Procedure for building a consistent embedding at the QM-CM interface

We propose and test a method for a consistent embedding of a domain treated with detailed quantum mechanical methods (QM) inside a domain treated using classical mechanical (CM) potentials. The physical context of this embedding is the response of a system to mechanical strain which leads to fracture. To provide a quantitative test of qualitative ideas, a model system capable of being treated by QM in its entirety is chosen: a silica nano-rod, comprised of 108 atoms. The embedding is constructed so that the CM description yields the same linear response to mechanical strain as the QM description to within a few percent. An acceptable composite representation of the full system requires (1) a CM potential for the classical domain with appropriate linear mechanical response, (2) pseudo-atoms for the termination of dangling bonds at the QM/CM interface, and (3) a dipole description for the polarization of the remainder of the CM region. A key test for the fidelity of the modeled QM domain is accurate forces and electronic charge densities. We show that the composite has the small strain behavior of the full QM treatment of the nano-rod. We find similar success in the application of this method to two other silica model systems: the notched rod, and a nano-ring. Both transfer Hamiltonian (TH) and density functional theory (DFT) are used for the underlying QM.