Cluster analyses of metal-organic fragments using the dSNAP software.

The dSNAP computer program has been used to classify searches of the Cambridge Structural Database for two ligands: -O-CH(2)-CH(2)-O- and N(CH(2)CH(2)O-)(3) commonly found in metal-organic systems. The clustering method used is based on total geometries (i.e. all the lengths and angles involving all the atoms in the search fragment, whether bonded or not) and proved capable of distinguishing in a wholly automatic, objective way between different types of metal complex purely on the basis of the geometry of the ligand and the relative positions of the O atoms to the metals.

Solving the crystal structures of zeolites using electron diffraction data. I. The use of potential-density histograms.

The maximum-entropy and likelihood method for solving zeolite crystal structures from electron diffraction data is modified to use potential-map-density histograms as an additional figure of merit. The experimental histogram is compared to an idealized one (based on known zeolite structures) using Pearson and Spearman correlation coefficients. These supplement the use of log-likelihood estimates as figures of merit to select the optimal solution from a collection of phase sets. The method has been applied with success to seven zeolite and one inorganic crystal structures that have varying associated data quality. The technique works easily even with two-dimensional data sets of less than 50 unique diffraction data and a resolution of less than 2 A. The method is very fast, and the computer time needed on a modest PC was never more than a few minutes.

Solving the crystal structures of zeolites using electron diffraction data. II. Density-building functions.

A density-building function is used to solve the crystal structures of zeolites from electron diffraction data using both two- and three-dimensional data sets. The observed data are normalized to give unitary structure factors |U(h)|(obs). An origin is defined using one to three reflections and a corresponding maximum-entropy map, q(ME)(x), is calculated in which the constraints are the amplitudes and phases of the origin-defining reflections. Eight strong reflections are then given permuted phases and each phase combination is used to compute P(deltaq) = integral(V)deltaq(x)(2)/q(ME)(x)dx, where deltaq(x) is the Fourier transform of |U(h)|(obs)exp(i\phi_(perm)h - |U(h)|(ME)exp(i\phi_(ME)h), phi_(perm)h is the permuted phase for reflection h and phi_(ME)h is the phase angle for reflection h predicted from the Fourier transform of q(ME)(x). The 64 phase sets with minimum values of P(deltaq) are subjected to entropy maximization and, following this procedure, those with the five highest log-likelihood gains are examined. Sometimes auxiliary potential histogram information is also used. The method worked routinely with seven zeolite structures of varying complexity and data quality, but failed with an eighth structure.

Using small molecule crystal structure data to obtain information about sulfonamide conformation.

Understanding the conformations adopted by the sulfonamide group is essential to the understanding of the way that sulfa drugs act upon the body. The relative energies of these conformations in the solid state are estimated from the Cambridge Structural Database (CSD) using cluster analysis, and are used to confirm earlier findings that many high-level ab initio calculations do not reproduce the observed solid-state structure. These conformational studies have been extended to the adjacent torsion angles, and it has been shown that the sulfonamide group significantly affects the form adopted. The relative energies of the observed forms in the solid state have been estimated using data available in the CSD.

Using cluster analysis to study transition-metal geometries: four-coordinate complexes with two salicylaldiminato or related ligands.

Cluster analysis is shown to be an effective method to analyse and classify metal coordination geometry in a very large number of four-coordinate bis-salicylaldimato (or bis-beta-iminoketonate) transition-metal complexes available in the Cambridge Structural Database. The methods described require no prior knowledge of chemistry to be input; retrieved structures are automatically clustered into groups based purely on the geometric similarity of the fragments and these groupings can then be interpreted by the structural chemist.

The application of cluster analysis to identify conformational preferences in enones and enimines from crystal structural data.

Cluster analysis can be an effective tool for analysing large quantities of data. Here it has been applied to the conformational analysis of enones and enimines in the crystalline solid state, using structural information mined from the Cambridge Structural Database. The forms that are common in the gaseous state and in solution are already known from spectroscopic studies. These forms are also found to be the most common conformations observed in the solid state; however, the clustering method highlights those structures that do not conform to the expected geometries. The study is supported by ab initio gas phase calculations on simple enone and enimine fragments.

Direct electron crystallographic determination of zeolite zonal structures.

The prospect for improving the success of ab initio zeolite structure investigations with electron diffraction data is evaluated. First of all, the quality of intensities obtained by precession electron diffraction at small hollow cone illumination angles is evaluated for seven representative materials: ITQ-1, ITQ-7, ITQ-29, ZSM-5, ZSM-10, mordenite, and MCM-68. It is clear that, for most examples, an appreciable fraction of a secondary scattering perturbation is removed by precession at small angles. In one case, ZSM-10, it can also be argued that precession diffraction produces a dramatically improved 'kinematical' data set. There seems to no real support for application of a Lorentz correction to these data and there is no reason to expect for any of these samples that a two-beam dynamical scattering relationship between structure factor amplitude and observed intensity should be valid. Removal of secondary scattering by the precession mode appears to facilitate ab initio structure analysis. Most zeolite structures investigated could be solved by maximum entropy and likelihood phasing via error-correcting codes when precession data were used. Examples include the projected structure of mordenite that could not be determined from selected area data alone. One anomaly is the case of ZSM-5, where the best structure determination in projection is made from selected area diffraction data. In a control study, the zonal structure of SSZ-48 could be determined from selected area diffraction data by either maximum entropy and likelihood or traditional direct methods. While the maximum entropy and likelihood approach enjoys some advantages over traditional direct methods (non-dependence on predicted phase invariant sums), some effort must be made to improve the figures of merit used to identify potential structure solutions.

Electron crystallography of zeolites--the MWW family as a test of direct 3D structure determination.

The efficacy of direct methods for solving the crystal structures of zeolites from electron diffraction data is evaluated for a series of related materials, i.e. MCM-22, MCM-49 and ITQ-1. First, it is established by tilting experiments that all materials share the same MWW framework. The calcined product of a delaminated MCM-22 precursor, ITQ-2, also shares this framework structure within the limited number of stacked unit cells. For all materials, the underlying space group is P6/mmm where a approximately 14.21, c approximately 24.94 A. Traditional direct methods are useful for determining the projected structure down the hexagonal axis but are not very effective for finding the three-dimensional structure. On the other hand, maximum-entropy and likelihood approaches are effective for determining either 2D projections or 3D frameworks. The major restriction to 3D determinations by direct methods is the limited goniometric tilt range of the electron microscope, hence the ;missing cone' of information. Potential maps from the most accurate phase sets are, therefore, observed as continuous density envelopes to the true structure. Some improvement is found when the Sayre equation predicts missing amplitudes and phases but it is clear that better specimen preparation methods are required to include projections containing the c( *) axis of the reciprocal lattice.