On the Reliability of Global and Local Electrophilicity Descriptors Ram Kinkar Roy* Department of Chemistry, Birla Institute of Technology and Science (BITS), Pilani 333031, Rajasthan, India ReceiVed: December 28, 2003; In Final Form: March 30, 2004 The global electrophilicity index w (as defined by Parr et al. J. Am. Chem. Soc. 1999, 121, 1992) and local “philicity” index, w k R (as defined by Chattaraj et al. J. Phys. Chem. A 2003, 107, 4973) of some carbonyl compounds are evaluated on the basis of Mulliken population analysis (MPA) and Hirshfeld population analysis (HPA) schemes. It is observed that the local electrophilicity indices (i.e., w k + ), extracted from both HPA and MPA based charge, produce reliable intermolecular electrophilicity trends except in one case each. However, the reliability is lost in some cases when w is used. It is also shown both through numerical demonstrations and analytical proof that for generating intramolecular reactivity trends “philicity” index does not provide any extra reliability over local softness or Fukui function values. “Relative electrophilicity” and “relative nucleophilicity”, as defined by Roy et al. (J. Phys. Chem. A 1998, 102, 3746), generate the most reliable intramolecular reactivity (i.e., site selectivity) sequences. 1. Introduction In the last two decades, several global and local reactivity descriptors, based on density functional theory (DFT), have been proposed. Prominent among those are global hardness and softness, 1 local hardness, 2,3 local softness 3 and Fukui function, 4 and the corresponding condensed forms, 5 “relative electrophi- licity” and “relative nucleophilicity”, 6 “global electrophilicity”, 7 and most recently the “philicity” index. 8 Although the global reactivity descriptors are supposed to provide intermolecular reactivity trends, the local counterpart generates the intramo- lecular reactivity sequence or site selectivity of an individual chemical system. In a recent article, Parr et al. 7 have proposed a new definition of global electrophilicity, which may be regarded as a quantita- tive formulation of the model of Maynard et al. 9 A successful application of this newly defined global reactivity descriptor was made by Domingo et al., 10 who could characterize quantitatively the global electrophilicity power of common diene/dienophile pairs used in Diels-Alder reactions. In a separate interesting study, 11 the same group has extended the concept of global electrophilicity index to define the local electrophilicity index and successfully explained the regio- selectivity in Diels-Alder reactions. Solvent effects on this electrophilicity index were studied by Pe ´rez et al. 12 In this context, it should also be mentioned that intermolecular reactiv- ity trends in carbonyl compounds and organic acids was explained successfully by Krishnamurty and Pal 13 using “group softness” as the reactivity parameters. Chandrakumar and Pal 14,15 have proposed a model, based on the local hard and soft acid- base (HSAB) 16 principle, which explains the preferable site of attack considering both single site 14 and multiple site 15 interac- tions. For a detailed descritption and for the most authentic information on the development of all aspects of the hard and soft acid-base concept, the recent review by Geerlings et al. 17 is highly recommended. Based on this global electrophilicity index as defined by Parr et al., 7 very recently Chattaraj et al. 8 proposed a more broad and very general local reactivity descriptor. This is named as the “philicity” index, which encompass all types of reactions (i.e., electrophilic, nucleophilic, and radical reactions). This local philicity is promised to be a more powerful quantity than global reactivity indicators because the former contains the information of the later in addition to the site selectivity of a molecule toward electrophilic, nucleophilic, and radical attacks. Also, according to the argument of the authors, “because the global electrophi- liciy of two different molecules are different, best sites of two different molecules for a given reaction can be explained only in terms of the ‘philicity’ and not Fukui function”. In the present study, an investigation is carried out on the relative reliability of the global electrophilicity index as proposed by Parr et al. 7 and the philicity index as proposed by Chattaraj et al. 8 in predicting intermolecular reactivity sequence. Also to generate intramolecular reactivity sequence (i.e., site selectivity), a comparative study of the “philicity” index with “relative electrophilicity” and “relative nucleophilicity”, as proposed by Roy et al., 6 is performed. The article is structured as follows. A brief theoretical background of the global electrophilicity indicator, local philicity index, “relative electrophilicity”, and “relative nucleophilicity” is presented in different subsections of section 2. The compu- tational techniques and methodologies adopted and the details of the systems chosen are elaborated in section 3. In section 4, the results are presented and the generated trends in terms of the global and local reactivity descriptors are analyzed. An effort is made to explain the observed trends from the analytical expressions of the reactivity descriptors. Finally, in the conclud- ing section (i.e., section 5), the net outcome of the work is summarized. Potential areas of future development are also pointed out. 2. Reactivity Descriptors A. Global Electrophilicity Indicators. Prompted by a qualitative suggestion by Maynard et al., 9 a new reactivity * To whom correspondence should be addressed. E-mail: rkoy@bits- pilani.ac.in. 4934 J. Phys. Chem. A 2004, 108, 4934-4939 10.1021/jp038025i CCC: $27.50 © 2004 American Chemical Society Published on Web 05/11/2004