Application of Least-Squares Method to Gaseous Benzene in Electron Diffraction Investigation

The intensity data of gaseous benzene obtained at 18°C by the sector-microphotometer technique in electron diffraction were analyzed by use of a least-squares method, D6h symmetry being assumed for the molecule. A total of thirteen parameters comprising two bond distances, seven root-mean-square amplitudes, three background parameters, and one intensity scale factor were refined in the least-squares treatment. Uncertainties in these parameters were determined by computing standard errors due to the over-all errors involving systematic and random errors. Results for bond distances r and root-mean-square amplitudes l are as follows: r(C–C)=1.3969±0.003 A;r(C–H)=1.0845±0.0020 A;l(C1–C2)=0.0456±0.003 A;l(C1···C3)=0.0555±0.005 A;l(C1···C4)=0.0614±0.009 A;l(C1–H1)=0.0748±0.010 A;l(C1···C3)=0.0975±0.008 A;l(C1···H3)=0.0925±0.016 A;l(C1···H4)=0.0960±0.0023 A. These values were compared with data available in the literature. An empirical formula is proposed for experimental background scattering and the selection of weighting factors in least-squares refinement is discussed.