Distances, root-mean-square amplitudes of vibration, and vibrational anharmonicity in carbon tetrabromide from a gas-phase electron-diffraction investigation

Abstract

Carbon tetrabromide has been reinvestigated in the gas phase at 100°C by electron diffraction. Unlike the rather noisy diffraction data from most bromine-containing organic compounds, the CBr 4 data are of high quality. Vibrational anharmonicity as reflected by the parameters κ in the intensity function has been investigated for both the bond and nonbond distances; optimum values found are κ(CBr)=4×10 −6 Å −3 and κ(Br·Br) = 11 × 10 −6 Å −3 corresponding to Morse-potential anharmonicity constants a 3(CBr)=2.2Å −1 and a 3(Br·Br)=1.3 Å −1. The fit of theoretical to experimental intensity over our data range (7.0 ⩽ s/ (Å) ⩽ 39) is not very sensitive to κ(CBr), but is significantly improved by inclusion of κ(Br·Br) at the optimum value. Similarly, the distance measurements are not affected by κ(CBr) over the reasonable range 0–8×10 −6 Å −3, but small, marginally significant distance changes result from introduction of κ(Br·Br) near its optimum value. The vibrational amplitude measurements are unaffected by any reasonable values of either κ. With the optimum κ values and assumed T d molecular symmetry the following distances ( r in Å) and r.m.s. amplitudes of vibration ( l in Å) with estimated 2σ uncertainties are obtained: r g(CBr)=1.942 (2), r g(Br·Br)=3.167 (4), l(CBr)=0.056 (7), l(Br·Br)=0.085 (4). With retention of the anharmonicity factors but removal of the geometry restriction imposed by T d symmetry (i.e., the two distances and the two amplitudes are regarded as four independent parameters), the results are r a(CBr)=1.938 (6) Å, r a (Br·Br)=3.165 (4) Å, l(CBr)=0.056 (7) Å, and l(Br·Br)=0.084 (4) Å. The distances from the latter set correspond exactly to a tetrahedral bond angle; “shrinkage” in CBr 4 is thus negligible. Results obtained without inclusion of anharmonicity effects are consistent with a very small shrinkage, which suggests that shrinkage interpretations be made with care in sensitive work. The measured amplitudes of vibration are in excellent agreement with the calculated values: l(CBr)=0.0574 Å and l(Br·Br)=0.0834 Å.