Statistical analysis of structure data

III. STATISTICAL ANALYSIS OF STRUCTURAL DATA RETRIEVED FROM THE CSD... 

More than 700 individual Si—N bond lengths were known at the time Sheldrick15 wrote his review (1989). Although he did not make any remark on the source of the data, it seems that most were available from X-ray crystal structure analysis. At the time of writing the present review (July 1996) more than 3000 individual experimental Si—N bond lengths were obtained from the CSD bank for crystal structure data. It is not possible to present a comprehensive list in this review and therefore we provide a statistical analysis of the data and mention a few typical and exceptional compounds together with their Si—N structural features. 

The scope of computational chemistry can be inferred from the methodologies it encompasses. Some of the more common tools include computer graphics, molecular modeling, quantum chemistry, molecular mechanics (MM), statistical analysis of structure-property relationships, and data management (informatics). As with any dynamic field of research, computational... 

To any casual reader who scans a textbook on statistical methods, there appears to be a myriad of techniques that can be used in data analysis. Which ones are likely to prove useful in the chemical context The answer is that the choice of technique is dictated entirely by the type of data we wish to analyse and the type of problem we wish to solve. A wide variety of statistical methods has already been applied to the analysis of structural data and has generated results of some significance. In this chapter, we discuss these methods under three broad headings ... 

In this respect, the psychometric paradigm , which occupies a dominant position since the late seventies, turns out to be a valuable resource. Basically, the methodology of all psychometric studies is structured in five steps the design of questionnaires, the selection of the population sample, the administration of questionnaires, the statistical analysis of the data, and the interpretation ofthe results. Each of these steps implies lund ental presuppositions, which have drastic consequences on the interpretation of the results. It is therefore absolutely necessary for the risk manager to be aware of these presuppositions. Likewise, several criticisms can be addressed to psychometric smdies. These also have to be highlighted in order to avoid a misuse of the results. 

As a result of Napping, each subject provides two vectors of coordinates of dimension 7x1 each (one for the X-axis, one for the F-axis), where I denotes the number of stimuli to be positioned on the rectangle. Hence, the final data set to be analysed, denoted X, is obtained by merging the N pairs of vectors of coordinates, where N denotes the number of subjects. In other words, X can be seen as a data set structured into N groups of two variables each. Typically, the statistical analysis of such data set X should take into account the natural partition on the variables. 

Y(Ti,Nb)2 06 . However, as he mentioned, the classification cannot be used directly to ascertain the chemical and structural relations of the members, because it was derived from a statistical analysis of published data in the absence of structural or morphological data. The minerals cited above usually occur in the metamict state, and the crystallographic data of these minerals are often ambiguous. 

More recently, new quantitative structure-property relationships for Tg have been developed (1) they are based on the statistical analysis of experimental data for 320 linear (uncross-linked) polymers collected from many different sources, containing a vast variety of compositions and structural features. The Tg of the atactic form was used, whenever available, for polymers manifesting different tac-ticities. The Tg values of a subset of the polymers listed in this extensive tabulation are reproduced (with some minor revisions) in Table 1. (It is important to caution the reader here that these data were assembled from a wide variety of sources. Many different experimental techniques were used in obtaining these data.) The resulting relationship for Tg has the form of a weighted sum of structural terms mainly taking the effects of chain stiffness into account plus a term proportional to the solubility parameter S which takes the effects of cohesive interchain interactions in an explicit manner, as shown in equation (1) ... 

Details of applicable methods of statistical analysis of experimental data about thermophysical properties of gases and liquids are given in Refs. [0.4, 0.5, 0.29, 0.32, 1.3, 1.4, 3.2, 3.3, and 4.3]. The derivations of experimentally substantiated equations of state of the form (0.7) and (0.8) for Freons-21, -22, and -23 are given and discussed in the following chapters of the present handbook. Short commentary is given on references in which equations of state of nonconventional structure are derived for freons of the methane series under consideration. The specific searching techniques for the coefficients are also given there. 

The data analysis module of ELECTRAS is twofold. One part was designed for general statistical data analysis of numerical data. The second part offers a module For analyzing chemical data. The difference between the two modules is that the module for mere statistics applies the stati.stical methods or rieural networks directly to the input data while the module for chemical data analysis also contains methods for the calculation ol descriptors for chemical structures (cl. Chapter 8) Descriptors, and thus structure codes, are calculated for the input structures and then the statistical methods and neural networks can be applied to the codes. 

Analysis and prediction of side-chain conformation have long been predicated on statistical analysis of data from protein structures. Early rotamer libraries [91-93] ignored backbone conformation and instead gave the proportions of side-chain rotamers for each of the 18 amino acids with side-chain dihedral degrees of freedom. In recent years, it has become possible to take account of the effect of the backbone conformation on the distribution of side-chain rotamers [28,94-96]. McGregor et al. [94] and Schrauber et al. [97] produced rotamer libraries based on secondary structure. Dunbrack and Karplus [95] instead examined the variation in rotamer distributions as a function of the backbone dihedrals ( ) and V /, later providing conformational analysis to justify this choice [96]. Dunbrack and Cohen [28] extended the analysis of protein side-chain conformation by using Bayesian statistics to derive the full backbone-dependent rotamer libraries at all... 

---