromolecules and other complex molecular systems with the goal to achieve realistic and reliable descriptions. Computationally efficient implementations into widely used software packages such as ADF for density functional theory and AMBER for classical and mixed quantum/classical molecular dynamics simulations.

jump to: QM/MM - Subsystem DFT - OEP and TDDFT - Density Fitting (PhD) - Work camp

Information will be added soon.

I have been and still continue to work on the extension of the frozen density embedding (FDE) method in density functional theory (DFT). The main research topics are analytical gradients for FDE and nuclear spin-spin coupling constants in the framework of FDE. The research work is done with Dr. L. Visscher at the chair of theoretical chemistry at the Vrije Universiteit Amsterdam which is headed by Prof. Dr. E.-J. Baerends.

DFT is undoubtedly the most popular computational method for the investigation of the electronic structure of molecules. It allows to obtain accurate information on molecular properties at a moderate computational cost. Studies of molecules of interest for classic organic or inorganic chemistry are routine by now. It is the time to find new approaches to be able to study also more complex systems in fields of increasing importance such as life sciences and nanotechnology.

The extension of FDE to a general subsystem DFT has a tremendous potential as an accurate (in principle exact) multi-scale modelling method. Such methods allow to focus the computational effort on those parts of the system which is of importance for the property of interest, while still taking into account the interaction with the remaining parts of the system. Proper implementations will allow to tackle the investigation of properties of chemical systems of unprecedented size and complexity. The implementation is done in the Amsterdam Density Functional (ADF) program package.

In order to broaden my horizon after my PhD, I switched my research topic to time-dependent density functional theory (TD-DFT) and the optimized effective potential (OEP) method.

TD-DFT is a very efficient and in many cases encouragingly accurate method to describe excited states of molecules. A fundamental problem which has not yet been solved concerns excited states with charge-transfer (CT) character. Such excited states, which are of importance for a great deal of applications, cannot be described by presently available density functionals. A very promising avenue to solve this problem is the extension of the exact-exchange (EXX) method to excited states [1]. Although the theory has been worked out already in 1998, no practical implementation for molecules exists so far.

I have worked out algorithms and implemented these into the TD-DFT module of the quantum chemical program package TURBOMOLE. During the course of this work it turned out, that one encounters similar numerical problems as in optimized effective potential (OEP) methods with localized basis sets for ground states. Together with Dr. A. Heßelmann I was able to solve this problem and we have published our results [2]. The way is now open to apply our knowledge of this numerically stable approach to the TD-DFT implementation. Research along these lines is at present pursued in Prof. Dr. A. Görling's group.

The ultimate goal of developing and implementing methods of computational quantum chemistry is to provide the ability to answer chemical questions of practical relevance. To put my knowledge of such theoretical approaches at work, I have set up some cooperations with experimentalists. Among others, this has lead to the elucidation of the redox process in a novel hydrogenase model complex via analysis of its electronic structure [3].

I started my PhD thesis in theoretical chemistry at the University of Erlangen in the research group of Prof. Dr. B. A. Heß (University of Bonn, deceased) and finished my PhD under the supervision of Prof. Dr. A. Görling. I spent most of my time on the implementation of the LEDO-DFT[4] formalism into the quantum chemical program package TURBOMOLE. LEDO is an acronym for limited expansion of diatomic overlap densities.

Conventional density fitting methods as generally employed in density functional theory (DFT) expand the complete electron density into a fit basis which is distributed over the whole system (molecule). As a result only one- to three-center two-electron integrals have to be evaluated and the computational expense is O(N³) with respect to the size of the system under investigation. In the LEDO-DFT formalism each individual diatomic overlap density is expanded into a fit basis which is restricted to the atoms of that overlap density. Thus, two-center matrix elements of the Coulomb- and Exchange-Correlation contribution to the Kohn-Sham matrix can be expressed in terms of the one-center elements using the LEDO expansion coefficients. Consequently only one- and two-center two-electron integrals have to be evaluated and the computational expense of a LEDO-DFT calculation is only O(N²).

During my PhD I have implemented the calculation of analytical gradients [5] within the LEDO-DFT formalism [4]. Furthermore, I have worked out criteria for the optimization of auxiliary basis sets for the LEDO expansion and optimized auxiliary orbitals which allow for LEDO-DFT calculations with sufficient accuracy [6].

My PhD thesis can be downloaded in pdf format from the opus server of the University of Erlangen.

My diploma thesis was accomplished during the time from April to October 2001 under the supervision of Prof. Dr. B. A. Heß (University of Bonn, deceased) at the University of Erlangen. It is entitled Implementierung eines vereinfachten Dichtefunktionalverfahrens (Implementation of a Simplified Density Functional Formalism) and deals with the implementation of the LEDO-DFT[4] formalism (see PhD thesis) in the SCF part of the DFT programs of the quantum chemical program package TURBOMOLE.

Unfortunately my thesis is available only in German. If you are interested anyway, you can download it here: ps / pdf

In September 1995, after finishing school and before university started, I participated in a workcamp organized by SCI (Service Civil International). It took place in a small village near Àcqui Terme which is close to the town of Asti in the Piemont region in northern Italy.

The philosohpy of the workcamps organized by SCI is to bring together the working and/or creative power of people from different countries in order to realize a project of social welfare. In general the participants have to pay the trip to the workcamp by themselves, but board and lodging at the working place are for free. In my case the project of the work camp was to renovate the run-down accomodations of a small protestant church for future use as a cost-free excursion center for schools or other institutions or people in need. We have been a dozen people from Great Britain, the Netherlands, Germany and Italy. It was hard work, but also a lot of fun.

The duration of the workcamp was two weeks, rather short. Nevertheless it was a unique and worthy experience. If you have time, I can just recommend to participate in a workcamp organized by SCI.

[1] A. Görling, Int. J. Quant. Chem. 69, 265-277 (1998).

[2] A. Heßelmann, A. W. Götz, F. Della Salla, A. Görling, J. Chem. Phys. 127, 054102 (2007).

[3] F. Lauderbach, R. Prakash, A. W. Götz, M. Munoz, F. W. Heinemann, U. Nickel, B. A. Hess, D. Sellmann, Eur. J. Inorg. Chem. 21, 3385-3393 (2007).

[4] C. Kollmar, B. A. Hess, Molec. Phys. 100, 1945-1955 (2002).

[5] A. W. Götz, C. Kollmar, B. A. Hess, Molec. Phys. 103, 175-182 (2005).

[6] A. W. Götz, C. Kollmar, B. A. Hess, J. Comput. Chem. 26, 1242-1253 (2005).