D Descriptors for Spectrum-Like Representation

3-D desCTiptors for spectrum-like representation of a molecular structure, defined by 3-D coordinates of its atoms, are obtained by a projection of all atomic centers of a molecule onto a sphere in the center of which is the molecule [97,98], The projection ray from the central point of the sphere defines a pattern of points on the sphere, and each point represents a particular atom. Then, the center of each atom is represented by a beU-shaped function, the intensity of which is determined by the distance between the coordinate origin and a particular atom. The Mulliken charge of the particular atom is an additional parameter incorporated into this function. As the beU-shaped function of atoms has been taken Lorentzian curve with the form  

If only atom positions are considered, Oj are set to 1, and the representation contains only information about 3-D coordinates of all atomic centers. The total intensity for the entire molecule is obtained by adding intensities belonging to individual atoms  

Uniqueness (unique and distinct code for different structures). 

Uniformity, that is, the number, type, and domain of variables are the same for all structures regardless of the number of atoms they have. 

Reversibility, which means that by proper initial orientation of the structures, atomic coordinates can be obtained back from the code. 

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Descriptors used in the present study are calculated from the information about the connections between the atoms, from atomic 3-D coordinates, and from information about atomic electronic properties. In this work were used (i) graph theoretical (topological descriptors), (ii) geometric descriptors, (iii) electrostatic descriptors, (iv) 3-D descriptors for spectrum-like representation, and (v) density of states spectra. We elaborate on topological descriptors adopted in this particular work in view of a multitude of topological indices available and, in this way. 

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