How big are atoms in crystals?

Abstract

Atoms and bonds are central concepts in structural chemistry, but neither are concepts that arise naturally from the physics of condensed phases. It is ironic that the internuclear distances in crystals that are readily measured depend on the sizes of atoms, but since atoms in crystals can be defined in many different ways, all of them arbitrary and often incompatible, there is no natural way to express atomic size. I propose a simple coherent picture of Atoms-in-Crystals which combines properties selected from three different physically sound definitions of atoms and bonds. The charge density of the free atom that is used to construct the procrystal is represented by a sphere of constant charge density having the quantum theory of atoms in molecules (QTAIM) bonded radius. The sum of these radii is equal to the bond length that correlates with the bond flux (bond valence) in the flux theory of the bond. The use of this model is illustrated by answering the question: How big are atoms in crystals? The QTAIM bonded radii are shown to be simple functions of two properties, the number of quantum shells in the atomic core and the flux of the bond that links neighbouring atoms. Various radii can be defined. The univalent bonded radius measures the intrinsic size of the atom and is the same for all cations in a given row of the periodic table, but the observed bonded radius depends also on the bond flux that reflects the chemical environment.