Charge-density analyses for molecular crystals using Bragg diffraction data: the effects of error

Abstract

Charge-density analyses have been carried out on twelve sets of X-ray data. For materials containing first-row atoms intensities measured by the 0:20 method yield gross populations concordant with electronegativities and the shapes of the distributions agree qualitatively with predicitions from forcefield arguments. Gross charges are sensitive to experimental errors systematic with Bragg angle, but are insensitive to deficiencies in the models for thermal motion. Noise in thermal parameters is a limiting factor for hydrogen populations determined from X-ray data alone, but mechanistic models for the hydrogen motions obviate this difficulty. Spherically symmetric functions centred at the nuclei give a poor representation of the density for bonded hydrogen. Slater-type orbital products with standard molecular exponents sample the valence density less efficiently for second-row atoms than for carbon, nitrogen and oxygen atoms. Two-centre density functions overlap heavily with neighbouring one-centre terms, and do not provide a useful extension to basis sets for charge-density studies. There are discrepancies between experimental populations and semi-empirical INDO calculations for strongly polar systems.

Early days of quantum crystallography: A personal account

“…The X‐ray scattering from orbital densities of s 2 and + + type as well as those from some of the two‐center terms, , resembles each other; as a result, the normal least square equations are ill‐conditioned due to the linear parameter dependences. The orthogonal transformation to the statistically uncorrelated set of electronic parameters or using the hybrid localized orbital basis set to decrease a number of coefficients to be determined formally led to the solution. However, the eigenvalues of P matrix, p i , anyway may violate condition , as the theory requires .…”