I study atomic clusters made of anywhere between three and a few hundred atoms with various methods of computational chemistry. I am also interested in molecular ions and transition metal complexes. We are using standard methods of computational chemistry in combination with global optimization and simulation methods that we are developing. For example, we have done global optimization for several clusters --- Aln, Aun, A13, A4B12 (A, B are metals) --- by Taboo Search in Descriptor Space (TSDS) where all energies are calculated by first-principles Kohn-Sham Density Functional Theory (KS DFT).


      Clusters Xn made of n atoms of an element X display properties (optical, structural, magnetic ...) that are often very different from those of the bulk material and which depend on n. There are two main reasons for this. First, the fraction of atoms at the surface ranges roughly between 10% and 100% in clusters while it is essentially zero in bulk materials. Second, depending on the material, electrons can have an effective deBroglie wavelength which is comparable to, or smaller than, the dimension of the clusters: those electrons "feel" the boundaries of a cluster and that manifests itself in electronic properties different from those of the bulk. Clusters are interesting at a fundamental level because they are intermediate between atoms (or molecules) and solids: their study involves concepts from both chemistry and solid state physics. They are interesting from a practical viewpoint because clusters with special stability or properties ("magic clusters") might be used as building blocks for new materials.

      Determining the geometry of atomic clusters is quite difficult because they do not obey any simple set of rules unlike, say, organic molecules which follow closely the predictions of Lewis and VSEPR theories. For that reason, and because clusters of more than 10 atoms have thousands or even millions of possible isomers (local minima on the potential energy surface), we must perform global optimization. We do this with our TSDS code and in combination with KS DFT as implemented in programs like deMon, Gaussian, VASP, etc. Calculated relative energies give predictions of structures one expects to find in experiments. We calculate properties such as ionization energy (IE), electron affinity (EA) and vertical detachment energies (VDEs), vibrational frequencies and IR intensities, and spin magnetic moments, that may help assign structure through comparisons with experiments. The atomic structure of any given cluster, in itself, is usually not very interesting: most clusters are unstable and can not be isolated or used as chemical reagents. Taken in isolation, the physical properties of any given cluster means very little. What is interesting are trends in cluster structure and properties. By studying trends we hope to find new empirical rules, or make existing rules more precise, for predicting the structure and stability of clusters. In a sense, we are trying to develop a low-level theory of cluster structure that would do, for clusters, what Lewis and VSEPR theory do for molecules of main group elements. Armed with a few simple and reliable structural principles, we should be in a much better position to elucidate the structure of any isolated or surface-adsorbed cluster, or predict the composition and structure of clusters that have special stability and could be used in making new materials.

Computational methods.

      We are using many of the standard methods of computational chemistry as implemented in software packages such as Gaussian. We also develop new methods, and relatively simple computer code, to do special kinds of calculations:
    global optimization (TSDS);
    empirical potentials for metals and semiconductors, including an electronegativy equalization model of atomic charges and ionic interactions;
    model hamiltonians based on EWMO theory and fitted to KS DFT orbital energies;
    automated potential functions that interpolate KS DFT energies and "learn" as the number of KS DFT calculations increases;
    various algorithms for analyzing geometries structures, such distance and angle distributions, molecular descriptors, and data clustering algorithm (DCA);
    simulated annealing (SA) and related simulation protocols for optimizing molecular properties other than energy.

Selected Publications

  1. R. Fournier, Bimetallic Clusters , "Handbook of Nanophysics / Clusters and Fullerenes", chapter 4, (Klaus Sattler Editor-in-Chief, Taylor & Francis, 2010)

  2. Yan Sun, Min Zhang, and R. Fournier, Periodic Trends in the Geometric Structures of 13-Atom Metal Clusters, Phys. Rev. B 77 (2008) 075435.

  3. Yan Sun and R. Fournier, Geometric and Electronic Structure of Closed-Shell Bimetallic A4B12 Clusters , Phys. Rev. A 75 (2007) 063205 (9 pages).

  4. J. Cheng and R. Fournier, Structural optimization of atomic clusters by tabu search in descriptor space , Theor. Chem. Acc. 112 (2004) 7-15.

Full publication list.

Group Members, Research Collaborators

Joey Cheng

ACD Labs, Toronto, Canada
David Fung ACD Labs, Toronto, Canada
Sun Yan Department of Physics, York University, Toronto, Canada sunyan@yorku.ca
Min Zhang Department of Physics, York University, Toronto, Canada zhangmin@yorku.ca
René Fournier Department of Chemistry, York University, Toronto, Canada renef@yorku.ca