Theory of the Collision-Induced Rotational Spectrum of Tetrahedral Molecules

Abstract

The general theory of induced absorption resulting from binary collisions has been extended and applied to the pressure-induced far-infrared spectrum of a gas of tetrahedral molecules. The molecular octopole moment is related to the integrated intensity resulting from the modulation of the octopole-induced dipole moment by the rotational motion of the molecules. Translational effects are not considered. The intensity resulting from the overlap moment is estimated and found to be negligible. The quantum-mechanical analysis is presented using both unsymmetrized and symmetry-adapted wavefunctions. The results are compared, and the limitations of the unsymmetrized approach are discussed. The techniques developed in the symmetrized treatment are generally useful in integrated-intensity calculations for molecules with a high degree of symmetry and will be discussed in detail. The analysis is applied to recent room-temperature far-infrared data on CH4, CD4, and CF4. The octopole moments deduced from the experimental spectra agree well with those obtained by other techniques. The general features of the spectrum are derived from the theory. The theoretical predictions concerning these features are found to agree well with experiment. The variation of the shape and integrated intensity of the theoretical spectrum with temperature over the range 110–500°K is also discussed.