Direct phase determination methods

Currently, Patterson and direct methods are the most frequently employed classical structure solution approaches. The direct phase determination methods are especially successful in solving structures from single crystal data, but their use in powder diffraction increases progressively as the quality of powder data improves, better deconvolution techniques are developed and more precise individual structure factors become available. 

It is worth noting that practically all non-traditional methods for solving crystal structures have been initially developed for both powder and single crystal diffraction data to manage intrinsic incompleteness or poor quality that cannot be improved experimentally. Despite a variety of structure solution approaches, traditional direct phase determination methods appear to be the most common and successful when powder diffraction data are adequate. Patterson methods also work quite well but they require the presence of a heavy atom and, perhaps, more extensive crystallographic expertise. The non-traditional methods are generally employed when other techniques fail and their use is somewhat restricted by both the complexity and limited availability of computer codes. 

Patterson synthesis by itself cannot solve even moderately large molecular structures (five or six equally heavy atoms) unless concrete structure information already exists so that the vector space can be systematically searched for a presumed structure or substructure. A search of this kind might be done with a computer, perhaps by the method of pattern-seeking functions, or the convolution molecule method [57]. [75]. These techniques, however, are not so often used today, having been supplanted by direct phase-determination methods (Section 15.2.2.2), which make it possible to reach the goal quickly on the basis of relatively little prior knowledge [76], Patterson synthesis may return to prominence when used to identify sets of starting phases (Section 15.2.2.2). 

The fundamental reason for this situation is that the relationships in direct phase-determination methods are nothing more than probability relations. If these can be turned into true equations, single-crystal X-ray structure analyses would become a routine analytical procedure. H. Haupt-... 

Hendrickson WA, Smith JL, Sheriff S. Direct phase determination based on anomalous scattering. Methods Enzymol 1985 115 44-55. 

Direct methods, direct phase determination A method of deriving relative phases of diffracted beams by consideration of relationships among the Miller indices and among the structure factor amplitudes of the stronger Bragg reflections. These relationships come from the conditions that the structure is composed of atoms and that the electron-density map must be positive or zero everywhere. Only certain values for the phases are consistent with these conditions. 

J. Karle and H. Hauptman, A theory of phase determination for the four types of non-centrosymmetric space groups, Acta Cryst. 9, 635 (1956). Jerome Karle, US crystallographer, and Herbert A. Hauptman, US mathematician, laid a foundation towards the development of modem direct phase determination techniques. They won 1985 Nobel Prize in Chemistry for their outstanding achievements in the development of direct methods for the determination of crystal stmctures - http //www.nobel.se/ chemistry/laureates/1985/. 

However, due to the cheap computer power available, evaluation of single-crystal neutron diffraction data (at the level of atomic coordinates in the unit cell and the Debye-Waller factors associated with them) is a routine task nowadays. The trick is to apply direct methods of phase determination - methods that depend on the many mutual relationships (inequalities and probabilities) between structure factors and their phases. The simplest such constraint is that scattering power in solids is concentrated on atoms, which are well-defined regions by their size and shape. (For pioneering applications, see the works published by Karle and Karle (1966), Bernal and Watkins (1972) and Jonsson and Hamilton (1972).) Similar conditions cannot be cast into exact mathematical equations, but computer algorithms can easily cope with them. 

Fluorescence Lifetimes. Fluorescence lifetimes were determined by the phase shift method, utilizing a previously-described phase fluorimeter. The emission from an argon laser was frequency doubled to provide a 257 nm band for excitation. Fluorescence lifetimes of anisole and polymer 1 in dichloro-methane solution were 2.2 and 1.4 nsec, respectively. Fluorescence lifetimes of polymer films decreased monotonically with increasing DHB concentration from 1.8 (0) to 0.7 nsec (9.2 x 10 3 MDHB). Since fluorescence lifetimes (in contrast to fluorescence intensities) are unaffected by absorption effects of the stabilizer, these results provide direct evidence in support of the intensity measurements for RET from polymer to stabilizer. 

