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Int. J. Mol. Sci. 2016, 17(6), 812; doi:10.3390/ijms17060812

Physico-Chemical and Structural Interpretation of Discrete Derivative Indices on N-Tuples Atoms

Computer-Aided Molecular “Biosilico” Discovery and Bioinformatic Research International Network (CAMD-BIR IN), Cumbayá-Tumbaco, Quito 170184, Ecuador
Department of Chemical Science, Faculty of Chemistry-Pharmacy, Universidad Central “Martha Abreu” de Las Villas, Santa Clara 54830, Villa Clara, Cuba
Universidad San Francisco de Quito (USFQ), Grupo de Medicina Molecular y Traslacional (MeM&T), Colegio de Ciencias de la Salud (COCSA), Escuela de Medicina, Edificio de Especialidades Médicas, Hospital de los Valles, Av. Interoceánica Km 12 ½—Cumbayá, Quito 170157, Ecuador
Universidad San Francisco de Quito (USFQ), Instituto de Simulación Computacional (ISC-USFQ), Diego de Robles y vía Interoceánica, Quito 170157, Ecuador
Grupo de Investigación Microbiología y Ambiente (GIMA), Programa de Bacteriología, Facultad Ciencias de la Salud, Universidad de San Buenaventura, Calle Real de Ternera, Cartagena de Indias, Bolívar 130010, Colombia
Departamento de Química, Universidade Federal de Lavras (UFLA), Caixa Postal 3037, Lavras 37200-000, MG, Brazil
School of Medicine and Pharmacy, Vietnam National University, Hanoi (VNU) 144 Xuan Thuy, Cau Giay, Hanoi 100000, Vietnam
Universidad San Francisco de Quito (USFQ), Grupo de Química Computacional y Teórica (QCT-USFQ), Departamento de Ingeniería Química, Diego de Robles y Vía Interoceánica, Quito 170157, Ecuador
Grupo de Investigación en Estudios Químicos y Biológicos, Facultad de Ciencias Básicas, Universidad Tecnológica de Bolívar (UTB), Parque Industrial y Tecnológico Carlos Vélez Pombo Km 1 vía Turbaco, Cartagena de Indias, Bolívar 130010, Colombia
Instituto de Investigaciones Biomédicas (IIB), Universidad de Las Américas (UDLA), Quito 170513, Ecuador
Grupo de Química Cuántica y Teórica, Facultad de Ciencias, Universidad de Cartagena, Cartagena de Indias, Bolívar 130001, Colombia
Grupo CipTec, Fundación Universitaria Tecnológico de Comfenalco, Facultad de Ingenierías, Programa de Ingeniería de Procesos, Cartagena de Indias, Bolívar 130001, Colombia
Author to whom correspondence should be addressed.
Academic Editor: Humberto González-Díaz
Received: 31 January 2016 / Revised: 27 April 2016 / Accepted: 4 May 2016 / Published: 27 May 2016
View Full-Text   |   Download PDF [15608 KB, uploaded 27 May 2016]   |  


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. View Full-Text
Keywords: discrete derivative; GDIs; derivative indices; structural interpretation; reactivity; activation entropy; 17O-RMN; free valence; resonance energy discrete derivative; GDIs; derivative indices; structural interpretation; reactivity; activation entropy; 17O-RMN; free valence; resonance energy

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Martínez-Santiago, O.; Marrero-Ponce, Y.; Barigye, S.J.; Le Thi Thu, H.; Torres, F.J.; Zambrano, C.H.; Muñiz Olite, J.L.; Cruz-Monteagudo, M.; Vivas-Reyes, R.; Vázquez Infante, L.; Artiles Martínez, L.M. Physico-Chemical and Structural Interpretation of Discrete Derivative Indices on N-Tuples Atoms. Int. J. Mol. Sci. 2016, 17, 812.

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