Structure determination by direct methods

Duax, W L., Hauptman, H., Weeks, C. M., and Norton, D. A. Valinomycin crystal structure determination by direct methods.Science 176, 911-914 (1972). 

The determination of a molecular structure from X-ray diffraction data is of critical importance to modem chemical and biological sciences. For small molecules, the structure is normally determined by direct methods. The X-ray diffraction pattern resulting from the interaction of X-rays with the electron clouds of different elements gives a pattern from which the elements present and their connectivity may be deduced. The expected diffraction pattern calculated for an apparent structure is then compared with the observed data to refine the result. Refinement factors (usually expressed as Rw) of 1-3% are common in modem small molecule structure determinations. 

How is it possible to derive phase information when only structure amplitudes have been measured An answer can be found in what are called direct methods of structure determination. By these methods the crys-tallographer estimates the relative phase angles directly from the values of F hkl) (the experimental data). An electron-density map is calculated with the phases so derived, and the atomic arrangement is searched for in the map that results. This is why the method is titled direct. Other methods of relative phase determination rely on the computation of phase angles after the atoms in a trial structure have been found, and therefore they may be considered indirect methods. Thus, the argument that phase information is lost in the diffraction process is not totally correct. The phase problem therefore lies in finding methods for extracting the correct phase information from the experimental data. 

A comparative n.m.r. study of dihydrogalanthamine and dihydroepigalanthamine and their acetyl derivatives has been reported. The crystal structure of ( )-norgalanthamine (6), incorrectly named ( )-galanthamine, but corrected in Chemical Abstracts, has been determined by direct methods. 

Other Sulphur-containing Compounds.—The crystal structure of rubidium hydroxylamine-NN-disulphonate, Rb5 [0N(S03)2]2H, 3H20, has been determined by direct methods and refined.264 The structure contains two formula units in the space group Pi, and the two [0N(S03)2]2H 5 anions... 

Electron diffraction is the other of the two important sources of gas-phase structural data. As discussed by Hedberg (this volume), the intensity of electrons scattered by molecules is modulated by the interatomic distances, both bonded and nonbonded. Since interatomic distances enter explicitly into electron diffraction determinations, the method is in some ways more direct than spectroscopy. Moments of inertia are functions of Cartesian coordinates of individual atoms rather than distances between atoms. On the other hand, electron diffraction is much more susceptible to experimental error than spectroscopic techniques.15 Problems with structural determinations by spectroscopic methods often stem almost entirely from model error, whereas in electron diffraction both experimental and model error are important. Experimental and model error in electron diffraction are discussed elsewhere in this volume by Hedberg, and we shall confine ourselves here to definitions of the various structural parameters that arise in electron diffraction studies and the relationships among them and spectroscopic quantities. 

SD (6), colorless prisms, mp 232-234°, C27H3605, [cc]d-34.2° (MeOH), was obtained as a minor component. Although the structure of SD was suggested to be similar to that of SDB by spectral comparison of both compounds, its l3C-NMR spectrum showed the presence of an oxygenated quarternary sp3 carbon instead of ketonic carbon observed in that of SDB. The final structure of SD was determined to be 6 by X-ray crystallography on a single crystal obtained by crystallization from acetone. The crystal structure solved by direct method indicates that the carbon skeleton of SD is aphidicolan-type. 

The chemical and physical structure of the adsorbent surface controls the energy of adsorption of an individual compound and hence determines its A value i.e., adsorbent selectivity is determined by adsorbent surface structure. Unfortunately, the structure of an adsorbent surface can seldom be determined by direct methods. In most cases we are forced to infer the nature of the surface from the gross physical properties and composition of the adsorbent and from its performance in chromatographic separation. Section 6-1 summarizes and discusses those adsorbent properties which we of major interest in this connection. Section 6-2 provides a general treatment of sample A values as a function of adsorbent surface area, surface activity, and extent of water deactivation. Section 6-3 discusses the standardization of the adsorbent with respect to sample A values. 

P. T. Beurskens et al.. DIRDIF, a Computer Program System for Crystal Structure Determination by Patterson Methods and Direct Methods applied to Difference Structure Factors. 1992. 

Once the positions of some atoms have been determined, by whatever method, the phase of every reflection can be calculated. Of course, all this hard work is usually done by powerful software packages, some of them automated to the extent that space-group determination, structure solution by direct methods and atom assignment is all done in one go. The user is provided with a three-dimensional picture, which often is close to the final structure. 

Direct methods constitute the third important approach to the phase problem. Certain physical properties of crystals (such as the fact that the electron density is always positive) place restrictions on the magnitudes and phases of the structure factors. For centrosymmetric crystals, the structure factors are real, and the phase problem is therefore one of sign determination. Sayre s equation for intense reflections is an example of sign determination by direct methods ... 

Stmcture determination of unknown crystals by electron diffraction was performed by several research groups, on Al-Fe alloys by Gjonnes et al. (1998), on metal-cluster compounds by Weirich et al. (2000) and on zeolites by Wagner et al. (1999). Selected area electron diffraction or electron diffraction collected by a precession technique were used and the structure factor phases were deduced by direct methods, Patterson method or from convergent beam electron diffraction. 

The structure of (/i2-H)(H)Os3(CO)n is, unfortunately, subject to some disorder and it was not possible to locate the hydride ligands by direct methods. However, their locations could be determined unambiguously from the geometry of the cluster the derived ordered structure is illustrated in Figure 4. The position... 

Part II deals, in six chapters, with the principles underlying the progressive stages in the elucidation of internal structure. Chapters VI and VII deal with the principles of structure determination by trial Chapter VIII with the use of physical properties (such as habit, cleavage, and optical, magnetic, pyro- and piezo-electric properties) as auxiliary evidence in structure determination. In Chapter IX are to be found several examples of the derivation of complete structures. Chapter X gives an introductory account of the use of direct and semi-direct methods based on the calculation of electron density distributions and vector distributions from X-ray diffraction data. 

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