The structure of the diatomic molecular solids

Abstract

A simple model of the low temperature phases of the diatomic molecular solids is examined. The model consists of molecules, interacting via a Lennard-Jones atom-atom potential and quadrupole-quadrupole interactions. The internal energy of any crystallographic structure (excluding thermal effects) can then be given in terms of two dimensionless parameters, which describe the deviation of the molecular shape from a sphere and the relative importance of the quadrupole energy. The minimum energies and optimum molecular configurations in several structures are computed, for values of these dimensionless variables which span the values appropriate to the actual homonuclear diatomic molecular solids, H$_{2}$, N$_{2}$, O$_{2}$, F$_{2}$, Cl$_{2}$, Br$_{2}$ and I$_{2}$. Despite its great simplicity, the model is able to explain several features of these structures. These are (i) $o-\text{H}_{2}$ and N$_{2}$ have the optimum quadrupole structure, Pa3; (ii) $\beta $-O$_{2}$ is one of the optimum van der Waals' structures, R$\overline{3}$m; (iii) the monoclinic $\alpha $-F$_{2}$ structure is the most stable structure for parameter values very close to those appropriate to F$_{2}$; (iv) the orthorhombic Cmca structure (observed for Cl$_{2}$, Br$_{2}$ and I$_{2}$ is the most stable structure for a large range of quadrupole moments which may be appropriate to these molecules. The model, is, of course, unable to take into account intermolecular bonding or spin-dependent interatomic forces. The former is important for the halogens and the latter for the (magnetic) oxygen molecule. The case of $\alpha $-O$_{2}$ is treated in the following paper.