Hauptmann method

Structure determination has greatly advanced with the invention of new ways to use x-ray crystallography, mainly new mathematical methods that permit the interpretation of the observed patterns of diffraction of x-rays by a crystal, translating it into the molecular structures in the crystal. A Nobel Prize in 1985 to Herbert Hauptmann and Jerome Karle recognized such an advance. 

The best approach to date to automatic structure solution is the direct method (DM), introduced by Hauptmann,154 Jerome Karle,155 and Isabella Karle,156 and made possible by efficient computer programs, such as MULTAN (Main,15 Germain,158 and Woolfson59) and SHELX... 

Direct methods replaced trial and error and other methods of deducing model structures in the middle of the 20th century. In these techniques, statistical relationships between the amplitudes and phases of the strong reflections were established, and the mathematical methodology between these quantities was worked out, particularly by Hauptmann and Karle, in the 1940 s and 1950 s. (The Nobel Prize was awarded to these scientists in 1985 for these studies.) A number of algorithms, which exploited the growing power of electronic computers, used this mathematical framework to derive structures directly from the experimental data set of position, intensity and hkl index. The use of these programs allows the structures of molecular compounds with up to 100 or so atoms to be... 

Other than the measurement of damage, there does not exist a separate method to validate the probability of occurrence (Tittes, 1986 Hauptmanns et al., 1987 Kaplan and Garrik, 1993). The term probability of occurrence is used for such events of damage where information or even only presumptions about the relative frequency of the event have been given, but where the precise time remains uncertain. Risk statements always describe probabilities,... 

Hauptmann, H. The Direct Methods of X-Ray Crystallography. Sdence 23>% 178-183 (1986). [A discussion of improvements in methods of doing the calculations involved in determining protein strucmre based on a Nobel Prize address. This article should be read in connection with the one by Karle, and it provides an interesting contrast with the articles by Perutz, both of which describe early milestones in protein crystallography.]... 

A great deal of effort bas been expended by Hauptmann s laboratory in the study of the oxidation of a,/3-bishydrazones (6.1-3) with metal oxides, but the yields are only fair (Eq. 9). " Comparable results have been obtained by El Khadem and his collaborators in the similar oxidation of osazone arylhydrazones. Recently, Alexandrou has reported the important observation that bissemicarbazones react well with lead tetraacetate to produce ureido-l,2,3-triazoles (6.1-4), which can be hydrolyzed to the corresponding amines (Eq. 10). Although the yields are still not very high, the method should receive further attention. 

One or more stable conformations can also be assumed for cyclic peptides which can adopt more or less rigid structures stabilized by hydrogen or other bridges or, strongly, by complexing various metal ions. As an example of many published structures [41], there is the Li-complex of the antitoxic mushroom peptide antamanide (see p. 215), a structure which was determined in 1973 by Isabella L. Karle [42] using the direct method of Jerome Karle (Nobel Prize 1987, shared with J.A. Hauptmann). 

The lack of data to support claims for failure rates is an issue which is widely investigated by data uncertainty analyses. For example, Hauptmanns, 2008 compares the use of reliability data stemming from different sources on probabilistic safety calculations, and tends to prove that results do not differ substantially. Wang, 2004 discusses and identifies the inputs that may lead to SIL estimation changes. Propagation of error, Monte Carlo, and Bayesian methods (Guerin, 2003) are quite common. Fuzzy set theory is also often used to handle data uncertainties, especially into fault tree analyses (Tanaka, 1983, Singer, 1990). Other approaches are based on evidence, possibihty, and interval analyses (Helton, 2004). 

The direct method is a mathematical process in which diffrent phase and amplitudes of the molecular transform are related to the contribution of individual atoms. This method is based on statistical procedures used to extract the phase information. The missing phase information is believed to be present in the statistical intensity distribution. One of the most well-known statistical proposals was offered by Karle and Hauptmann (1986). These authors assumed that the Fourier transform of the intensity represents the probability of finding interatomic distances in a molecule and that the transform is nonnegative. 

Such methods are called direct methods. The one that was most commonly used was based on probabilities. Sayre in 1952, and earUo" in an equivalent fashion Karl and Hauptmann, showed that undo" cratain circumstances the following relation holds ... 

Sayre s relations work better if the structure factors are of similar values. However, normally values vary widely. Therefore, a new function with a smaller variation in values must be established for use in direct methods the so-called normalized stmcture factor was proposed by Karl and Hauptmann, thus ... 

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