Research topics

Overview

The scientific work is centered on the detailed understanding and the adequate computation of electronic correlations in large molecules and solids. Both aspects are related to each other since no feasible concept for a purely numerical approach to this problem has not yet been developed.

The ab-initio scheme Local Ansatz (LA) was develloped during the last decades[1,2]. It has similarities to quantum chemical (QC) correlation methods, but is distinguished by an intelligent construction and selection of correlation operators with a specific local meaning each. Here, interpretation and understanding play an important role. Thanks to this selection, the LA can, at negligible costs in accuracy, easily handle systems that have so far been out of reach for QC methods, namely large molecules with delocalised electrons and metals [3].

The only approximation in the LA is the reduction of the correlation space, and this is easily controllable. No uncontrollable approximation is introduced. In this, the LA is different from all those ab-initio methods of solid state theory which are based on the density functional (DF) method, and consequently on a homogeneous electron gas approximation to exchange and correlations. All attempts during the last decades to improve the latter approximation have failed, at least for the case of the correlation part.

An additional advantage of the LA is that it allows not only to unambigously generate single-particle model Hamiltonians on an atomic orbital basis, but that it also allows to unambigously parametrize effective local and short range interactions in terms of atomic orbitals [4]. This generates a continous transition from ab-initio calculations to models and their treatment.

At the moment, the LA is applied to the areas listed below. In addition, work is in progress to make the LA available to the other two theoretical projects of the group, namely structure prediction and Quantum Chemistry.

Superstructures and charge density waves in metals and C60

Due to their Fermi surface, simple metals are prone to lattice instabilities. An adequate treatment requires a good coverage of exchange and correlations. DF methods fail in fact for a case that is very well understood, namely the dimerization of polyacetylene [5]. At present, the high pressure bcc superstructure of Li is investigated. DF-calculations display serious deficiencies for this case as well as for the R9 ground state structure at zero pressure. Further applications are planned.

Bond alternation of C60 and its negative ions fits into this context [6]. We were able to explain measured structure data and to use them for the unambiguous determination of the respective ground state. Also in this case, a good treatment of exchange and correlations is necessary [7].

Magnetism and magnetic correlations

Magnetism is coupled intrinsically to the understanding of correlations. Here, in the past, a detailed understanding of the itinerant ferromagnetism of the transition metals was gained with the help of calculations for generalized Hubbard models [8]. At present, this investigation is generalized to an ab-initio treatment.

Magnetic correlations also play a role for the high T_c superconductors. In a few cases, they can be experimentally determined. They occur far away from the magnetic phase and can not be understood as residual effects of order parameter fluctuations. With the help of ab-initio calculations, the origin of these correlations could be determined. The underlying features also lead to a charge redistribution. The resulting occupations differ from those of DF-calculations [9,10].

Selected publications

1. G. Stollhoff, P. Fulde:
   J. Chem. Phys. 73, 4548 (1980).
2. G. Stollhoff:
   J. Chem. Phys. 105, 227 (1996).
3. A. Heilingbrunner, G. Stollhoff:
   J. Chem. Phys. 4, 6799 (1993).
4. G. Stollhoff:
   Europhys. Lett 30, 99 (1995).
5. G. König, G. Stollhoff:
   Phys. Rev. Lett. 65, 1239 (1990).
6. G. Stollhoff, H. Scherrer:
   Material Science Forum 191, 81 (1995).
7. H. Scherrer, G. Stollhoff:
   Phys. Rev. B 47, 16570 (1993).
8. G. Stollhoff:
   Angew. Chemie 39, 4471 (2000).
9. G. Stollhoff:
   Phys. Rev. B 58, 9826 (1998).
10. G. Stollhoff:
    Proceedings Cimtec (2002).