Constructing a small strain potential for multi-scale modeling

Simulation of bulk materials with some components locally far from equilibrium usually requires a computationally intensive quantum mechanical description to capture the relevant mechanisms (e.g. effects of chemistry). Multi-scale modeling entails a compromise whereby, the most accurate quantum description is used only where needed and the remaining bulk of the material is replaced by a simpler classical system of point particles. The problem of constructing an appropriate potential energy function for this classical system is addressed here. For problems relating to fracture, a consistent embedding of a quantum (QM) domain in its classical (CM) environment requires that the classical system should yield the same structure and elastic properties as the QM domain for states near equilibrium. It is proposed that an appropriate classical potential can be constructed using ab initio data on the equilibrium structure and weakly strained configurations calculated from the quantum description, rather than the more usual approach of fitting to a wide range of empirical data. This scheme is illustrated in detail for a model system, a silica nanorod that has the proper stiochiometric ratio of Si:O as observed in real silica. The potential energy is chosen to be pair wise additive, with the same pair potential functional form as familiar phenomenological TTAM potential. Here, the parameters are determined using a genetic algorithm with force data obtained directly from a quantum calculation. The resulting potential gives excellent agreement with properties of the reference quantum calculations both for structure (bond lengths, bond angles) and elasticity (Young's modulus). The proposed method for constructing the classical potential is carried out for two different choices for the quantum mechanical description: A transfer Hamiltonian method (NDDO with coupled-cluster parameterization) and density functional theory (with plane wave basis set and PBE exchange correlation functional). The quality of the potentials obtained in both cases is quite good, although the two quantum rods have significant differences.