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 pairwise 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.
In quantum/classical (QM/CM) partitioning methods for multi-scale modeling, one is often forced to introduce uncontrolled phenomenological effects of the environment (CM) in the quantum (QM) domain as ab initio quantum calculations are computationally too intensive to be applied to the whole sample. We propose a method, in which two qualitatively different components of the information about the state of the CM region are incorporated into the QM calculations. First, pseudoatoms constructed to describe the chemistry of the nearest neighbor exchange interactions replace the atoms at the boundary of the CM and the QM regions. Second, the remaining effect of the CM bulk environment due to long-range Coulombic interactions is modeled in terms of dipoles. We have tested this partitioning method in a silica nanorod and a 3-membered silica ring for which ab initio quantum data for the whole system is available to assess the quality of the proposed partitioning method.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.