Nearsightedness of Oxygen-Containing Functional Groups

Matter is nearsighted, that is, for a fixed chemical potential, the charge density is only sensitive to perturbations within a radius R. While it is known that the resultant change in the density at point r0 from some perturbation at some other point R (Δn(r0,R)) is a monotonically decreasing function, a plausible range of a chemically significant Δn(r0,R) and the value of R needed to cause these perturbations has not been well studied. Using the functional group, which upon satisfying the necessary atoms/bonds specific to that functional group retains a characteristic chemistry, this paper provides an initial study into the magnitude of both Δn and R, the radius beyond which to affect a given property. Values for Δn are shown to be robust across a variety of DFT functionals and provide a framework for the transfer of the functional group concept to other disciplines, such as metallurgy.