The normal vibrations of bridgeX2Y6molecules

Abstract

The molecular model considered is $ \matrix Y\diagdown \\ Y\diagup \endmatrix X \matrix \diagup \\ \diagdown \endmatrix $ \matrix Y\diagdown \\ Y\diagup \endmatrix X \matrix \diagup \\ \diagdown \endmatrix $ \matrix Y \\ Y \endmatrix $, with a tetrahedral distribution of valencies round the atom X. This structure applies to the dimeric trihalides of aluminium, indium and gallium, and to the hydrides B$_{2}$H$_{6}$ and Ga$_{2}$H$_{6}$. Symmetry classes and selection rules are given, followed by equations for the normal vibration frequencies derived from a valency-force treatment, taking into account the interactions between unlinked atoms in the ring. A special treatment is necessary for the bending vibration in which the potential energy is proportional to the fourth power of the displacement. The observed infra-red and Raman spectra of diborane can be satisfactorily assigned on the basis of this model, fifteen out of the seventeen active fundamentals being observed. These fifteen frequencies are predicted with an average error of 2% and a maximum error of 6% by the insertion of six adjustable force constants in the theoretical equations. The observed and calculated vibration frequencies are used to calculate the specific heat of diborane in the range 100-300 degrees K. The calculated values agree with experiment, except for a small discrepancy at the highest temperature which can be reasonably accounted for. The above results provide strong evidence that diborane has a bridge configuration rather than one resembling ethane. The force-constants obtained show that the terminal B-H links are normal single bonds, while the bonds forming the bridge are considerably weaker. This is in harmony with the greater length of the bridge links, and the small number of electrons available for their formation. It is concluded that the hypothetical reaction 2BH$_{3}\rightarrow $B$_{2}$H$_{6}$ involves the absorption of at least 15 kcal./mol. A simplified form of the frequency equations is used to calculate the Raman frequencies of the dimeric halides of aluminium. The results are in semi-quantitative agreement with the observed frequencies, and lead to an assignment which is consistent with the observed intensities.