Multiscale modeling of materials based on force and charge density fidelity

The approximate representation of a quantum solid as an equivalent composite semiclassical solid is considered for insulating materials. The composite is comprised of point ions moving on a potential energy surface. In the classical bulk domain this potential energy is represented by potentials constructed to give the same structure and elastic properties as the underlying quantum solid. In a small local quantum domain the potential is determined from a detailed quantum calculation of the electronic structure. The new features of this well-studied problem are (1) a clearly stated theoretical context in which approximations leading to the model are introduced, (2) the representation of the classical domain by potentials focused on reproducing the specific quantum response being studied, (3) development of "pseudoatoms" for a realistic treatment of charge densities where bonds have been broken to define the environment of the quantum domain, and (4) inclusion of polarization effects on the quantum domain due to its distant bulk environment. This formal structure is illustrated in detail for a Si O2 nanorod. More importantly, each component of the proposed modeling is tested quantitatively for this case, verifying its accuracy as a faithful multiscale model of the original quantum solid. To do so, the charge density of the entire nanorod is calculated quantum mechanically to provide the reference by which to judge the accuracy of the modeling. The construction of the classical potentials, the rod, the pseudoatoms, and the multipoles is discussed and tested in detail. It is then shown that the quantum rod, the rod constructed from the classical potentials, and the composite classical/quantum rod all have the same equilibrium structure and response to elastic strain. In more detail, the charge density and forces in the quantum subdomain are accurately reproduced by the proposed modeling of the environmental effects even for strains beyond the linear domain. The accuracy of the modeling is shown to apply for two quite different choices for the underlying quantum chemical method: transfer Hamiltonian and density functional methods.