Analysis of the Far Infrared Collision-Induced Absorption Spectrum of Cyclopropane.

The far infrared rotational collision-induced absorption (CIA) of gas phase cyclopropane (Cp) and cyclopropane -argon (Cp-Ar) mixtures has been observed. This is the first oblate symmetric top molecule for which rotational CIA has been reported. The maximum absorption coefficient for Cp-Cp CIA occurs at 65 reciprocal centimeters and equals 5.6 times 10^{ -5} per centimeter per square amagat. The classical multipolar field model, a point charge model, and quantum mechanical calculations are compared to the experimental results. The theoretical band calculated from the superposition of translationally broadened rotational lines using the isotropic polarizability and the quadrupole and octapole moments for cyclopropane with a Lennard-Jones pairwise distribution function and a normalized line shape function peaks at 60 reciprocal centimeters with an absorption coefficient several times smaller than the observed value. This is contrasted with the observed CIA results of prolate nonpolar hydrocarbons (i.e., allene, ethane, ethylene) which exhibited maxima in CIA bands at frequencies much higher than that calculated from this quadrupole-polarizability term. Rotational CIA results from the electric field of a rotating molecule inducing a dipole moment in the collision partner. During a collision, this field is more complicated than the multipolar fields alone can represent. The actual field results from a combination of the multipolar fields and a large contribution from asymmetrical interactions. The contribution to the field which is in addition to the multipolar field has been represented with an asymmetrical interaction parameter. The size of this parameter indicates the strength of the asymmetrical interaction and properly converges to the multipolar field at large R. In cyclopropane, the three-fold oscillation in the amplitude of the quantum mechanical electric field has been shown to scale approximately with R^{-10 }. The parameter has the appropriate symmetry and nuclear spin properties to generate the K transitions necessary to account for the observed "excess" absorbance. This asymmetrical interaction parameter leads to an absorption coefficient which has the proper frequency dependence and intensity to fit the observed spectrum when added to the multipolar absorption of the molecules cyclopropane, ethylene, and allene.