Berechnung der Frequenzverschiebungen von isotopen CO-Molekülkristallen

Abstract

The frequencies of the optically active lattice vibrations of carbon monoxide in the low temperature phase are calculated. The crystal structure is reported to be cubic with space group symmetry Pa3 and with four molecules per unit cell. The infrared spectrum of solid carbon monoxide at 20 °K (2000—3000 cm-1) given by Ewing and Pimentel is used. The molecular crystal is considered as an ensemble of harmonic oscillators, and the FG-matrix method of Wilson is applied. With the help of the F- and G-Matrices of a single unit cell, representing the interactions with 18 neighbouring unit cells too, 21 frequencies of the normal crystal and the isotopic crystals 13CO, 14CO, C17O, C18O are calculated. The frequencies of the translational and rotational lattice vibrations contribute to a combination band in the observed region in accord with the expected halfwidth. The calculated F- and G-matrix elements may be used for all diatomic molecular crystals with space group symmetry Pa3.