Electron population analysis of accurate diffraction data. IV. Evaluation of two-center formalisms in least-squares refinement

Abstract

Least-squares formalisms which explicity include scattering by both one and two-center orbital products are applied to a set of theoretical scattering factors for diborane and to the experimental data on cyanuric acid. The diborane calculations confirm the accuracy of the formalisms employed and indicate the importance of selecting an appropriate basis set of atomic orbitals. They further indicate that (1) net electron populations in bonds and on atoms can be determined more precisely than individual population parameters; (2) the set of parameters should be limited by molecular symmetry and assumptions about the symmetry of the bonds; (3) only one of a set of highly correlated parameters on an atom or in a bond should be allowed to vary; (4) the most reasonable basis set is the one giving the best agreement factor. This experience is applied to the refinement of cyanuric acid. It is found that the isolated atom HF functions give the best description of the experimental density. A Mulliken population analysis of the results reproduces the chemical symmetry of the molecule. In general the conclusions reached on diborane are compatible with the analysis of the experimental data. Electron-density maps on cyanuric acid, based on the least-squares population parameters, show that a good description of the density is obtained with a number of parameter sets. These electron-density maps show significant disagreement with thermally-smeared theoretical maps, indicating that the INDO and ab initio minimal basis set (STO-3G) calculations do not properly predict the density in the bonding and lone-pair regions of the cyanuric acid molecule. A transformation to uncorrelated combinations of population parameters is proposed to facilitate analysis of the numerical results and comparison with theoretical population parameters.