Development of a new topological index for the prediction of normal boiling point temperatures of hydrocarbons: The Fi index Fernando C.G. Manso a, b, d , Hélio Scatena Júnior a , Roy E. Bruns c , Adley F. Rubira d , Edvani C. Muniz d, ⁎ a Universidade Federal do Rio Grande do Norte, Departamento de Química, UFRN, Natal-RN, Brazil b Universidade Tecnológica Federal do Paraná, UTFPR, Campo Mourão-PR, Brazil c Universidade Estadual de Campinas, Instituto de Química, Campinas-SP, Brazil d Grupo de Materiais Poliméricos e Compósitos – GMPC, Departamento de Química, Universidade Estadual de Maringá, UEM, 87020-900, Maringá-PR, Brazil abstract article info Article history: Received 3 January 2011 Received in revised form 27 October 2011 Accepted 28 October 2011 Available online 12 November 2011 Keywords: Topology Molecular descriptors Normal boiling temperature Topological indexes The goal of this paper is proposing a simple molecular descriptor, based on the molecular structures, for predicting the normal boiling temperature (B.T.) of hydrocarbons. To this end, the topological index Fi was developed and used to correlate the topology of alkanes, alkenes, alkynes and cycloalkanes possessing nor- mal or branched chains to their B.T. The robustness of predictor Fi was evaluated by comparison with the most cited predictors in the literature: Weiner, Hosoya and Randić. The quadratic model developed in this work predicts very well the B.T. of hydrocarbons. In the first moment, the developed model was tested for predicting the B.T. of alkanes. After, it was applied with success for predicting the B.T. of other compounds (alkenes, alkynes and cycloalkanes). The topological index Fi proved to be rather effective and produced small deviations, as compared to other topological indexes used for comparison. Based on the topological index Fi, other properties of interest can also be further explored and the concepts developed in this work can be easily adapted to other families of compounds, mainly in liquid phase. © 2011 Elsevier B.V. All rights reserved. 1. Introduction The use of molecular descriptors in quantitative structure–activity relationship analysis (QSAR) and in quantitative structure–property relationship (QSPR) targets the estimation of specific characteristics based on the structures of the compounds under study. Thus the main goal is simply to correlate, as accurately and unequivocally as possible, some important functionality to the molecular structure. To this end, topological indexes or molecular descriptors were proposed in QSPR studies based on Wiener's pioneering studies in the late 1940s [1]. Since then, some hundreds of molecular descriptors have been pro- posed for predicting the values of several physical properties, as well as the properties related to biological activities through QSAR (quantita- tive structure–activity relationships). Graph theory is used for building these topologies and new concepts are developed to transform such graphs, which are non-numerical mathematical objects, into related numbers that are topological indexes or molecular descriptors. Since the pioneering work of Harry Wiener [1] in the late 1940s, of Huruo Hosoya [2] and of Millan Randić [3] in the 1970s, and of many others, the study of quantitative correlations of molecular structure and properties has experienced many advances. Topological indexes have been successfully used for estimating several physical properties [4,5], including normal boiling temperature (B.T.) [6]. These indexes have been successfully used for estimating data related to biological activities as well. First, molecular descriptors (or topological indexes) that numeri- cally represent the structural characteristics of molecules are obtained by the use of graph theoretical concepts applied to molecular struc- ture. Next, these descriptors are correlated to the properties of interest for obtaining quantitative structure–property correlations. According to Mihalic and Trinajstic [7], a fundamental chemistry concept is that the structural characteristics of a molecule are responsi- ble for its properties. Thus, it is possible to link the molecular structure to the molecular properties, and to quantify them through structure– property correlations, the so-called quantitative structure–property relationships (QSPR) have been used. The term topological (from topos in Greek, meaning place) originates from topology, a branch of pure mathematics that deals only with the properties of a figure X that hold for every figure into which X can be transformed with a one-to-one correspondence, that is continuous in both directions [8]. A topological property remains constant when an object is sub- mitted to deformations without undergoing rupture. This is what happens if molecular structures are subjected to relaxation points of bonded atoms as a function of several vibrational movements. Thus, several molecular properties are, in fact, topological properties and, therefore, they are functions of their structures. Theoretical tools have played a fundamental role in the develop- ment of science over the years, and this is the function of molecular Journal of Molecular Liquids 165 (2012) 125–132 ⁎ Corresponding author. Tel.: + 55 44 3011 3664; fax: + 55 44 3011 4125. E-mail address: ecmuniz@uem.br (E.C. Muniz). 0167-7322/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2011.10.019 Contents lists available at SciVerse ScienceDirect Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq