Calculation of the lattice modes of the isotopic CO2 molecules and their reduced partition function ratios

Abstract

The lattice dynamics of a unit cell with four CO2 molecules have been calculated from the Raman, infrared, and inelastic neutron scattering spectra. The vibrational frequencies of the isotopic 12C16O2, 13C16O2, 12C18O2, and 12C16O18O are calculated in a pseudoharmonic oscillator approximation. From these vibrational frequencies and the gas phase frequencies, the reduced partition ratios of the various isotopic CO2 molecules are calculated in good agreement with experiment. The lattice dynamics calculation are also compared with calculation from a simple cell model. It is shown that the simple cell model is an excellent approximation for the calculation of the reduced partition function ratios as a consequence of the large separation between the eigenvalues of the internal and external modes, the magnitude of the external eigenvalues relative to kT, and the symmetries of the lattice and the molecule.