Sander van Smaalen

EDMA : a computer program for topological analysis of discrete electron densities

EDMA is a computer program for topological analysis of discrete electron densities according to Baders theory of atoms in molecules. It locates critical points of the electron density and calculates their principal curvatures. Furthermore, it partitions the electron density into atomic basins and integrates the volume and charge of these atomic basins. EDMA can also assign the type of the chemical element to atomic basins based on their integrated charges. The latter feature can be used for interpretation of ab initio electron densities obtained in the process of structure solution. A particular feature of EDMA is that it can handle superspace electron densities of aperiodic crystals in arbitrary dimensions. EDMA first generates real-space sections at a selected set of phases of the modulation wave, and subsequently analyzes each section as an ordinary three-dimensional electron density. Applications of EDMA to model electron densities have shown that the relative accuracy of the positions of the critical points, the electron densities at the critical points and the Laplacian is of the order of 10−4 or better.

The maximum-entropy method in superspace

One of the applications of the maximum-entropy method (MEM) in crystallography is the reconstruction of the electron density from phased structure factors. Here the application of the MEM to incommensurately modulated crystals and incommensurate composite crystals is considered. The MEM is computed directly in superspace, where the electron density in the (3+d)-dimensional unit cell (d > 0) is determined from the scattering data of aperiodic crystals. Periodic crystals (d = 0) are treated as a special case of the general formalism. The use of symmetry in the MEM is discussed and an efficient algorithm is proposed for handling crystal symmetry. The method has been implemented into a computer program BayMEM and applications are presented to the electron density of the periodic crystal NaV(2)O(5) and the electron density of the incommensurate composite crystal (LaS)(1.14)NbS(2). The MEM in superspace is shown to provide a model-independent estimate of the shapes of the modulation functions of incommensurate crystals. The discrete character of the electron density is found to be the major source of error, limiting the accuracy of the reconstructed modulation functions to approximately 10% of the sizes of the pixels. MaxEnt optimization using the Cambridge and Sakata-Sato algorithms are compared. The Cambridge algorithm is found to perform better than the Sakata-Sato algorithm, being faster, always reaching convergence, and leading to more reliable density maps. Nevertheless, the Sakata-Sato algorithm leads to similar density maps, even in cases where it does not reach complete convergence.

A New Half-Condensed Schiff Base Compound: Highly Selective and Sensitive pH-Responsive Fluorescent Sensor

A new probe, 3-[(3-benzyloxypyridin-2-ylimino)methyl]-2-hydroxy-5-methylbenzaldehyde (1-H) behaves as a highly selective fluorescent pH sensor in a Britton-Robinson buffer at 25 °C. The pH titrations show a 250-fold increase in fluorescence intensity within the pH range of 4.2 to 8.3 with a pK(a) value of 6.63 which is valuable for studying many of the biological organelles.

Generation of (3 + d)-dimensional superspace groups for describing the symmetry of modulated crystalline structures

A complete table of (3 + 1)D, (3 + 2)D and (3 + 3)D superspace groups (SSGs) has been enumerated that corrects omissions and duplicate entries in previous tables of superspace groups and Bravais classes. The theoretical methods employed are not new, though the implementation is both novel and robust. The paper also describes conventions for assigning a unique one-line symbol for each group in the table. Finally, a new online data repository is introduced that delivers more complete information about each SSG than has been presented previously.

Scheelite CaWO4 at high pressures

The high-pressure room-temperature behaviour of scheelite CaWO4 (I41/a,Z = 4) is studied using high-resolution synchrotron angle-dispersive x-ray powder diffraction in diamond anvil cells loaded with helium or a mixture of methanol and ethanol as the pressure-transmitting media. At about 10 GPa, there occurs a phase transition to the fergusonite type (I 2/a,Z = 4) without any discontinuity in the pressure dependence of the unit cell volumes. These observations are discussed in relation to the high-pressure–high-temperature systematics of the AMX4 and AX2 type compounds.

An elementary introduction to superspace crystallography

Aperiodic crystals are defined as a crystalline state of matter, that has atomic structures with long-range order but without translational symmetry. Experimentally, they are characterized by sharp Bragg reflections in the Xray diffraction, that can be indexed by integers, if four or more reciprocal basis vectors are used. An introduction is given to the basic concepts of the superspace theory for structural analysis of incommensurately modulated crystals and incommensurate composite crystals [De Wolff, Janner and Janssen, Acta Crystallogr. 37 (1981) 625–636]. It is concluded that major challenges of the crystallography of incommensurate phases lie in the determination of the precise shapes of modulation functions, and in finding the relations between physical properties of incommensurate crystals and their atomic structures.

Equivalence of superspace groups

The standard settings of (3 + d)-dimensional superspace groups are determined for a series of modulated compounds, especially concentrating on d = 2 and 3. The coordinate transformation in superspace is discussed in view of its implications in physical space.

The generalized F constraint in the maximum-entropy method : a study on simulated data

One of the classical problems in the application of the maximum-entropy method (MEM) to electron-density reconstructions is the uneven distribution of the normalized residuals of the structure factors [|F(obs)(H)|-|F(calc)(H)|]/sigma(H) of the resulting electron density. This distribution does not correspond to the expected Gaussian distribution and it leads to erroneous features in the MEM reconstructions. It is shown that the classical chi(2) constraint is only one of many possible constraints, and that it is too weak to restrict the resulting distribution to the expected Gaussian shape. It is proposed that constraints should be used that are based on the higher-order central moments of the distribution of the structure-factor residuals. In this work, the influence of different constraints on the quality of the MEM reconstruction is investigated. It is proposed that the use of a combined constraint on more than one central moment simultaneously would lead to again improved results. Oxalic acid dihydrate was chosen as model structure, from which several data sets with different resolutions and different levels of noise were calculated and subsequently used in the MEM. The results clearly show that the use of different constraints leads to significantly improved results.

Topological properties of hydrogen bonds and covalent bonds from charge densities obtained by the maximum entropy method (MEM)

The maximum-entropy charge densities of six amino acids and peptides reveal systematic dependencies of the properties at bond critical points on bond lengths. MEM densities demonstrate that low-order multipoles (l max = 1) and isotropic atomic displacement parameters for H atoms in the multipole model are insufficient for capturing all the features of charge densities in hydrogen bonds.

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

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.