The accuracy of bond-length estimations obtained by double Fourier series methods from X-ray data

Abstract

The accuracy obtainable by two-dimensional Fourier series methods has been studied experimentally for a hypothetical structure containing twelve atoms in general positions. An f curve appropriate to average hydrocarbon structures has been employed, and the results should be applicable to a wide range of organic crystals. Errors due to incompleteness in the Fourier series, and to random and systematic errors in the F values have been investigated. It is concluded that in careful determinations with extremely small and symmetric crystal specimens and with reliable photometric or very careful visual estimates of intensities, carried to the limit of copper radiation, the maximum error in a complex structure should not exceed 0⋅03 A, and the probable error will be about 0⋅015 A for atom separations of between 1⋅0 and 1⋅4 A. If the series is incomplete, or if systematic errors are present (such as might be due to absorption in a crystal specimen of irregular shape or to instrumental faults), then these limits will be exceeded.