Self-Consistent and Environment-Dependent Hamiltonians for Materials Simulations : case Studies on Silicon Structures

A reliable semi-empirical Hamiltonian for materials simulations must allow electron screening and charge redistribution effects. Using the framework of linear combination of atomic orbitals (LCAO), a self-consistent and environment-dependent (SCED) Hamiltonian has been constructed for quantum mechanics based simulations of materials. This Hamiltonian contains environment-dependent multi-center interaction terms and electron-electron correlation terms that allow electron screening and charge-redistribution effects. As a case study, we have developed the SCED/LCAO Hamiltonian for silicon. The robustness of this Hamiltonian is demonstrated by scrutinizing a variety of different structures of silicon. In particular, we have studied the following: (i) the bulk phase diagrams of silicon, (ii) the structure of an intermediate-size Si71 cluster, (iii) the reconstruction of Si(100) surface, and (iv) the energy landscape for a silicon monomer adsorbed on the reconstructed Si(111)-7x7 surface. The success of the silicon SCED/LCAO Hamiltonian in the above applications, where silicon exists in a variety of different co-ordinations, is a testament to the predictive power of the scheme.