Radial distribution function code

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]. 

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. 

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Figure 10.1-5. Predicted versus experimental solubility values of 496 compounds in the test set by a back-propagation neural network with 32 radial distribution function codes and eight additional descriptors.

These descriptors are based on the distance distribution in the - geometrical representation of a molecule and constitute a radial distribution function code (RDF code) that shows certain characteristics in common with the - 3D-MoRSE code. 

Formally, the radial distribution function of an ensemble of A atoms can be interpreted as the probability distribution of finding an atom in a spherical volume of radius R. The general form of the radial distribution function code (RDF code) is represented by ... 

D autocorrelation, 3D MoRSE code, and radial distribution function code... 

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

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]. 

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]. 

The potential parameters for the water molecule were empirically fitted to reproduce the experimental dipole moment, 0-H bond length and H-O-H angle of the water monomer and the structure of the water dimer and infra-red data. Molecular dynamics simulations were then used to calculate the self-diffusion coefficient, radial distribution functions (RDFs) and energy of evaporation of liquid water. The computer code DL POLY 2.6 code (Forester and Smith 1995) was employed. We simulated a box containing 256 water molecules at a temperature of 300 K where the conditions were initially set at the experimental density of p= 1.0 g/cm and run with an NPT ensemble. We chose a mass for the oxygen shell of 0.2 a.u., which is small compared to the mass of the hydrogen atom of 1.0 a.u. However, due to the small shell mass we needed to run the MD simulation with the small timestep of 0.2 fs in order to keep the system stable. With this timestep we obtained data at constant pressure and temperature for a period of 100 picoseconds. 

And of course statistic accumulation parts of the code have to be changed accordingly. Energy, pair radial distribution function (PRDF), or diffusion coefficient should be calculated separately for molecules in each of the... 

FIGURE 2.1 Plots of simulated overall radial distribution function (g r)) for systems with different compositions. Two insets represent g(r) for r 0.75 and 1 for better visualization. Different curves are color coded and explained in the plot, represents the mole fraction of the first component (k = 2) in the binary mixture. 

Figure 2-10. Radial Distribution Functions of O ions around in the PrV04 crystal,xerogel and glass. From Rocca (1998). Note the asymmetry at high R, well evident in the two latter cases. The curve was reconstructed from the experimental EXAFS data, using the EDA code (Kuzmin, 1997).

Since the transient subchannel analysis code does not have the functions prepared in typical system analysis codes, several parameters are taken from the calculation results by the single channel safety analyses performed in Sect. 6.7. These parameters are the flow rate, temperature and pressure at the inlet of the hot fuel assembly, and the relative power. The radial and axial power distributions are assumed not to change with time. This is reasonable because the reactivity is not locally changed at the flow decreasing events. 

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