Multidimensionality of Delocalization Indices and Nucleus Independent Chemical Shifts in Polycyclic Aromatic Hydrocarbons STIJN FIAS, SOFIE VAN DAMME, PATRICK BULTINCK Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium Received 2 April 2007; Revised 21 May 2007; Accepted 22 May 2007 DOI 10.1002/jcc.20794 Published online 13 July 2007 in Wiley InterScience (www.interscience.wiley.com). Abstract: The aromaticity and local-aromaticity of a large set of polycyclic aromatic hydrocarbons (PAHs) is stud- ied using multicenter delocalization indices from generalized population analysis and the popular nucleus independent chemical shift (NICS) index. A method for the fast computation of the NICS values is introduced, using the so-called pseudo-π -method. A detailed examination is made of the multidimensional nature of aromaticity. The lack of a good correlation between the NICS and the multicenter delocalization indices is reported and the grounds discussed. It is shown through a thorough statistical analysis that the NICS values arise not only from local aromaticity of the benzenoid rings, but also from other circuits. It is shown that the NICS indices do not reveal the individual aromatic nature of a specific ring, contrary to the delocalization indices. © 2007 Wiley Periodicals, Inc. J Comput Chem 29: 358–366, 2008 Key words: aromaticity; local-aromaticity; generalized population analysis; NICS; chemical bond Introduction The so-called conceptual approach to chemistry has been extremely successful, and as a consequence many of these concepts play a dominant role in chemical reasoning. Examples are ubiquitous, and are likely to remain within chemical speech and reasoning for a long time to come. Paradoxically, many of these concepts do not have a very clear definition. As a consequence of this lack of a proper definition, concepts are used in a rather loose sense. Examples of such problematic concepts are the chemical bond, the definition and even the presence of atoms in molecules 1–4 and many more. Proba- bly one of the most dramatic examples is aromaticity. 5–7 Although every chemist has some appreciation and understanding of the con- cept, there is still no conclusive definition, and as a consequence different workers in the field have a slightly different understanding. This naturally hampers attempts to quantify such a concept. Nevertheless, there have already been numerous attempts to quantify molecular aromaticity and even local aromaticity. Local aromaticity in the context of the present paper refers to the degree of aromaticity of a fragment of a molecule, typically the degree of aromaticity of a specific benzenoid ring in a polyaromatic hydro- carbon. As there exists no conclusive definition of aromaticity, different indices have been introduced to measure aromaticity. 6, 7 These include geometry-based indices, 8 molecular similarity of a benzenoid ring in a molecule to isolated benzene, including the well-known Polansky index, 9, 10 electron occupation numbers and graph theory-based indices, 11 resonance energies, 5 aromatic stabi- lization energy, 12 and many more. Intuitively, on the basis of the above mentioned more or less common understanding of molecular aromaticity one would expect that all these indices correlate more or less well. Surprisingly, this is not the case. Within e.g., the group of aromatic molecules, different indices may very well attribute dif- ferent degrees of aromaticity to the same molecules. The fact that all indices are widely accepted as reflecting a degree of aromatic- ity and the fact that they do not correlate mutually, has resulted in the acceptance of aromaticity as a so-called multidimensional concept. 12–15 In the present paper, the correlation is examined between a mag- netic index of aromaticity and an index based on the extent of electron delocalization. It is well-known that aromatic compounds exhibit special magnetic properties. 5 The most prominent effect is Cartesian coordinates of the PAHs used in this study as well as their total SCF energy, charge and multiplicity are available as supplementary material, together with a graphical representation of their σ -framework This article contains supplementary material available via the Internet at http://www.interscience.wiley.com/jpages/0192-8651/suppmat Correspondence to: P. Bultinck; e-mail: patrick.bultinck@ugent.be Contract/grant sponsors: Ghent University; Institute for the Promotion of Innovation through Science and Technology (IWT PhD grant); The fund for Scientific Research, Flanders, Belgium © 2007 Wiley Periodicals, Inc.