If the Patterson method cannot be applied because the structure has no or too many heavy atoms, it is possible to use another approach for phase determination, the so-called direct methods. By the term direct methods is meant that class of methods which exploits relationships among the structure factors in order to go directly from the observed magnitudes E to the needed phases < ) (Herbert A. Hauptman, Nobel lecture, 9. Dec., 1985). The direct method approach for solving the phase problem uses probability... 

A number of methods have been described for determination of tetracycline (chlortetracycline, tetracycline, and oxytetracycline) residues in tissues of food-producing animals (53-62), fish (63), eggs (64), and honey (65,66). Most of these methods use reversed-phase HPLC for determination. However, one uses TLC with UV densitometry ( ) and one uses GLC ( ), and one uses a direct mass spectrometric method CAD MIKE spectrometry (collisionally activated decomposition mass-analyzed ion kinetic spectrometry) for oxytetracycline in milk and meat (62). Several use solid-phase extraction in the cleanup procedure using XAD-2 resin (56,58) or Cj g cartridges... 

When it is assumed that the phases of the structure factors are unknown, the analysis proceeds well, after fixing the origin of the cubic unit cell by choosing the sign of the strong (111) reflection. This corresponds to a direct structure determination without any prior knowledge of the structure, and supports the value of the maximum entropy method in the early stages of structure determination. 

Therefore, direct Group I methods for the determination of enantiomeric purity are generally preferred. A most important merit of the direct methods is the fact that the chiral auxiliary compounds, e.g., the chromatographic stationary phase, need not be enantiomerically pure. 

The present chapter deals first with all the preliminary steps which must be taken to obtain suitable data for structure determination (whether by direct or indirect methods)—the measurement of the intensities of diffracted beams, and the application of the corrections necessary to isolate the factors due solely to the crystal structure from those associated with camera conditions. It then goes on to deal with the effect of atomic arrangement on the intensities of diffracted beams, the procedure in deducing the general arrangement, and finally the methods of determining actual atomic coordinates by trial. It follows from what has been said that, as soon as atomic positions have been found to a sufficient degree of approximation to settle the phases of the diffracted beams, then the direct method can be used this, in fact, is the normal procedure in the determination of costal structures. 

The sample homogenization with an MeCN THF mixture was used for the simultaneous determination of SMM, miloxacin, and oxolinic acid. The supernatant was filtered and injected directly into the ion-pair chromatographic system using a shielded hydrophobic phase. This method did not require time-consuming and complex extraction procedures moreover, the use of a restricted-access-material column prevented both column clogging and peak broadening throughout the analysis. On the other hand, no preconcentration of the sample affected the LOD... 

Solid-Solution Models. Compared with the liquid phase, very few direct experimental determinations of the thermochemical properties of compound-semiconductor solid solutions have been reported. Rather, procedures for calculating phase diagrams have relied on two methods for estimating solid-solution model parameters. The first method uses semiem-pirical relationships to describe the enthalpy of mixing on the basis of the known physical properties of the binary compounds (202,203). This approach does not provide an estimate for the excess entropy of mixing and thus... 

TLC is the preferred separation method because of its high separation efficiency, rapidity, and large variety of detection possibilities. Usually 0.5 mm thick silica-gel-G-plates are used, activated at 120°C for 30 min. in a supersaturated atmosphere. Well-known of poly techniques such as multiple separation in opposite or parallel direction allow the selectivities to be further increased. The selection of an appropriate mobile phases determines the efficiency of separation. Advantage is taken of specific interactions and also of reactivity with the stabilizers under investigation. 

The most powerful direct means of phase determination are based on the heavy-atom and isomorphous-substitution methods (Robertson, 1936 Robertson and Woodward, 1937, 1940). The method based on anomalous dispersion (Okaya and Pepinsky, 1961) is also now becoming more important. These methods are of most value, and indeed are the only possible methods, when the chemical structure is unknown and it is impossible to set up a trial model with any certainty of success. 

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