Atomic properties weight

ADRIANA.code Global physicochemical descriptors, size and shape descriptors, atom property-weighted 2D and 3D autocorrelations and RDF, surface property-weighted autocorrelations 1,244... 

Depending on the kind of weighting scheme, different covariance matrices and different principal axes (i.e., principal components t ) are obtained. For example, using atomic masses as the weighting scheme, the directions of the three principal axes are the directions of the —> principal inertia axes. Thus, the WHIM approach can be viewed as a generalized search for the principal axes with respect to a defined atomic property (—> weighting schemes). 

Equation 1-5 was written for a sample containing a single element upon which monochromatic x-rays are incident. In so far as x-ray absorption is an atomic property, the mass absorption coefficients for other samples are additive functions of the weight-fractions of the elements, free or combined, that are present that is,... 

Autocorrelation descriptors can also be calculated for 3D-spatial molecular geometry. In this case, the distribution of a molecular property can be a mathematical function /(x, y, z), x, y, and z being the spatial coordinates, defined either for each point of molecular space (i.e. a continuous property such as electronic density or molecular interaction energy) or only for points occupied by atoms (i.e. atomic properties). An example of 3D autocorrelation descriptors are the - spectral weighted invariant molecular descriptors defined by - SWM signals. 

The origin of the coordinates is the barycentre of the environment of the considered atom and the eigenvectors Vi, V2> Vs associated with the eigenvalues are unit vectors which define the three principal axes of this environment. The considered ith atom can be included or not in its environment. To each atom of the environment is assigned an atomic property pj (e.g. unitary property, atomic mass, atomic electronegativity, atomic van der Waals volume) and a weight wj which is a function of the distance of the /th environment atom from the / th atom. 

The weights w can be any chemical or topological atomic properties. Examples of chemical -> atomic properties are - van der Waals volume, atomic mass, - polarizability examples of -> local vertex invariants are - vertex degree, - path degree, - walk degree. 

The atomic properties constitute the weights used to characterize molecule atoms the most common atomic properties are atomic mass, - atomic charge, -> van der Waals radius, -> atomic polarizability, and hydrophobic atomic constants. Atomic properties can also be defined by the - local vertex invariants (LOVIs) derived from graph therory. 

Spectral weighted molecular signals are calculated within the framework on which the WHIM descriptors are defined. For each molecule, the ith atom score of each mth principal axis represents the atom projection along the axis, and the weight Wy of the atom is taken as the signal intensity in that position [Todeschini et al, 1999], The weights w are atomic properties, e.g. the weights used in the WHIM approach. 

When the adjacency between a pair of atoms i-j is represented by a bond weight (for example, -> bond order, force constant, ionic character, - dipole moment, -> bond distances or its inverse) and/or each atom is represented by some - atomic properties such as atomic numbers, several weighted-vertex adjacency matrices called atom connectivity matrices ACM can be defined [Spialter, 1963 Spialter, 1964a Spialter, 1964b] and their entries are ... 

All of the RDF functions presented already can be calculated including properties p of the individual atoms. These properties can be inserted in a preexponential term as a product leading to the property-weighted RDF descriptor, sometimes called RDF code ... 

This method transforms the frequency dimension into a property-weighted frequency dimension. The selection of atomic properties determines the characterization of the atoms within an RDF descriptor. Particularly, the classification of molecules by a Kohonen network is influenced by a decision for an atomic property. We can distinguish between static and dynamic atom properties. 

Includes atom properties as weight factors in the first dimension. 

Property-Weighted Descriptors are molecular descriptors that use a specific atom property to weight the individual function values. 

The weighted center is analogously defined, but each ith atom coordinate is weighted by W , which represents an atomic property... 

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