Lattice dynamics ofαcarbon monoxide

Previous calculations of the lattice dynamics of $\alpha -\mathrm{CO}$ have neglected the mass asymmetry of the molecules and have assumed a centrosymmetric $\mathrm{Pa}3\mathrm{}$ structure for the crystal rather than the observed $P{2}_{1}3$ structure. Coupling between translational and librational lattice modes has been ignored and anharmonic effects have not been considered in detail. This work includes these factors in lattice-dynamics calculations for $\alpha -\mathrm{CO}$ and examines their effect on computed frequencies for $\overrightarrow{\mathrm{k}}=0\mathrm{}$. Anharmonic effects are treated in the quasiharmonic approximation of Boccara and Sarma. The model assumes rigid mass-asymmetric molecules, end-for-end ordering, and molecular pair interactions consisting of a point quadrupole interaction with adjustable quadrupole moment $Q$ and an atom-atom Lennard-Jones (6-12) interaction with three adjustable parameters $\sigma$, $\epsilon$, and $b$, an effective bond length. Dipole interactions are neglected. Parameters were adjusted to fit the observed cohesive energy and lattice constant, and to give an optimal representation of the seven lattice frequencies in the Raman and infrared spectra. Calculations were performed in both harmonic and quasiharmonic approximations for bond lengths $b=0\mathrm{} \mathrm{and} 0.282$ Å. Frequencies calculated in the quasiharmonic approximation for the two bond lengths give a much better fit to the observed spectrum than the corresponding harmonic results, and for a given approximation the one-center potential yields a better fit than the two center. The $P{2}_{1}3$ distortion predicted by the model in the harmonic approximation is very small and in a direction opposite to that observed by Vegard, and in the quasiharmonic approximation is either in the direction opposite to that measured or in the observed direction but less than 20% of the observed magnitude. Comparison of the frequency spectra for symmetric and asymmetric molecules indicates that the mass dissymmetry has only a slight effect on the calculated frequencies.