Quantum topological molecular similarity. Part 5. Further development with an application to the toxicity of polychlorinated dibenzo-p-dioxins † (PCDDs) P. L. A. Popelier,* U. A. Chaudry and P. J. Smith Dept. of Chemistry, UMIST, 88 Sackville Street, Manchester, UK M60 1QD. E-mail: pla@umist.ac.uk Received (in Cambridge, UK) 8th April 2002, Accepted 30th April 2002 First published as an Advance Article on the web 23rd May 2002 A new method called quantum topological molecular similarity (QTMS), which was previously introduced, is further developed and applied. An excellent and statistically validated QSAR is obtained for the Hammett acidity constants of a set of 68 carboxylic acids including p- and m-benzoic acids, p-phenylacetic acid, 4-X-bicyclo[2.2.2]octane- 1-carboxylic acids and poly-substituted benzoic acids. This investigation shows that the previously imposed condition for a minimal and restricted common molecular skeleton can be relaxed. The O–H and the C–O bonds are recovered as the active center as expected. The first time use of atomic properties instead of bond properties leads to valid QSARs. Finally QTMS is applied to predict three different activities (pEC 50 ) of the ecologically relevant polychlorinated dibenzo-p-dioxins (PCDDs). We find that the active center is concentrated near the lateral C–Cl bonds. 1 Introduction Relating the properties or activity of molecules to their structure is an area of scientific interest dating back to the second half of the 19th century. 1 The potential rewards of finding such relationships at quantitative level with relevance to the agrochemical or pharmaceutical industry cannot be underestimated. More recently studies of toxicity and biodegrad- ability 2 have also benefited increasingly from quantitative structure–activity/property relationships (QSAR/QSPR) under growing environmental awareness. As QSAR techniques established themselves 3 after the systematisation of Hansch and Fujita, 4 molecular similarity was considered as a source of descriptors. 5–9 The number and variety of theoretical molecular descriptors ever applied in QSAR is overwhelming. They have recently been classified by Karelson 10 into the following categories: constitutional and geometric, topological, electrostatic- or charge distribution- related, quantum chemical- or MO-related, solvational, thermodynamic or “combined”. To the best of our knowledge the method we present here cannot be found in this extensive categorisation, but would reside in both the charge distribution and the quantum chemical categories. Over the last few years we have been interested in injecting quantum mechanical data into QSAR/QSPRs, in particular by the topological approach 11 according to the theory of “atoms in molecules” (AIM). 12–16 AIM properties have also been used to model aromaticity 17 and hydrogen bond donor capacity. 18 The dramatic enhancement of computational power now makes it feasible to investigate the predictive capability of topo- logical descriptors drawn from ab initio wavefunctions. The first successful use of AIM topological descriptors showed how they accurately predict Hammett σ values of p- and m-benzoic acids. 19 This led to the introduction of quantum topological molecular similarity (QTMS), which is a new method that we continue to explore and fine-tune. 20 The same paper 19 inspired the development of StruQT, 21 a 3D representation using quan- † The IUPAC name for dibenzo-p-dioxin is dibenzo[b,e][1,4]dioxin. tum chemical topology. Quantum chemical topology generates graphs endowed with a physical basis, which is usually less well-defined in classical chemical graph theory, revisited by Wiener, 22 developed by Randic, 23,24 Balaban 25 and Hosoya 26 and extended by Kier and Hall. 27,28 QTMS consists of three phases: generation of quantum data, extraction of topological descriptors, and model construction and interpretation. The essence of our method is reviewed in Section 3 and full details are explained elsewhere. 29 Since QTMS is a novel method its range of applicability is not clear at present, although ongoing work has produced a growing number of successful QSARs, subject to rigorous statistical treatment and with a minimum of chemometric manipulation. One of QTMS’s main features is its ability to localise the “active center”. More precisely QTMS is able to rank bonds according to their importance or influence in explaining the observed activity. It should be pointed out that the “active center” can be rather diffuse or contain unexpected bonds, which could turn out to be true “contaminations”. In the first part of this paper we demonstrate how the active center can be localised in an extensive set of carboxylic acids. As explained below we prove that QTMS can be used beyond a set of strictly congeneric molecules, with a restricted or minimal common skeleton. Then, having established the capacity of QTMS to point out the active center we predict it for a set of ecologically relevant molecules, namely polychlorinated dibenzo-p-dioxins (PCDD). As such, this study complements a previous one on medically relevant (E )-1-phenylbut-1-en- 3-ones. 30 In this contribution we introduce for the first time (topological) atomic properties into QTMS. 2 Quantum chemical topology This theory of AIM is the most elaborately researched and documented way of partitioning a quantum system (e.g. a molecule, van der Waals complex or crystal) into atomic constituents, based on the electron density ρ. AIM provides a consistent way of partitioning and hence localising chem- ical information, irrespective of the particular mathematical 2 PERKIN DOI: 10.1039/b203412c J. Chem. Soc., Perkin Trans. 2, 2002, 1231–1237 1231 This journal is © The Royal Society of Chemistry 2002