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Topological Model on the Inductive Effect in Alkyl Halides Using Local Quantum Similarity and Reactivity Descriptors in the Density Functional Theory

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Topological Model on the Inductive Effect in Alkyl Halides Using Local Quantum Similarity and Reactivity Descriptors in the Density Functional Theory Hindawi Publishing Corporation Journal of Quantum Chemistry Volume 2014, Article ID 850163, 12 pages http://dx.doi.org/10.1155/2014/850163 Research Article Topological Model on the Inductive Effect in Alkyl Halides Using Local Quantum Similarity and Reactivity Descriptors in the Density Functional Theory Alejandro Morales-Bayuelo1,2 and Ricardo Vivas-Reyes1 1 Grupo de Qu´ımica Cuantica´ y Teorica,´ Universidad de Cartagena, Programa de Qu´ımica, Facultad de Ciencias Exactas y Naturales, Cartagena de Indias, Colombia 2 Departamento de Ciencias Qu´ımicas, Universidad Nacional Andres Bello, Republica 275, Santiago, Chile Correspondence should be addressed to Alejandro Morales-Bayuelo; [email protected] and Ricardo Vivas-Reyes; [email protected] Received 19 September 2013; Revised 16 December 2013; Accepted 16 December 2013; Published 19 February 2014 Academic Editor: Daniel Glossman-Mitnik Copyright © 2014 A. Morales-Bayuelo and R. Vivas-Reyes. 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. We present a topological analysis to the inductive effect through steric and electrostatic scales of quantitative convergence. Using the molecular similarity field based in the local guantum similarity (LQS) with the Topo-Geometrical Superposition Algorithm (TGSA) alignment method and the chemical reactivity in the density function theory (DFT) context, all calculations were carried out with Amsterdam Density Functional (ADF) code, using the gradient generalized approximation (GGA) and local exchange correlations PW91, in order to characterize the electronic effect by atomic size in the halogens group using a standard Slater-type- orbital basis set. In addition, in this study we introduced news molecular bonding relationships in the inductive effect and the nature of the polar character in the C–H bond taking into account the global and local reactivity descriptors such as chemical potential, hardness, electrophilicity, and Fukui functions, respectively. These descriptors are used to find new alternative considerations on the inductive effect, unlike to the binding energy and dipole moment performed in the traditional organic chemical. 1. Introduction Quantum Similarity Indexes (MQSI) based on the electron density proposed by Carbo-Dorca´ and coworkers [5–9]. The inductive effect is one of the most important electronic Several concepts and theories have been proposed in the effects in chemistry1 [ ]. According to the International Union literature in order to explain the molecular chemical bond of Pure and Applied Chemistry (IUPAC) the inductive effect [10–19]. Nowadays, the most used theories are the molecular is defined as transmission effect of charge on a chain of orbital theory [20, 21] and the valence bond method [22, atoms via electrostatic induction [2]. The inductive effect is 23]. In this paper was used the concept of chemical bond experimentally observable via molecular polarization of polar as minimization of equilibrium interactions determined by covalent bonds produced by electrostatic induction, due to the bond distances at the experimental level. We propose to differences in electronegativity between the atoms involved relate these experimental distances with the dis(similarity) [3]. In this contribution, our attention will be focused in the electrostatic and steric, using quantum similarity descriptors quantification of the molecular polarization from the point such as overlap and Coulomb indexes, with their Euclidean of view of the molecular bond in alkyl halides molecules distances. such as 3HC–X, (X = F, Cl, Br) taken as example. Using an On the other hand, we present in this contribution a atomic approach of molecular quantum similarity performed theoretical investigation in order to relate the inductive effect by Cioslowski and Nanayakkara [4]andtheMolecular in these alkyl halides and analyze its dependence on the bond 2 Journal of Quantum Chemistry distance with respect to the variation of electronegativity of And is another alternative of quantification of the quantum substituent atoms (–F, –Cl, –Br). This approach could shed similarity. somelightontosomemolecularaspectsthatcancontribute to the knowledge behind interactions of these molecules. 