The Physics and Chemistry of Cluster-based Catalyst Systems
In this project we used first principles calculations to investigate the physical and chemical properties of atomic clusters, small clumps of matter containing up to a few hundred atoms. The calculations are based on density functional theory, the most efficient and accurate method available for computing and thereby predicting the properties of molecules, clusters, and solids. An initial focus of our work involved studying the reactivity of small Pd clusters. We demonstrated that H2 molecules readily dissociate on Pd clusters and that multiple dissociations can occur on clusters larger than a few Pd atoms. For example, up to eight H2 molecules will dissociate on Pd13 at room temperature. A second focus of the project was to study the evolution of the electrical behavior of clusters, in particular, the evolution of metallic behavior in clusters of metal atoms. We developed a technique for using the electric dipole polarizability of the clusters – the response of the cluster to an applied electric field -- as a probe of this behavior. By decomposing the polarizability into so-called charge transfer (or metallic) and local (or insulating) contributions, we obtained the remarkable result that the per atom charge transfer contributions in sodium clusters attain the same value as occurs in bulk sodium metal for clusters containing as few as 10 atoms. Our calculated total polarizabilities matched experimentally measured trends essentially perfectly, validating the reliability of the calculations and supporting our conclusion that tiny clusters already display bulk-like metallic character. Similar results were obtained for other metal atom clusters, including potassium, aluminum, and zinc. We discovered that the evolution toward bulk metallic behavior for each of these cluster species is essentially identical, when judged using these polarizability-based descriptors. This suggests a universality in the approach of metal clusters to bulk-like metallicity. This discovery is a major outcome of our project. We also used our polarizability-based metrics to investigate the evolution of the properties of Si and NaCl clusters. These systems are non-metallic in the bulk limit. For Si, we find the behavior of small clusters to be metal-like and we attribute this to bonding arrangements in the clusters that are very different from the open structure of crystalline silicon. As the clusters get larger, the bonding in the cluster interior becomes more and more like that of the bulk material. We expect a transition from metal-like to insulator-like behavior to accompany this change is structure. Our results point to a transition at sizes beyond 146 atoms, the largest size treated in our study. We hope to study this transition further in the future. A third thrust of our project involved work on a new approach to eliminating unphysical electron self-interaction from density functional theory calculations. Two electrons exert repulsive forces on each other, but a single electron should not interact with itself. Because of approximations made in density functional theory, individual electrons effectively interact with themselves. The effect of this self-interaction is often small, especially when atoms are near their equilibrium positions in molecules. But the effects can be pronounced when bonds are stretched and also in some situations involving transition metals even when the atoms are near equilibrium. Our research involved the further development of a method for removing self-interaction called the Fermi-Löwdin orbital self-interaction correction or FLO-SIC. We conducted the first systematic FLO-SIC calculations for the individual atoms ranging from Li – Kr. We also carried out a critical comparison of the results of FLO-SIC with an older method known as the Perdew-Zunger self-interaction correction (PZ-SIC). FLO-SIC can be thought of as a modified approach to PZ-SIC that is expected to be computationally more efficient. We demonstrated that the two methods are distinct, but give essentially the same results for quantities such as molecular binding energies or electron removal energies. We are continuing to develop the FLO-SIC methodology with a goal of creating a computationally efficient method that is free of self-interaction effects.