Accurate charge density of trialanine: a comparison of the multipole formalism and the maximum entropy method (MEM)

Abstract

An accurate charge density study of trialanine is presented with the maximum entropy method (MEM), on the basis of the same reflection data as was used for a multipole refinement [Rödel et al. (2006). Org. Biomol. Chem. 4, 475–481]. With the MEM, the optimum fit to the data is found to correspond to a final value of χ2 which is less than its statistical expectation value N Ref, where N Ref is the number of reflections. A refinement strategy is presented that determines the optimal goal for χ2. It is shown that the MEM and the multipole method are on a par with regard to the reproduction of atomic charges and volumes, general topological features and trends in the charge density in the bond critical points (BCPs). Regarding the values of the charge densities in the BCPs, agreement between quantum chemical calculations, the multipole method and MEM is good, but not perfect. In the case of the Laplacians, the coincidence is not as good and especially the Laplacians of the C—O bonds differ strongly. One of the reasons for the observed differences in the topological parameters in the BCPs is the fact that MEM densities still include the effects of thermal motion, whereas multipole densities are free from the effects of thermal motion. Hydrogen bonds are more convincingly reproduced by the MEM than by multipole models.