  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.
