ARTICLE OBC www.rsc.org/obc Quantum chemical topology (QCT) descriptors as substitutes for appropriate Hammett constants P. J. Smith and P. L. A. Popelier* School of Chemistry, Faraday Building, Sackville Site, University of Manchester, Manchester, M60 1QD, Great Britain. E-mail: pla@manchester.ac.uk; Fax: +44 (0)161 306 4559; Tel: +44 (0)161 306 4511 Received 18th May 2005, Accepted 26th July 2005 First published as an Advance Article on the web 17th August 2005 A technique called quantum topological molecular similarity (QTMS) was recently proposed [J. Chem. Inf. Comput. Sci., 2001, 41, 764] in order to construct a variety of medicinal, ecological and physical organic QSAR/QSPRs, based on modern ab initio wave functions of geometry optimised molecules, in combination with quantum chemical topology (QCT). The current abundance of computing power can be utilised to inject realistic descriptors into QSAR/QSPRs. In previous work [J. Chem. Soc., Perkin Trans. 2, 2002, 1231] it was proven that a set of Hammett constants (r p , r m , r I and r 0 p ) for a sizeable set of mono- and polysubstituted carboxylic acids can be replaced by QCT bond descriptors. Using QTMS and proper statistical validation we examined seven data sets in total. The first three sets (para-substituted phenols (r − ), substituted toluenes (r + ) and bromophenethylamines (r + )) corroborate that a wider class of Hammett constants can also be replaced by QCT descriptors. A fourth set (benzyl radicals) focuses on non-Hammett behaviour being superimposed on Hammett behaviour. QCT descriptors selectively correlate with Hammett behaviour. The QTMS analysis of the last three sets (toxicity of benzyl alcohols, chromatographic capacity factors of chalcones and herbicidal activity of 5-chloro-2,3-dicyanopyrazines) screens for false positives. This test is successfully passed in that QCT descriptors fail when lipophilicity/hydrophobicity is in charge. Hence, overall, the discriminatory capacity of QCT descriptors is established, in detecting Hammett behaviour and specifically replacing the Hammett constants by more modern and non-empirical descriptors. Introduction The Hammett substituent constants, which quantify the electron withdrawing or donating capabilities of a given substituent, have enjoyed enormous success as structural descriptors in quantitative structure–activity relationships (QSARs) and quan- titative structure–property relationships (QSPRs). 1 The physical chemical database of Hansch and co-workers contains over 8900 QSARs, of which 8875 are based on the r parameters. 2 It is apparent that electronic effects are of considerable importance in describing chemical reactions, and hence biological systems. Some time ago 3 we used for the first time quantum chemical descriptors defined by quantum chemical topology (QCT) 4–7 to set up a QSAR to predict r constants and, therefore, also the acidity of substituted benzoic acids. Other than being a generalisation of quantum mechanics to subspaces 8–10 QCT is widely appreciated as a theory that extracts chemical insight from modern wave functions. 11,12 The acronym QTMS (quantum topological molecular similarity) covered the initial develop- ment and intention of QCT to provide an economic alternative to Carbo-like indices. 13 It was proven that superposition of (complete molecular) electron densities is not necessary to set up a successful QSAR. Instead, as explained below, special points in 3D space sufficed. Although QCT descriptors could have been fed into molecular similarity indices, they immediately appeared in a “supervised” regression context. In other words, models 14 were constructed using partial least squares (PLS) for a variety of medicinal 15–17 and ecological 18–21 QSARs. The estimation of the pK a of carboxylic acids, anilines and phenols 22 and prediction of r p , r m , r I and r 0 p parameters of mono- 3 and polysubstituted benzoic acids, phenylacetic acids and bicyclo carboxylic acids 19 feature as examples of physical organic properties. The QTMS approach inspired work in other groups (e.g.ref. 23–24). A strong and important feature of QTMS is that it is able to localise a part in the molecule where the chemical change associated with the observed activity actually happens. For example, the O–H bond is highlighted as the active center in the deprotonation of carboxylic acids if their acidity is studied. QTMS typically uses so-called bond critical point (BCP) properties, as in this study, but (integrated) atomic properties can also feature. BCPs are 3D saddle points in the electron density, located by computation 25 and appearing at the boundary between two QCT atoms. Certain functions, such as the electron density, are evaluated at each BCP, thereby characterising the bond that the BCP represents. A BCP can be represented by an arbitrarily high number of properties, which serve as vector components locating the BCP as a “quantum chemical fingerprint” in BCP-space. 3 In view of the ubiquity of the Hammett parameters in formulating QSARs, coupled with the promising results ob- tained so far in capturing substituent effects, we aimed at extending the range of r constants investigated by QTMS. In addition, the range of systems is hereby also increased, beyond the domain of carboxylic acid datasets. We examined four data sets: para-substituted phenols (r − ), bromophenethylamines (r + ), substituted toluenes (r + ), and benzyl radicals in order to investigate non-Hammett behaviour. We will show that excellent statistics are obtained for the first three sets, and that the active centers highlighted make sense. The last set is a “false positive” test, adopted to see whether QTMS still performs well when conventional “polar effect” Hammett constants fail. We will show that QTMS passes this test and hence operates successfully for the right reasons. Methods The full details of how QTMS operates have been published before 13 and repeated in the applications mentioned in the Introduction. In the interest of making this paper self-contained it is useful to summarise the procedure here. Geometry-optimised wave functions were generated at HF/6- 31G*//HF/6-31G* level using the program GAUSSIAN98. 26 In previous QTMS work we varied the level of theory between DOI: 10.1039/b507024d This journal is © The Royal Society of Chemistry 2005 Org. Biomol. Chem. , 2005, 3 , 3399–3407 3399