Direct methods crystal structures

The utility of considering, when applicable, crystal structures as based on complex modules that occur in varied structures, has been demonstrated on describing inorganic materials in several series. In particular, the method has been applied to modelling unknown modular crystal structures. The method is useful when a direct solution of the crystal structure is impracticable, e.g. because suitable single crystals are not available and because information from the powder diffraction pattern is... 

Approach (ii), on the other hand, relies on the possibility of determining the crystal structure directly from powder diffraction experiments. Powder data treatment and ab initio structure determination methods are evolving rapidly. 

H. A. Hauptman (Buffalo, NY) and J. Karle (Washington, DC) outstanding achievements in the development of direct methods for the determination of crystal structures. 

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. 

Multiple isomorphous replacement allows the ab initio determination of the phases for a new protein structure. Diffraction data are collected for crystals soaked with different heavy atoms. The scattering from these atoms dominates the diffraction pattern, and a direct calculation of the relative position of the heavy atoms is possible by a direct method known as the Patterson synthesis. If a number of heavy atom derivatives are available, and... 

With the chemical structure of PbTX-1 finally known and coordinates for the molecule available from the dimethyl acetal structure, we wanted to return to the natural product crystal structure. From the similarities in unit cells, we assumed that the structures were nearly isomorphous. Structures that are isomorphous are crystallographically similar in all respects, except where they differ chemically. The difference between the derivative structure in space group C2 and the natural product structure in P2. (a subgroup of C2) was that the C-centering translational symmetry was obeyed by most, but not all atoms in the natural product crystal. We proceeded from the beginning with direct methods, using the known orientation of the PbTX-1 dimethyl acetal skeleton (assuming isomorphism) to estimate phase... 

X-ray structural analysis. Suitable crystals of compound 14 were obtained from toluene/ether solutions. X-ray data were collected on a STOE-IPDS diffractometer using graphite monochromated Mo-Ka radiation. The structure was solved by direct methods (SHELXS-86)16 and refined by full-matrix-least-squares techniques against F2 (SHELXL-93).17 Crystal dimensions 0.3 0.2 0.1 mm, yellow-orange prisms, 3612 reflections measured, 3612 were independent of symmetry and 1624 were observed (I > 2ct(7)), R1 = 0.048, wR2 (all data) = 0.151, 295 parameters. 

Crystal data and parameters of the data collection (at -173°, 50 < 20 < 450) are shown in Table I. A data set collected on a parallelopiped of dimensions 0.09 x 0.18 x 0.55 mm yielded the molecular structure with little difficulty using direct methods and Fourier techniques. Full matrix refinement using isotropic thermal parameters converged to R = 0.I7. Attempts to use anisotropic thermal parameters, both with and without an absorption correction, yielded non-positive-definite thermal parameters for over half of the atoms and the residual remained at ca. 0.15. 

The three dimensional structure was obtained by means of single crystal X-ray diffraction. CuKa radiation, a graphite monochromator, and a photomultiplier tube were used to collect 1825 total reflections on an automated diffractometer. Of these, 1162 were used for the analysis. Figure 2 shows a computer generated drawing of halcinonide. The position of the chlorine atom was not clear from the Patterson map, but the direct method program "MULTAN" gave its position. 

The relatively recent development27 of the direct methods of crystal structure analysis has produced a great increase in the number of crystal structures reported in the literature, particularly with regard to the possible hydrogen bonds (also for biological molecules). Hence, the classical spectroscopic data on hydrogen bonding in solution are backed up by X-ray diffraction analysis data. 

Broadly speaking, chiral space groups may be divided into two classes those that contain polar axes, for example, the commonly observed space groups P2, and C2 and those that do not, such as P2,2,2,. Crystal structures belonging to the latter class contain polar directions, but these do not coincide with the crystal axes. We shall focus on chiral crystals containing polar axes, although the method can in principle be applied to all chiral crystals. 

---