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

Abstract

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.

Atomic Scale Chemo-mechanics of Silica: Nano-rod Deformation and Water Reaction

“…The nano-rod which we adopt here is one system which satisfies this requirement. As discussed in the work by Mallik et al in this collection [47], the 108-atom silica nano-rod (Figure 7) is formed by a stack of four rings of corner-sharing silica tetrahedra, capped by two rings of edge-sharing tetrahedra. The resulting structure has the SiO 2 stoichiometry and is free of dangling bonds without artificial saturation.…”

“…If the atoms as structureless objects (i.e., without distinguishing nuclei and electrons) are sufficient to describe the problem under consideration, one may treat the electrons implicitly and resort to classical atomistic simulations to track the atoms as driven by classical inter-atomic interaction potentials. Preceding papers in this collection [47,55,95] discuss such potentials and their parameterization in detail. The advantage of this approach, which we adopt in the study of mechanical deformation, is that the constraint on the number of atoms that can be handled is not severe.…”

“…The empirical potential used in our mechanical deformation studies is the two-body BKS form already discussed at length in this collection [47,55,95]. Recall that it is comprised of the electrostatic interaction between two point charges and short-range interactions of the Buckingham form [81].…”

Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets

“…The QM results were therefore considered as "benchmark" results, with the difference between the QM/MM and the QM computation indicating errors due to coupling. QM/MM methods are ubiquitous in many areas of chemistry but they are much less common for the study of fracture, 21,[39][40][41][42][43][44][45] and quantitative comparisons of these methods to full QM methods are needed to explore their effectiveness.…”

Pupil

“…However, the user also may use any of the quantum atoms allowed by the external QM engine to saturate the free valence of the QM atom. An example is pseudoatoms with a parameterized effective core potential which can be adjusted to mimic the properties of the original chemical bond being cut (Mallik, Taylor, Runge, Dufty, & Cheng, 2006).…”