Molecular descriptors radial

Beside the descriptors, further attempts have been made to encode the 3D molecular structures with functions. Such are 3D-MoRSE code [54] spectrum-like representations [55] and radial distribution functions [56]. Also, experimentally determined infrared, mass, or NMR spectra can be taken to represent a molecule [57]. Another example is comparative molecular field analysis (CoMFA) where the molecular 3D structures are optimized together with the receptor [58]. This approach is often applied in drug design or in specific toxicology studies where the receptor is known. The field of molecular descriptors and molecular representations has exploded in the recent decades. Over 200 programs for calculating descriptors and different QSAR applications are listed on web page [59]. 

A slight modification of the general form of an RDF leads to a molecular descriptor, the radial distribution function (RDF) code, which includes atom properties that address characteristic atom features in the molecular environment. Fields of application for RDF codes are the simulation of infrared spectra and deriving molecular structure information from infrared spectra [40,41]. 

Let us evaluate the different properties and applications of a molecular descriptor while keeping the aforementioned requirements for descriptors in mind. We will focus on a particular descriptor type the radial distribution function (RDF). RDF descriptors grew out of the research area of structure-spectrum correlations but are far more than simple alternative representations of molecules. The flexibility of these functions from a mathematical point of view allows applying them in several other contexts. This chapter will give a theoretical overview of RDF descriptors as well as their application for the characterization of molecules, in particular for similarity and diversity tasks. 

Li, Q., Chen, X. and Hu, Z. (2004) Quantitative structure-property relationship studies for estimating boiling points of alcohols using calculated molecular descriptors with radial basis function neural networks. Chemom. Intell. Lab. Syst., 72, 93-100. 

D MoRSE codes are valuable for conserving molecular features, but it is not possible to interpret them directly. This drawback leads to investigations of related types of descriptors. Steinhauer and Gasteiger picked up the idea of radial distribution... 

RDF descriptors (or Radial Distribution Function descriptors) were proposed based on a radial distribution function different from that commonly used to calculate molecular transforms I s) [Hemmer, Steinhauer et al, 1999 Selzer, Gasteiger et al, 2000]. The radial distribution function selected here is that quite often used for interpretation of the diffraction patterns obtained in powder X-ray diffraction experiments. 

For any pD-model p 3), we can develop descriptors of variable dimensionality d. Examples of zero-dimensional descriptors are single numbers such as the radius of gyrationio (used for OD, ID, and 2D models) or the molecular volume 1 (used for 2D models). One-dimensional descriptors such as radial distribution functions or knot polynomials are used in OD and ID models, respectively. Two-dimensional descriptors include distance maps and Rama-chandran torsional-angle maps for some OD and ID models. Similarly, molecular graphs (2D descriptors) can be associated with ID models (contour lines), 2D models (molecular surfaces), or 3D models (e.g., the entire electron density function). Shape descriptors of higher dimensionality can also be constructed. 

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