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 chi(2) 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 chi(2). 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.

Accurate electron densities of a-glycine have been obtained by the maximum entropy method (MEM) applied to low-temperature X-ray diffraction data by Destro et al. (J. Phys. Chem. A, 2000, 104, 1047-1054. Difference Fourier maps have been found to provide a good stopping criterion for the iterations in the MEM, in agreement with our previous findings for trialanine. Properties according to Bader's atoms-in-molecules theory are reported for the MEM electron density. These properties are found to be in agreement with the properties of the MEM electron density as they have been obtained previously for the tripeptide trialanine, thus showing the consistency of the MEM approach when applied to centrosymmetric and acentric organic compounds. The dynamic MEM electron density compares favourably with the static electron density obtained from the multipole model by Destro et al. (2000), with differences being attributed to the specific nature of each method. The independent spherical atom model (ISAM) and the multipole model provide different phases for 17 reflections of which only two are of the type 'observed'. A MEM calculation with reflection phases from the multipole model leads to an electron density that is only marginally different from the MEM electron density with phases from the ISAM refinement. This suggests, at least for centrosymmetric structures, that the ISAM is sufficiently good to be used as basis for the MEM approach to accurate electron density studies. Computational detailsSingle-crystal X-ray diffraction data were obtained from Destro et al., 19 who also reported a multipole refinement with

The maximum entropy method (MEM) can be used to determine the electron density in the unit cell from phased x-ray diffraction data. A critical discussion is given of the possibilities and limitations of the MEM for the determination of accurate electron densities in chemical bonds. An overview is given of the principles of the MEM, and recent extensions and modifications are discussed, as they are required for a successful application of the MEM in accurate charge-density studies. The quantitative interpretation of MEM electron densities according to Bader's atoms-in-molecules (AIM) theory is discussed, and it is compared to AIM properties of densities obtained from multipole refinements. Applications are presented concerning the analysis of covalent bonds and hydrogen bonds in molecular crystals.

Charge densities have been determined by the Maximum Entropy Method (MEM) from the high-resolution, low-temperature (T ≃ 20 K) X-ray diffraction data of six different crystals of amino acids and peptides. A comparison of dynamic deformation densities of the MEM with static and dynamic deformation densities of multipole models shows that the MEM may lead to a better description of the electron density in hydrogen bonds in cases where the multipole model has been restricted to isotropic displacement parameters and low-order multipoles (l max = 1) for the H atoms. Topological properties at bond critical points (BCPs) are found to depend systematically on the bond length, but with different functions for covalent C—C, C—N and C—O bonds, and for hydrogen bonds together with covalent C—H and N—H bonds. Similar dependencies are known for AIM properties derived from static multipole densities. The ratio of potential and kinetic energy densities |V(BCP)|/G(BCP) is successfully used for a classification of hydrogen bonds according to their distance d(H...O) between the H atom and the acceptor atom. The classification based on MEM densities coincides with the usual classification of hydrogen bonds as strong, intermediate and weak [Jeffrey (1997). An Introduction to Hydrogen Bonding. Oxford University Press]. MEM and procrystal densities lead to similar values of the densities at the BCPs of hydrogen bonds, but differences are shown to prevail, such that it is found that only the true charge density, represented by MEM densities, the multipole model or some other method can lead to the correct characterization of chemical bonding. Our results do not confirm suggestions in the literature that the promolecule density might be sufficient for a characterization of hydrogen bonds.

1] Wang, J.; Dauter, M.; Alkire, R.; Joachimiak, A.; Dauter