New approach to the nonparametric determination of the internal rotation potential from electron diffraction data. Reinvestigation ofm-bromonitrobenzene

Abstract

A numerical algorithm for the nonparametric determination of the internal rotation potential from electron diffraction data using Tikhonov's regularization method is described. The range of admissible values of the regularization parameter is estimated using Hamilton's statistical criterion. m-Bromonitrobenzene was reinvestigated using this approach. It was found that the form of the potential may be reliably established only in the region of the minimum corresponding to the planar conformation of the molecule. Fourier series approximation of the experimental values of the potential in the region of the minimum gives the rotation barrier of 4.6–5.4 kcal/mole. The following basic geometrical parameters have been obtained (ra in A, ∠α in deg, the error equals triple standard deviation): r(C−C)ave=1.399(3), r(C−N)=1.459(16), 1.459(16), r(N=O)=1.244(3), r(C−Br)=1.884(6), r(C−H)=1.099(20), ∠CCNC=123.9(1.4), ∠CNCCBr=116.8(1.5), ∠CNCC=116.6(1.9), ∠CNO=118.8(0.8). The results are compared with the data for the related compounds.