Metal Clusters in Quantum Matrices

The physical properties of metallic clusters depend strongly on their size and differ significantly from those of both the initial constituents and the bulk material. This project proposes to examine the geometric and electronic structure of metal clusters that are embedded in a quantum fluid matrix, specifically 4 He. Such a matrix guarantees that the interactions between clusters and the environment are minimized, and that the clusters are automatically cooled to 0.4 K. Our first goal is to develop an innovative numerical method for the execution of our research. We plan to develop a high-order forward propagation method in imaginary time. Preliminary tests give rise to the expectation that the method will be very effective for both solving the Kohn Sham equations of density functional theory, as well as improving the convergence of quantum Monte Carlo simulations. It is essential to take into account the influence of the quantum fluid matrix to understand the physical properties of metallic clusters in a number of points. These are, first of all, structural properties: Even the very location of (earth-)alkali clusters in a quantum fluid matrix, i.e., whether the clusters reside on the surface or in the interior, is often unknown. The structure of the cluster, however, is expected to depend on its location. The existence and stability of isomers, i.e., meta-stable configurations of different geometric structure, is also expected to be affected by the external matrix. The observed quantity that needs to be understood and explained is in both cases the photo-ionization spectrum and the vibrational spectrum. In magnesium clusters, a transition from molecule-like complexes, bound by covalent bonds, to bulk metal with delocalized electrons is observed as a function of cluster geometry and size. Signatures of such a transition will be seen in the electronic structure of these systems.

The project Metal Clusters in a Quantum Matrix deals with the description of metallic clusters in an environment of liquid helium. Embedding clusters in a helium matrix guarantees that the interaction with the environment is minimized and that the clusters are automatically cooled to temperatures of approximately 0.4 K. In fact, some clusters can be generated only in a helium matrix because the surface of the cluster would otherwise interact with the surrounding gas.The new algorithmic developments of the project were quite successful and will, in the future, lead to broader applications. Our methods have also inspired advances in path-integral Monte Carlo algorithms which have been internationally acclaimed, see below. The analysis of cluster-helium interactions has, on the other hand, been somewhat resilient and we cannot report the desired progress. To bring the project to a useful end we have therefore resorted to phenomenological approaches which explored the regime of possibilities within reasonable limits.