Chris Leahy

Energetics, relative stabilities, and size-dependent properties of nanosized carbon clusters of different families: Fullerenes, bucky-diamond, icosahedral, and bulk-truncated structures

Structures and relative stabilities of carbon clusters belonging to different families have been investigated for diameters d < or = 5 nm based on an efficient semiempirical molecular dynamics (MD) scheme as well as a density functional theory based simulation. Carbon clusters studied include fullerenes and fullerene-derived structures (e.g., cages and onions), icosahedral structures, bucky-diamond structures, and clusters cut from the bulk diamond with spherical and facetted truncations. The reason for using a semiempirical MD is partly due to the large number of different cases (or carbon allotropes) investigated and partly due to the size of the clusters investigated in this work. The particular flavor of the semiempirical MD scheme is based on a self-consistent and environment-dependent Hamiltonian developed in the framework of linear combination of atomic orbitals. We find that (i) among the families of carbon clusters investigated, fullerene structures have the lowest energy with the relative energy ordering being E(fullerene) < E(onion) < E(icosahedral) < E(bucky-diamond) < E(bulk-truncated), (ii) a crossover between bucky-diamond and icosahedral structures is likely at d approximately 8 nm, (iii) the highest occupied molecular orbital-lowest unoccupied molecular orbital gap as a function of the diameter for the case of fullerenes shows an oscillatory behavior with the gap ranging from 2 eV to 6 meV, and the gap approaching that of gapless graphite for d > 3.5 nm, and (iv) there can be three types of phase transformations depending on the manner of heating and cooling in our simulated annealing studies: (a) a bucky-diamond structure --> an onionlike structure, (b) an onionlike --> a cage structure, and (c) a bucky-diamond --> a cage structure.

Next generation of the self-consistent and environment-dependent Hamiltonian: Applications to various boron allotropes from zero- to three-dimensional structures

An upgrade of the previous self-consistent and environment-dependent linear combination of atomic orbitals Hamiltonian (referred as SCED-LCAO) has been developed. This improved version of the semi-empirical SCED-LCAO Hamiltonian, in addition to the inclusion of self-consistent determination of charge redistribution, multi-center interactions, and modeling of electron-electron correlation, has taken into account the effect excited on the orbitals due to the atomic aggregation. This important upgrade has been subjected to a stringent test, the construction of the SCED-LCAO Hamiltonian for boron. It was shown that the Hamiltonian for boron has successfully characterized the electron deficiency of boron and captured the complex chemical bonding in various boron allotropes, including the planar and quasi-planar, the convex, the ring, the icosahedral, and the fullerene-like clusters, the two-dimensional monolayer sheets, and the bulk alpha boron, demonstrating its transferability, robustness, reliability, and predictive power. The molecular dynamics simulation scheme based on the Hamiltonian has been applied to explore the existence and the energetics of ∼230 compact boron clusters BN with N in the range from ∼100 to 768, including the random, the rhombohedral, and the spherical icosahedral structures. It was found that, energetically, clusters containing whole icosahedral B12 units are more stable for boron clusters of larger size (N > 200). The ease with which the simulations both at 0 K and finite temperatures were completed is a demonstration of the efficiency of the SCED-LCAO Hamiltonian.

Towards a Coherent Treatment of the Self-Consistency and the Environment-Dependency in a Semi-Empirical Hamiltonian for Materials Simulation

The construction of semi-empirical Hamiltonians for materials that have the predictive power is an urgent task in materials simulation. This task is necessitated by the bottleneck encountered in using density functional theory (DFT)-based molecular dynamics (MD) schemes for the determination of structural properties of materials. Although DFT/MD schemes are expected to have predictive power, they can only be applied to systems of about a few hundreds of atoms at the moment. MD schemes based on tight-binding (TB) Hamiltonians, on the other hand, are much faster and applicable to larger systems. However, the conventional TB Hamiltonians include only two-center interactions and they do not have the framework to allow the self-consistent determination of the charge redistribution. Therefore, in the strictest sense, they can only be used to provide explanation for system-specific experimental results. Specifically, their transferability is limited and they do not have predictive power. To overcome the size limitation of DFT/MD schemes on the one hand and the lack of transferability of the conventional two-center TB Hamiltonians on the other, there exists an urgent need for the development of semi-empirical Hamiltonians for materials that are transferable and hence, have predictive power.