Trends of the Bonding Effect on the Performance of DFT Methods in Electric Properties Calculations: A Pattern Recognition and Metric Space Approach on Some XY 2 (X 5 O, S and Y 5 H, O, F, S, Cl) Molecules CHRISTOS CHRISTODOULEAS, 1 DEMETRIOS XENIDES, 1,2 THEODORE E. SIMOS 1 1 Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, GR-22 100 Tripolis, Greece 2 Division of Theoretical Chemistry, Department of General, Inorganic, and Theoretical Chemistry, University of Innsbruck, A-6020, Innrain 52a, Austria Received 8 September 2008; Revised 31 March 2009; Accepted 14 April 2009 DOI 10.1002/jcc.21328 Published online 4 June 2009 in Wiley InterScience (www.interscience.wiley.com). Abstract: A test set of 10 molecules (open and ring forms of ozone and sulfur dioxide as well as water and hydro- gen sulfide and their respective fluoro- and chloro-substituted analogs) of specific atmospheric interest has been formed as to assess the performance of various density functional theory methods in (hyper)polarizability calcula- tions against well-established ab initio methods. The choice of these molecules was further based on (i) the profound change in the physics between isomeric systems, e.g., open (C 2v ) and ring (D 3h ) forms of ozone, (ii) the relation between isomeric forms, e.g., open and ring form of sulfur dioxide (both of C 2v symmetry), and (iii) the effect of the substitution, e.g., in fluoro- and chloro-substituted water analogs. The analysis is aided by arguments chosen from the information theory, graph theory, and pattern recognition fields of Mathematics: In brief, a multidimen- sional space is formed by the methods which are playing the role of vectors with the independent components of the electric properties to act as the coordinates of these vectors, hence the relation between different vectors (e.g., meth- ods) can be quantified by a proximity measure. Results are in agreement with previous studies revealing the accepta- ble and consistent behavior of the mPW1PW91, B3P86, and PBE0 methods. It is worth noting the remarkable good performance of the double hybrid functionals (namely: B2PLYP and mPW2PLYP) which are for the first time used in calculations of electric response properties. q 2009 Wiley Periodicals, Inc. J Comput Chem 31: 412–420, 2010 Key words: ab initio; DFT; pattern recognition; metric space; electric response properties Introduction Despite the unavoidable potential of density functional theory (DFT) methods, numerous studies have proven their inconsistent behavior in different types of calculations. Among others, Ber- suker 1 and Bartlett et al. 2 have pointed out some inherent inca- pabilities related to the formalism of the DFT approach, and Yang and coworkers in a recent study 3 provided some more insights on the DFT failure and success story. An interesting example is the widely, if not the most widely, used DFT method that is the B3LYP 4–6 : Truhlar and coworkers 7–11 as well as others 12–27 have shown its inadequacy in providing reliable results in divers aspects of computational organic chemistry, whereas it retains its popularity among the scientific commu- nity. 28 However, it should be noted that DFT is not a panacea and all the possible expectations are well framed by the fact that DFT, at the very best, provides a solid theoretical ground (to stress out this point we refer some other efforts from the field of applied mathematics 29–34 ) for the evolution of approximating methods toward the solution of Schro ¨dinger equation. We note that the vast majority of studies related to the evalu- ation of the performance of DFT methods toward (hyper)polariz- ability calculations have been focused on organic chemistry aspects: The studies by Adamo and his coworkers 35–37 and Champagne and his coworkers 38,39 are illustrative examples. To broaden the search space (i.e., enrich the available information) of such studies, we performed a systematic study on some XY 2 Additional Supporting Information may be found in the online version of this article. Correspondence to: D. Xenides; e-mail: xenides@uop.gr q 2009 Wiley Periodicals, Inc.