Cool Cluster Correctly Correlated

Atomic clusters are unique objects, which occupy an intermediate position between atoms and condensed matter systems. For a long time it was thought that physical and chemical properties of atomic dusters monotonically change with increasing size of the cluster from a single atom to a condensed matter system. However, recently it has become clear that many properties of atomic clusters can change drastically with the size of the clusters. Because physical and chemical properties of clusters can be adjusted simply by changing the cluster's size, different applications of atomic clusters were proposed. One example is the catalytic activity of clusters of specific sizes in different chemical reactions. Another example is a potential application of atomic clusters in microelectronics, where their band gaps can be adjusted by simply changing cluster sizes. In recent years significant advances in experimental techniques allow one to synthesize and study atomic clusters of specified sizes. However, the interpretation of the results is often difficult. The theoretical methods are frequently used to help in interpretation of complex experimental data. Most of the theoretical approaches have been based on empirical or semiempirical methods. These methods allow one to study large and small dusters using the same approximations. However, since empirical and semiempirical methods rely on simple models with many parameters, it is often difficult to estimate the quantitative and even qualitative accuracy of the results. On the other hand, because of significant advances in quantum chemical methods and computer capabilities, it is now possible to do high quality ab-initio calculations not only on systems of few atoms but on clusters of practical interest as well. In addition to accurate results for specific clusters, such methods can be used for benchmarking of different empirical and semiempirical approaches. The atomic clusters studied in this work contain from a few atoms to tens of atoms. Therefore, they are quantum objects. Some qualitative information about the geometries of such clusters can be obtained with classical empirical methods, for example geometry optimization using an empirical Lennard-Jones potential. However, to predict their accurate geometries and other physical and chemical properties it is necessary to solve a Schroedinger equation. If one is not interested in dynamics of clusters it is enough to solve the stationary (time-independent) Schroedinger equation (H{Phi}=E{Phi}). This equation represents a multidimensional eigenvalue problem. The solution of the Schroedinger equation is a set of eigenvectors (wave functions) and their eigenvalues (energies). The lowest energy solution (wave function) corresponds to the ground state of the cluster. The other solutions correspond to excited states. The wave function gives all information about the quantum state of the cluster and can be used to calculate different physical and chemical properties, such as photoelectron, X-ray, NMR, EPR spectra, dipole moment, polarizability etc. The dimensionality of the Schroedinger equation is determined by the number of particles (nuclei and electrons) in the cluster. The analytic solution is only known for a two particle problem. In order to solve the equation for clusters of interest it is necessary to make a number of approximations and use numerical methods.