Crystal vibrations of poly-1,3-dioxolane crystal form II and treatment of statistical errors due to uncertainties in the atomic positions

Abstract

Infrared and Raman spectra have been measured for poly-1,3-dioxolane crystal form II which belongs to an orthorhombic system with the space group Pbca- D 2 h 15 including four polymer chains in the unit cell. The normal coordinate treatment of the single polymer chain with the site symmetry of C s has been made using a modified Urey-Bradley force field. For the normal mode calculations of the three-dimensional crystal lattice, the van der Waals intermolecular interactions for the atomic pairs of H ⋯ H, O ⋯ H, and C ⋯ H were taken into account along with the intramolecular force constants determined by the least-squares method. The molecular modes which belong to the A′ species have been found to appear in the polarized i.r. spectra as pairs of bands with opposite polarization. These band splittings are due to the correlation field splitting between the B u (⊥) and B 3 u (|) species of the three-dimensional factor group of the crystal lattice, and the frequency gaps reflect the strength of the intermolecular forces. In the far i.r. and the Raman spectra in low-frequency range there are observed several weak but distinct bands assignable to the lattice modes. The observed frequencies of the lattice modes as well as the observed frequency gaps of the correlation field splittings are reproduced fairly well by the normal coordinate treatment of the crystal lattice, using a set of force constants derived from Lennard-Jones type interatomic potential functions. The obtained intermolecular force constants are found to be rather smaller as compared with those of benzene and cyclic ether crystals. The discrepancy is partly attributed to the errors in atomic parameters proposed by the X-ray work. In order to estimate the effect of the uncertainties in the atomic positions to the statistical errors in the resultant intermolecular forces Φ, lattice mode frequencies ν, and correlation splittings Δν which are derived from the given crystal structure, equations have been derived according to a method of error transfer and the standard deviations have been evaluated for Φ, Δν and ν.