Coherent treatment of the self-consistency and the environment-dependency in a semi-empirical Hamiltonian: Applications to bulk silicon, silicon surfaces, and silicon clusters

Abstract

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.

Self-consistent and environment-dependent Hamiltonian for quantum-mechanics materials simulations.

“…This concept of charge redistribution is of course not present in two-center models, having been lost in the various layers of approximation; the matter must be approached from a first-principles perspective. Our discussion follows closely that of our own recent publication [30].…”

“…The notation follows that of Ref. [30], which is slightly different from the notation used elsewhere in this report.…”

“…[30], which is slightly different from the notation used in out discussion; one should consult Ref. [30] if one is interested in using the parameters in Table 11. The same comments that apply to our results for Si also apply to these results for C and Ge.…”

“…The comparison of the calculated and reference values for these clusters are shown in Table 1, which is taken with some minor modifications from our Ref. [30]. "Another structure that we have considered is the edge-capped octahedron (7d).…”

“…The parameters shown in Figure 11 follow the notation used in Ref. [30], which is slightly different from the notation used in out discussion; one should consult Ref. [30] if one is interested in using the parameters in Table 11.…”