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 (SC) and environment-dependent (ED) multicenter Hamiltonian in the framework of linear combination of atomic orbitals (LCAO) 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: (i) the binding energy versus relative atomic volume of different phases of bulk silicon, (ii) the stable structure of an intermediate-size ${\mathrm{Si}}_{71}$ cluster, (iii) the reconstruction of Si(100) surface, and (iv) the energy landscape for a silicon monomer adsorbed on the reconstructed $\mathrm{Si}(111)\text{\ensuremath{-}}7\ifmmode\times\else\texttimes\fi{}7$ 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.