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, D_6h 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: $\mathrm{r(}\mathrm{C}–\mathrm{C}{\text{)=1.396}}_9\text{±0.003\hspace{0.17em}}\mathrm{A}\mathrm{;r(}\mathrm{C}–\mathrm{H}{\text{)=1.084}}_5\text{±0.0020\hspace{0.17em}}\mathrm{A}\mathrm{;l(}{\mathrm{C}}_1–{\mathrm{C}}_2{\text{)=0.045}}_6\text{±0.003\hspace{0.17em}}\mathrm{A}\mathrm{;l(}{\mathrm{C}}_1\mathrm{···}{\mathrm{C}}_3{\text{)=0.055}}_5\text{±0.005\hspace{0.17em}}\mathrm{A}\mathrm{;l(}{\mathrm{C}}_1\mathrm{···}{\mathrm{C}}_4{\text{)=0.061}}_4\text{±0.009\hspace{0.17em}}\mathrm{A}\mathrm{;l(}{\mathrm{C}}_1–{\mathrm{H}}_1{\text{)=0.074}}_8\text{±0.010\hspace{0.17em}}\mathrm{A}\mathrm{;l(}{\mathrm{C}}_1\mathrm{···}{\mathrm{C}}_3{\text{)=0.097}}_5\text{±0.008\hspace{0.17em}}\mathrm{A}\mathrm{;l(}{\mathrm{C}}_1\mathrm{···}{\mathrm{H}}_3{\text{)=0.092}}_5\text{±0.016\hspace{0.17em}}\mathrm{A}\mathrm{;l(}{\mathrm{C}}_1\mathrm{···}{\mathrm{H}}_4{\text{)=0.096}}_0\text{±0.0023\hspace{0.17em}}\mathrm{A}$ . 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.