title: Physico-Chemical and Structural Interpretation of Discrete Derivative Indices on N-Tuples Atoms.
abstract: This report examines the interpretation of the Graph Derivative Indices (GDIs) from three different perspectives (i.e., in structural, steric and electronic terms). It is found that the individual vertex frequencies may be expressed in terms of the geometrical and electronic reactivity of the atoms and bonds, respectively. On the other hand, it is demonstrated that the GDIs are sensitive to progressive structural modifications in terms of: size, ramifications, electronic richness, conjugation effects and molecular symmetry. Moreover, it is observed that the GDIs quantify the interaction capacity among molecules and codify information on the activation entropy. A structure property relationship study reveals that there exists a direct correspondence between the individual frequencies of atoms and Hückel's Free Valence, as well as between the atomic GDIs and the chemical shift in NMR, which collectively validates the theory that these indices codify steric and electronic information of the atoms in a molecule. Taking in consideration the regularity and coherence found in experiments performed with the GDIs, it is possible to say that GDIs possess plausible interpretation in structural and physicochemical terms.
authors.affiliation: Computer-Aided Molecular "Biosilico" Discovery and Bioinformatic Research International Network (CAMD-BIR IN), Cumbay&#225;-Tumbaco, Quito 170184, Ecuador. oscarms@uclv.edu.cu.|Department of Chemical Science, Faculty of Chemistry-Pharmacy, Universidad Central "Martha Abreu" de Las Villas, Santa Clara 54830, Villa Clara, Cuba. oscarms@uclv.edu.cu.
authors.forename: Oscar
authors.initials: O
authors.lastname: Martínez-Santiago
authors.affiliation: Computer-Aided Molecular "Biosilico" Discovery and Bioinformatic Research International Network (CAMD-BIR IN), Cumbay&#225;-Tumbaco, Quito 170184, Ecuador. ymarrero@usfq.edu.ec.|Universidad San Francisco de Quito (USFQ), Grupo de Medicina Molecular y Traslacional (MeM&amp;T), Colegio de Ciencias de la Salud (COCSA), Escuela de Medicina, Edificio de Especialidades M&#233;dicas, Hospital de los Valles, Av. Interoce&#225;nica Km 12 &#189;-Cumbay&#225;, Quito 170157, Ecuador. ymarrero@usfq.edu.ec.|Universidad San Francisco de Quito (USFQ), Instituto de Simulaci&#243;n Computacional (ISC-USFQ), Diego de Robles y v&#237;a Interoce&#225;nica, Quito 170157, Ecuador. ymarrero@usfq.edu.ec.|Grupo de Investigaci&#243;n Microbiolog&#237;a y Ambiente (GIMA), Programa de Bacteriolog&#237;a, Facultad Ciencias de la Salud, Universidad de San Buenaventura, Calle Real de Ternera, Cartagena de Indias, Bol&#237;var 130010, Colombia. ymarrero@usfq.edu.ec.
authors.forename: Yovani
authors.initials: Y
authors.lastname: Marrero-Ponce
authors.affiliation: Computer-Aided Molecular "Biosilico" Discovery and Bioinformatic Research International Network (CAMD-BIR IN), Cumbay&#225;-Tumbaco, Quito 170184, Ecuador. sjbarigye@yahoo.com.|Departamento de Qu&#237;mica, Universidade Federal de Lavras (UFLA), Caixa Postal 3037, Lavras 37200-000, MG, Brazil. sjbarigye@yahoo.com.
authors.forename: Stephen J
authors.initials: SJ
authors.lastname: Barigye
authors.affiliation: School of Medicine and Pharmacy, Vietnam National University, Hanoi (VNU) 144 Xuan Thuy, Cau Giay, Hanoi 100000, Vietnam. ltthuong1017@gmail.com.
