W0010

A Force Model for Chemical Bonds in Inorganic Crystals. I.D.Brown, Brockhouse Institute for Materials Research, McMaster University, Hamilton Ontario Canada L8S 4M1.

Physicists traditionally make quantitative predictions of the properties of a crystal by summing 2-body potentials over every pair of atoms in the crystal. Chemists cheerfully ignore most of these interactions, retaining only those nearest neighbour interactions that they call chemical bonds. Chemical bonds defy rigorous definition and their properties are notoriously difficult to quantify, but given the success of the chemical bond model such quantification should be possible. Using a simple electrostatic model, I propose the following expression for the force, F, exerted by a bond on its terminal atoms:

F = -(k_oq²/R²)(1-(R/R_e)²exp((R_e-R)/B))

where k_o = 23 nN.A².e^-2, R is the bond length, R_e is the ideal bond length, (the length at which the bond exerts zero force on its terminal atoms), B is the bond-valence softness parameter (= 0.37 Å) and q is the effective charge contributing to the bond. This expression can be used to calculate bond force constants and bond compressibilities. Good agreement is obtained with spectroscopically-determined force constants and diffraction-measured compressibilities by setting q² equal to (8S/3)^3/2, where S is the bond valence.