2.2. Local Similarity Indexes Another reason for carrying out this study is to relate the dis(similarity) between the inductive effect and the nature of 2.2.1. The Hirshfeld Approach. The Hirshfeld approach [32– chemical bond with differences of electronegativity between 38]. This approach is based on partitioning the electron ( ) ( ) atoms. In addition, this approach suggests a new perspective density 1 of a molecule in contributions A 1 .Inthis to the treating of the chemical bond with the inductive effect, study, the Hirshfeld approach is used to express the global takingintoaccountthatthesearchfornewinterpretations similarity index (4)tolocallevel. is a field of great interest in organic physical chemistry; These contributions are proportional to the weight (1) in addition to the inductive effect also can be used to of the electron density of the isolated molecule in the call determine the stability of molecule with respect to their promolecular density [39]. The “promolecular density” is charge distribution [24–26]. obtained as Prom ( )=∑0 ( ). A 1 1 (5) 2. Theory and Computational Details ( ) 2.1. Similarity Indexes. Reviews about concepts and applica- The contribution of atom A A 1 in the electron density ( ) tionsinquantumsimilaritycanbefoundelsewhere(see,for 1 is example, [5–9, 27, 28]); only general definitions will be given ( )= ( )( ). A 1 A 1 1 (6) at this point. Quantum similarity provides a quantitative measure of the resemblance between two quantum objects A The weight ((1))isobtainedas and B. 0 ( )= A , Carbo´ and coworkers introduced the similarity indexes A 1 0 (7) ∑ (1) [5, 27]; they defined the quantum similarity measure AB ( ) between molecules A and B with electron density A 1 and 0 ( ) where A 1 is the electron density of the isolated atom A (2), based on the idea of minimizing the expression for the B [40–46]. This idea has been applied in this study to CH3–F Euclidean distance: takenasmoleculeAandCH3–X, (X = Cl or Br) designating 2 2 2 as B. The atomic contribution of carbon atom (C) in the = ∫ (1)− (2) = ∫ ( (1)) 1 AB A B A molecule A is given by 2 ( )= ( ) ( ), + ∫ ( ( )) −2∫ ( ) ( ) (1) C,A 1 C 1 A 1 (8) B 2 2 A 1 B 2 1 2 with = + −2 , AA BB AB 0 ( ) = C,A 1 . , 0 (9) where AB is the Euclidean distance, involving the overlap C A ∑ ( ) 1 integral between the electron density AB of the molecule A and B and AA and BB are the self-similarity of molecules A For the atomic contribution of carbon atom (C) in the and B [27]. molecule B is obtained as The most common index is the generalized quantum , (2)= (2) (2), (10) similarity by the cosine, introduced by Carboetal.[´ 28]; this C B C B index can be expressed mathematically as with 0 ∫ ( ) ( ) (2) A 1 B 2 1 2 C,B = . , = , (11) AB (2) C B ∑ 0 ( ) √∫( ( ))2 ∫( ( ))2 2 A 1 1 B 2 2 so that we can express the numerator in the Carbo´ index Introducing ()elementsintheoperator(Ω)wecanwrite AB in (4)as (Ω) = AB , Local,C AB √ (Ω) (Ω) (3) A,B AA BB = ∫ ( , ) ( ) ( ) where ( AB)istheCarbo´ index; this index is mathematically C,A+B 1 2 A 1 B 2 1 2 definedintheinterval(0,1],where1istheself-similarityand calculates only the measures of “shape similarity,” as an other 0 0 , (1)+ , (2) alternative is the of Hodgkim-Richards index [29, 30]. This = ∫ ( C A C B ) ( ) ( ) , ∑ 0 ( )+∑ 0 ( ) A 1 B 2 1 2 index appears naturally when using the arithmetic mean and ,A 1 ,B 2 canbedefinedmathematicallyas (12) 2 (Ω) = AB . where it is possible to get atomic contributions and consider- AB (Ω) + (Ω) (4) AA BB ations of similarity. Journal of Quantum Chemistry 3 2.2.2. Description of Molecular Bond Proposed. To study (higher occupied molecular orbital) HOMO and (lowest the effects by varying electronegativity by substituents, we unoccupied molecular orbital) LUMO as propose a particular characterization of the chemical bond + which can be considered complementary to the Hirshfeld ≈ . (18) partition, considering that the inductive effect is dependent 2 on the interatomic bond length [2]. From (18), one can obtain quantitative expression for the Weproposetostudythemolecularbondbasedonthe chemical hardness ()[48, 55–57], and it is understood as physical concepts of bond length, defined as the minimum the opposition of the system to distort the electron cloud and length (equilibrium) of the interactions according to the mathematically can be written as chemical bond model proposed by Burrau [24], these equi- librium distances are represented by ( eq)andweproposeto − ≈ . (19) multiply the equilibrium lengths ( eq) with the (MQSI), so 2 that we can express: Ontheotherhand,wehavetheglobalelectrophilicity() = ( ), eq AB eq (13) introduced by Parr et al. [58], which is a measure of the stabilization energy of the system when it is saturated by = lim (A, B) electrons from the external environment and represented AB | ↔ | →1 eq A B mathematically as (14) Coulomb similarity index (CSI) → { }, 2 Overlap similarity index (OSI) = . 2 (20) where AB is (4). For the Euclidean distance, we have The Fukui function () was one of the descriptors used in this work and defined as = ( ), eq AB eq () () = ( ) = ( )
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