authors.forename: Huong
authors.initials: H
authors.lastname: Le Thi Thu
authors.affiliation: Universidad San Francisco de Quito (USFQ), Instituto de Simulaci&#243;n Computacional (ISC-USFQ), Diego de Robles y v&#237;a Interoce&#225;nica, Quito 170157, Ecuador. jtorres@usfq.edu.ec.|Universidad San Francisco de Quito (USFQ), Grupo de Qu&#237;mica Computacional y Te&#243;rica (QCT-USFQ), Departamento de Ingenier&#237;a Qu&#237;mica, Diego de Robles y V&#237;a Interoce&#225;nica, Quito 170157, Ecuador. jtorres@usfq.edu.ec.
authors.forename: F Javier
authors.initials: FJ
authors.lastname: Torres
authors.affiliation: Universidad San Francisco de Quito (USFQ), Instituto de Simulaci&#243;n Computacional (ISC-USFQ), Diego de Robles y v&#237;a Interoce&#225;nica, Quito 170157, Ecuador. czambrano@usfq.edu.ec.|Universidad San Francisco de Quito (USFQ), Grupo de Qu&#237;mica Computacional y Te&#243;rica (QCT-USFQ), Departamento de Ingenier&#237;a Qu&#237;mica, Diego de Robles y V&#237;a Interoce&#225;nica, Quito 170157, Ecuador. czambrano@usfq.edu.ec.
authors.forename: Cesar H
authors.initials: CH
authors.lastname: Zambrano
authors.affiliation: Grupo de Investigaci&#243;n en Estudios Qu&#237;micos y Biol&#243;gicos, Facultad de Ciencias B&#225;sicas, Universidad Tecnol&#243;gica de Bol&#237;var (UTB), Parque Industrial y Tecnol&#243;gico Carlos V&#233;lez Pombo Km 1 v&#237;a Turbaco, Cartagena de Indias, Bol&#237;var 130010, Colombia. jmuniz@unitecnologica.edu.co.
authors.forename: Jorge L
authors.initials: JL
authors.lastname: Muñiz Olite
authors.affiliation: Instituto de Investigaciones Biom&#233;dicas (IIB), Universidad de Las Am&#233;ricas (UDLA), Quito 170513, Ecuador. maykel.cruz@udla.edu.ec.
authors.forename: Maykel
authors.initials: M
authors.lastname: Cruz-Monteagudo
authors.affiliation: Grupo de Qu&#237;mica Cu&#225;ntica y Te&#243;rica, Facultad de Ciencias, Universidad de Cartagena, Cartagena de Indias, Bol&#237;var 130001, Colombia. rvivasr@unicartagena.edu.co.|Grupo CipTec, Fundaci&#243;n Universitaria Tecnol&#243;gico de Comfenalco, Facultad de Ingenier&#237;as, Programa de Ingenier&#237;a de Procesos, Cartagena de Indias, Bol&#237;var 130001, Colombia. rvivasr@unicartagena.edu.co.
authors.forename: Ricardo
authors.initials: R
authors.lastname: Vivas-Reyes
authors.affiliation: Computer-Aided Molecular "Biosilico" Discovery and Bioinformatic Research International Network (CAMD-BIR IN), Cumbay&#225;-Tumbaco, Quito 170184, Ecuador. dirfabrica@eppc.cfg.minag.cu.|Department of Chemical Science, Faculty of Chemistry-Pharmacy, Universidad Central "Martha Abreu" de Las Villas, Santa Clara 54830, Villa Clara, Cuba. dirfabrica@eppc.cfg.minag.cu.
authors.forename: Liliana
authors.initials: L
authors.lastname: Vázquez Infante
authors.affiliation: Computer-Aided Molecular "Biosilico" Discovery and Bioinformatic Research International Network (CAMD-BIR IN), Cumbay&#225;-Tumbaco, Quito 170184, Ecuador. jmuniz@unitecnologica.edu.co.
authors.forename: Luis M
authors.initials: LM
authors.lastname: Artiles Martínez
mesh_terms: D000465:Algorithms; D003196:Computer Graphics; D015195:Drug Design; D019277:Entropy; D004364:Pharmaceutical Preparations / Q000737:chemistry*
chemical_list: D004364:Pharmaceutical Preparations
keywords: 17O-RMN; GDIs; activation entropy; derivative indices; discrete derivative; free valence; reactivity; resonance energy; structural interpretation