The key to the construction of reliable and transferable semiempirical Hamiltonians for quantum mechanics-based simulations of materials is to capture the effect of screening by electrons for different condensed phases of materials. In the present work, this objective is achieved through the development of a scheme for constructing a self-consistent ͑SC͒ and environment-dependent ͑ED͒ multicenter Hamiltonian in the framework of linear combination of atomic orbitals ͑LCAO͒ that involves careful modeling and optimization of parameters for electron-electron correlations and multicenter interactions. As an illustration of our method, we have used this scheme to construct the SCED/LCAO Hamiltonian for silicon. The robustness of this Hamiltonian is demonstrated by scrutinizing the properties of both bulk silicon and other complex structures of silicon with reduced symmetries. In particular, we have studied the following: ͑i͒ the binding energy versus relative atomic volume of different phases of bulk silicon, ͑ii͒ the stable structure of an intermediate-size Si 71 cluster, ͑iii͒ the reconstruction of Si͑100͒ surface, and ͑iv͒ the energy landscape for a silicon monomer adsorbed on the reconstructed Si͑111͒-7 ϫ 7 surface. The success of the SCED/LCAO Hamiltonian in the above applications, where silicon exists in a variety of different coordinations, is a testament to the predictive power of the scheme.

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.

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.

Computer simulation studies of nanoscale materials, in particular nanoparticles or finite-length nanotubes/nanowires, via ab initio methods are challenging or impossible due to computational costs associated with the calculation of total energy and atomic forces of nanometer-sized systems. While molecular mechanics methods can handle large systems, they cannot describe manifestations of quantum effects in nanoscale materials. Therefore, we have developed a quantum-mechanics based semi-empirical Hamiltonian to bridge the accuracy and system-size gap between the above two methods. The key feature of this self-consistent and environment dependent (SCED) Hamiltonian is that it takes into account of environment-dependency, electron screening, and charge re-distribution effects within the LCAO (linear combination of atomic orbitals) framework. In the present study, we have used a relaxation scheme based on the SCED/LCAO Hamiltonian to determine the structure and electronic density of states of multi-shelled fullerenes ("fullerene onions") up to six shells. Our study reveals that inter-shell interactions are weak with a small charge transfer from the outer to the inner shells. The structure (or geometry) of fullerene shells in the onion structure is very similar to the geometries of corresponding isolated fullerenes, and, therefore, the energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital of a fullerene onion is similar to that of the corresponding outermost shell.

This paper describes experiments performed by undergraduate physics majors to measure the temperature dependence of Doppler-broadening in Rb absorption lines over the interval 290-500 K. We report measurements made with a laser-diode spectrometer on the resolved hyperfine transitions of 87 Rb ͑5 2 S 1/2 Fϭ1 to 5 2 P 1/2 , Fϭ1 and 2͒ near 795 nm, and on the unresolved envelope of the transitions of 85 Rb ͑5 2 S 1/2 Fϭ2 to 5 2 P 3/2 , Fϭ1, 2 and 3͒ near 780 nm. Agreement between measured and predicted linewidths is very good.