No abstract

Visualizing and predicting the response of the electron density, ρ(r), to an external perturbation provides a portion of the insight necessary to understand chemical reactivity. One strategy used to portray electron response is the electron pushing formalism commonly utilized in organic chemistry, where electrons are pictured as flowing between atoms and bonds. Electron pushing is a powerful tool, but does not give a complete picture of electron response. We propose using the motion of zero-flux surfaces (ZFSs) in the gradient of the charge density, ∇ρ(r), as an adjunct to electron pushing. Here we derive an equation rooted in conceptual density functional theory showing that the movement of ZFSs contributes to energetic changes in a molecule undergoing a chemical reaction. Using a substituted acetylene, 1-iodo-2-fluoroethyne, as an example, we show the importance of both the boundary motion and the change in electron counts within the atomic basins of the quantum theory of atoms in molecules for chemical reactivity. This method can be extended to study the ZFS motion between smaller gradient bundles in ρ(r) in addition to larger atomic basins. Finally, we show that the behavior of ∇ρ(r) within atomic basins contains information about electron response and can be used to predict chemical reactivity.

Efficient computational models that retain essential physics of the associated continuous mathematical models are important for several applications including acoustic horn optimization. For heterogeneous wave propagation models that are naturally posed on unbounded domains, a crucial physical requirement is that the scattered fields are radiating and satisfy a radiation condition at infinity. We describe and implement an efficient high-order coupled computer model for acoustic wave propagation in an unbounded region comprising a bounded heterogeneous media with several obstacles. Our unbounded and heterogeneous media computer model retains the radiation condition exactly and hence is readily applicable for the celebrated acoustic horn problem. This approach is more suitable than using a standard loworder approximation of the radiation condition. Using parallel computing environments, we demonstrate the high-order algorithm with extensive numerical experiments and computational analysis, including the model horn problem with several material property parameters. Our efficient computer models and validation in this work lead to some interesting mathematical and numerical analysis problems for the acoustic system defined on unbounded and heterogeneous media comprising smooth, non-smooth, horn, impenetrable, and penetrable obstacles.