Received: 2 December 2009, Revised: 20 April 2010, Accepted: 21 April 2010, Published online in Wiley Online Library: 15 July 2010 The polarisability potential as a steric index y Cristopher Camacho a and Julio F. Mata-Segreda b * The acid-catalysed hydrolysis of carboxylic esters is the reference chemical reaction used for the empirical evaluation of steric effects. In this work, the polarisability potential (Hehre, et al., J. Am. Chem. Soc. 1986, 108, 1711–1712) is identified as quantum-mechanical size of substituent groups. Correlation is found between this quantity and reactivity features of the reference reaction. Copyright ß 2010 John Wiley & Sons, Ltd. Keywords: acid-catalysed ester hydrolysis; moment of inertia; polarisability potential; steric effect; Taft parameter; torsional barrier INTRODUCTION The rate and product outcome of a chemical reaction can be influenced by the ability of a substituent group to occupy space. This observation is the phenomenological description of the so-called steric effect. The intuitive view points to situations where atom contacts between reaction sites are made more difficult by the electrostatic repulsion of moieties close to each other, that do not otherwise participate in the molecular change. The steric parameter E s was defined by Taft, based on a suggestion by Christopher Ingold, on the basis of kinetic mea- surements for the acid-catalysed hydrolysis of carboxylic esters: [1] X  CO 2 R þ H 2 O ! H þ ROH þ X  CO 2 H E s ¼ log k X k Me   This quantity was shown to be approximately insensitive to polar effects, and thus assumed to account for steric effects only (e.g. the cases where X ¼ alkyl and monohaloalkyl groups). Extensive tables have been assembled from data collected for the reference chemical reaction, in different reaction conditions. [2] Dubois defined the Taft–Dubois steric parameter E s 0 in the same way as E s , but the kinetic data were measured using only one standard chemical reaction: the acid-catalysed esterification of X—CO 2 H at 40 8C in methanol. [3] E s and E s 0 are useful as long as no interaction exists between the X and CO 2 R moieties via a mechanism such as conjugation. This is the case of phenyl and conjugated alkenyl substituents. Proposals to correct E s para- meters have been devised, [2] but no attempt is made in this paper to review E s . Correlation between quantum mechanical size and steric effect has given fruitful insights. Large groups have a greater number of occupied molecular orbitals with large amplitudes in the space occupied by the moiety. This means that stronger repulsions may arise between the occupied molecular orbitals of reacting mole- cules or groups situated at close distances within the same molecule (or transition-state complex). Fujimoto et al. [4] studied the nature of the steric effect of alkyl groups by paired-interacting orbitals analysis. The results of these authors agreed with the known experimental observation that steric repulsion is not governed by the global size of substituents but determined principally by their local arrangement of bonds. Hollett et al. [5] explored a quantum mechanical definition of molecular size and shape, as formulated from the electronic second moment of the Hartree–Fock wave function. This quan- tum-mechanical quantity correlated well with E s 0 for halogens and first-row hydrides, but significant positive deviations were observed for groups such as N — — — C, MeO, MeS or CH 2 — —CH. The experimental log (k X /k H ) values for HO and MeO are 0.55 and for both HS and MeS are 1.07. This observation indicates that the acid-catalysed hydrolysis of esters is mainly affected by the oxygen and sulphur atoms, and not by the entire substituent as calculated from the electronic second moment. In a more recent study of Liu and collaborators, [6] the so-called steric energy was related to E s 0 . This quantum mechanical quantity represents a hypothetical state with all electrons packed into the lowest orbital and other effects entirely excluded. Thus, it is a measure of the intrinsic space occupied by an electronic system. The quality of correlation between steric energy and E s was better for this model than for the result of Hollett et al. [5] A conceptually simpler structural parameter that may correlate with steric feature is the polarisation potential of Hehre, Taft and co-workers, s a . [7] This quantity gives the energy of interaction between a particular CH 3 —X molecule and a positive charge located 3 A ˚ ´ away from the methyl group, along the C—X axis. The stabilisation of the system depends on how easily is electron density ‘projected’ towards the positive charge. This electro- n-density plasticity depends on the polarisability of X. There is a general relationship between polarisability and molar refraction. This latter quantity gives the actual volume (without free space) (wileyonlinelibrary.com) DOI 10.1002/poc.1742 Research Article * Correspondence to: J. F. Mata-Segreda, Laboratory of Bio-organic Chemistry, School of Chemistry, University of Costa Rica, 11501-2060, Costa Rica. E-mail: julio.mata@ucr.ac.cr a C. Camacho Department of Applied Chemistry and Institute of Molecular Science, National Chiao Tung University, Hsinchu 30010, Taiwan b J. F. Mata-Segreda Laboratory of Bio-organic Chemistry, School of Chemistry, University of Costa Rica, 11501-2060, Costa Rica y This article is published in Journal of Physical Organic Chemistry as a special issue on Tenth Latin American Conference on Physical Organic Chemistry, edited by Faruk Nome, Dept de Quimica, Universidade Federal de Santa Catarina, Campus Universitario – Trindade 88040-900, Florianopolis-SC, Brazil. J. Phys. Org. Chem. 2010, 23 955–959 Copyright ß 2010 John Wiley & Sons, Ltd. 955