RDF,

Boyarkine O V, Settle RDF and Rizzo T R 1995 Vibrational overtone spectra of jet-cooled CFgH by infrared laser assisted photofragment spectroscopy Ber. Bunsenges. Rhys. Chem. 99 504-13... 

The RDF code discussed in Chapter VIll, Sections 2 and 3 of the Handbook) also can be used to this end. 

D MoRSE desaiptor, radial distribution function (RDF code), WHIM descriptors, GETAWAY descriptors,... 

Steinhauer and Gasteiger [30] developed a new 3D descriptor based on the idea of radial distribution functions (RDFs), which is well known in physics and physico-chemistry in general and in X-ray diffraction in particular [31], The radial distribution function code (RDF code) is closely related to the 3D-MoRSE code. The RDF code is calculated by Eq. (25), where/is a scaling factor, N is the number of atoms in the molecule, p/ and pj are properties of the atoms i and/ B is a smoothing parameter, and Tij is the distance between the atoms i and j g(r) is usually calculated at a number of discrete points within defined intervals [32, 33]. 

Figure 8-5. Procedure of encoding a structure with an RDF code,...

The length or dimension of the RDF code is independent of the number of atoms and the size of a molecule, unambiguous regarding the three-dimensional arrangement of the atoms, and invariant against translation and rotation of the entire molecule. 

Both regioisomers and different conformations can be distinguished with the RDF code. (Figures 8-6 and 8-7). 

Figure 8-7, Comparison of tlie RDF code for aromatic compounds with different subslilulic patterns (hydrogen atoms are not considered).

The compounds were described by a set of 32 radial distribution function (RDF) code values [27] representing the 3D structure of a molecule and eight additional descriptors. The 3D coordinates were obtained using the 3D structure generator GORINA [33]. 

The radial distribution Function (RDF) of an ensemble of N atoms can be interpreted as the probability distribution to find an atom in a spherical volume of... 

By including characteristic atomic properties, A. of atoms i andj, the RDF code can be used in different tasks to fit the requirements of the information to be represented. The exponential term contains the distance r j between the atoms i andj and the smoothing parameter fl, which defines the probability distribution of the individual distances. The function g(r) was calculated at a number of discrete points with defined intervals. 

A combination of physicochemical, topological, and geometric information is used to encode the environment of a proton, The geometric information is based on (local) proton radial distribution function (RDF) descriptors and characterizes the 3D environment of the proton. Counterpropagation neural networks established the relationship between protons and their h NMR chemical shifts (for details of neural networks, see Section 9,5). Four different types of protons were... 

Geometric descriptors were based on local RDF descriptors (see Eq, (16 ) for the proton j. 

In Eq. (16 i denotes an atom up to lour non-rotatable bonds away from the proton and is the total number of those atoms. A bond is deRned as non-rotatable if it belongs to a ring, to a. T-system, or to an amide functional group q- is the partial atomic charge of the atom i, and is the 3D distance between the proton j and the atom i. Figure 10.2-5 shows an example of a proton RDF descriptor. 

Figure 10.2.5. Example of a local RDF descriptoT for proton 6 used in the prediction of chemical shifts (e = 20 A...

The strncturcs in the database arc encoded using the radial distribution function (RDF) as a descriptor (cf Section 8,4,4). 

When a structure is input for spectra simulation this structuie is also coded as an RDF descriptor, which allows an easy comparison with the structures in the database, Those 50 stnictures which are most similai to the input structui e are then selected together with their spectra. 

Figure 10.2-9. Application of a counterpropagation neural network as a look-up table for IR spectra sinnulation, The winning neuron which contains the RDF code in the upper layer of the network points to the simulated IR spectrum in the lower layer.

The right-hand side of the form gives the network map in the upper part and to its right the simulated IR spectrum is plotted, which can be downloaded as a JCAMP File (cf. Section 2,4.5, Section 4,2,4.2). By clicking on tbe neurons in the map one obtains the RDF code and the spectrum of the corresponding structure in the lower part of the form and compared with those of the winning neuron,... 

Several methods have been developed for establishing correlations between IR vibrational bands and substructure fragments. Counterpropagation neural networks were used to make predictions of the full spectra from RDF codes of the molecules. 

Municipal Solid Waste. In the eady 1990s, the need to dispose of municipal soHd waste (MSW) ia U.S. cities has created a biofuels industry because there is Htde or no other recourse (107). Landfills and garbage dumps are being phased out ia many communities. Combustion of MSW, ie, mass-bum systems, and RDF, ie, refuse-derived fuel, has become an estabhshed waste disposal—energy recovery industry. 

Fig. 1. Simplified schematic flow sheet for the production of a moderate RDF, using trommel separation.

Physical Properties. Physical properties of waste as fuels are defined in accordance with the specific materials under consideration. The greatest degree of definition exists for wood and related biofuels. The least degree of definition exists for MSW, related RDF products, and the broad array of ha2ardous wastes. Table 3 compares the physical property data of some representative combustible wastes with the traditional fossil fuel bituminous coal. The soHd organic wastes typically have specific gravities or bulk densities much lower than those associated with coal and lignite. 

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