Linking chemical reactivity, magic numbers, and local electronic properties of clusters

I. INTRODUCTION For systems with reduced or no symmetry, the interplay among various features associated with the local environ- ments is the key in determining the global properties of a system. In situations where there is a redistribution of va- lence electrons and/or charge transfer, analysis of the local bonding and rebonding involved in the formation of defect configurations such as clusters, surfaces, and interfaces can provide invaluable information on the local electronic struc- ture and the energetics. Such information is critical for the understanding of system properties at the local microscopic level. In this paper, we use a local approach to investigate the existence of ''magic numbers'' in the chemical reactivity of Si clusters of intermediate sizes. 1 The approach defines local measures for the electronic structure in the framework of a nonorthogonal tight-binding Hamiltonian ~NOTB!. Local measures used in the analysis include local orbital energy, bond energy, bond charge, orbital charge, and local density of states ~LDOS!. Since the NOTB Hamiltonian is related to linear combination of atomic orbitals ~LCAO!-based meth- ods, the formalism of local analysis used in this paper be- comes identical to Mulliken's population analysis technique—a method well known in the quantum-chemistry community.2 The validity of the local analysis technique de- pends crucially on the nature of the basis functions used to expand the wave function. In the NOTB approach, although the basis functions are not explicitly stated, they are assumed to be localized. This makes the NOTB approach reliable to extract local information at the microscopic level. Our study of clusters in the intermediate range is based on structures derived from models constructed using the surface reconstruction induced geometries ~SRIG! proposed by Kaxiras.3,4 Of the clusters of different sizes that are compat- ible with the SRIG requirements and that are relatively stable ~see Sec. III!, only clusters with ''magic'' sizes 33, 39, and 45 would be expected to be chemically inert, while the rest ~clusters with sizes 49, 57, and 61! would have much higher ~by several orders of magnitude! reactivity, in agreement with experimental measurements for Si clusters in this range.1,5-8 This expectation is based on rather simple argu- ments related to the highest occupied molecular orbital- lowest unoccupied molecular orbital ~HOMO-LUMO! gap of these models.4 However, in order to establish this rigor- ously, a much more detailed analysis of the chemical reac- tivity properties of the models is required. Therefore, in this paper a detailed local analysis of the electronic structure based on the NOTB Hamiltonian has been carried out.