Novel local (fragment-based) topological molecular descriptors for QSPR/QSAR and molecular design

Atom, Atom-Type, and Total Linear Indices of the “Molecular Pseudograph’s Atom Adjacency Matrix”: Application to QSPR/QSAR Studies of Organic Compounds

“…12 and 13) explain more than 98% and 99% of the variance of the experimental Bp values, respectively. Similar equations were reported by Estrada and Molina [11] and Kier and Hall [13] using spectral moment and E-state/ biomolecular encounter parameters as molecular descriptors, respectively. These equations are given bellow with their statistical parameters: where, n is a number of carbon atoms in the molecule, µ k (C-O) are the k th spectral moment for C-O bond [11] and H_H 2 , H_O, S(-OH) are values of biomolecular encounter parameters and E-state, respectively [13].…”

“…In order to illustrate the possibilities of the total and local (atom and atom-type) linear indices in the QSPR/QSAR studies, we have selected the following two series to be investigated: 1) boiling point of 28 alkyl-alcohols (see Table 2) firstly studied by Kier and Hall using E-state/biomolecular encounter parameters [13] and recently by Estrada and Molina [11] using the local spectral moments of the edge adjacency matrix, and 2) a set of 34 2-furylethylene derivatives previously studied using total and local spectral moments, 2D/3D connectivity indices (vertex and edge ones) and to quantum chemical descriptors to model their partition coefficient (log P), specific rate constant (log k) and antibacterial activity. These chemicals have different substituents at position 5 of the furan ring as well as at the β position of the exocyclic double bond [38,39].…”

“…The first data set that will be studied here is composed by 28 alkyl alcohols (14 are primary, 6 secondary and 8 tertiary) for which the boiling point (Bp) has been reported previously [11]. The best linear regression model obtained to describe the Bp of these compounds using total linear indices is given below: The values of experimental and calculated values of the Bp for the data set (both models) are given in Table 2 and the linear relationships between them are illustrated in Figures 1 and 2.…”

“…The so-called topological indices (TIs) are among the most useful molecular descriptors known nowadays [5][6][7][8][9][10]. TIs can be classified as "global" and "local", according to the way in which they characterize the molecular structure [11]. However, most TIs known today can be considered as global molecular descriptors.…”

“…One exception in this sense is the electrotopological state (E-state) index [12][13]. Other "global" molecular descriptors, such as the spectral moments of the edge adjacency matrix, can be obtained in local form [11]. The great success of the E-state and total and local spectral moments in QSPR/QSAR stimulated us to propose and validate here some novel local descriptors based on a topological characterization of the molecular structure.…”