The refinement of electron-density distributions for noncentrosymmetric crystals from X-ray diffraction data may lead to a very good fit between model and data but to totally meaningless electron densities. This is to a large extent because varying certain parameters, or combination of parameters, in the model mainly leads to a change in the phases of the structure factors. A formal analysis of why this happens, when using multipole models, is given as well as specific examples using real data: the contributions of odd-order multipoles, which are invariant under crystal-class symmetry operations, are poorly determined. The importance of applying constraints on the models is stressed. The conclusions of this analysis can be carried over to refinements of anharmonic atomic vibrations.

The electron density distribution in lithium triborate LiB30 5 has been studied at room temperature by X-ray diffraction using Ag Ka radiation up to 1.02 A -t [1439 unique reflections with I > 3o-(/)]. Conventional refinements with a free-atom model yield R(F) = 0.0223, wR(F) = 0.0299, S = 1.632. Atom charge refinements show that the lithium should be considered a monovalent ion. Multipolar refinements were undertaken up to fourth order, imposing local non-crystallographic symmetry constraints in order to avoid phase problems leading to meaningless multipole populations due to the noncentrosymmetry of the structure (space group: Pna21). The residual indices decreased to: R(F) = 0.0147, wR(F) = 0.0193, S = 1.106. The net charges are in good agreement with what can be expected in borate chemistry. Deformation density maps are analysed in terms of o. and rr bonding. The experimental electron distribution in the Pz orbitals of triangular B atoms and surrounding O atoms has been analysed by introducing idealized hybridized states. In parallel, the electron density has been determined from ab initio Hartree-Fock calculations on fragments of the structure. Agreement with the X-ray determination is very good and confirms the nature of bonding in the crystal. The amount of transfer of rr electrons from the oxygen to the triangular B atoms is estimated to be 0.22 electrons by theory.