Cauchy pressure and the generalized bonding model for nonmagnetic bcc transition metals

The chemical bond as a physical linkage between atoms has proven to be an immensely powerful heuristic device, providing insight into the general relationships between the structure and properties of molecules and solids. Unfortunately, the bond concept is incomplete and fails to explain more subtle aspects of molecular and materials behavior. A rich set of examples is provided by attempts to identify the structural origins of nonzero Cauchy pressures, a quantity that has been said to reflect the nature of the bonding at the atomic level. We show that these deviations are easily explained by extending the concept of a bond from a linkage between atoms to a set of linkages between charge density critical points (maxima, minima, and saddle points). Further, we show that these links possess an identifiable structure with measurable characteristics. For the nonmagnetic bcc transition metals, we are able to write the Cauchy pressure as a function of these characteristic measures. Significantly, the model should be generalizable to other structures and will provide insight into the relationships between the charge density and elastic response.