REGULAR ARTICLE Activation enthalpies of pericyclic reactions: the performances of some recently proposed functionals Vincent Tognetti Æ Pietro Cortona Æ Carlo Adamo Received: 10 October 2008 / Accepted: 20 December 2008 / Published online: 28 January 2009 Ó Springer-Verlag 2009 Abstract We have assessed the performances of three recently proposed functionals, RC (Ragot and Cortona in J Chem Phys 121:7671, 2004), TCA (Tognetti et al. in J Chem Phys 128:034101, 2008), and RevTCA (Tognetti et al. in Chem Phys Lett 460:536, 2008) by calculating the activation enthalpies for ten pericyclic reactions and eighteen 1,3-dipolar cycloadditions. We have found that the local functional (RC) gives results only marginally better than the local-density approximation ones, while the two GGA functionals, TCA and RevTCA, both strongly improve the results with respect to PBE. The performances of RevTCA, in particular, are not far different from those of a hybrid functional such as B3LYP. Keywords Density-functional theory  Exchange-correlation functionals  Generalized-gradient approximation  Pericyclic reactions  1,3-Dipolar cycloadditions 1 Introduction The predictive ability of ab initio calculations performed in the framework of the density-functional theory (DFT) [1, 2] rests on the accuracy of the available approximations for the exchange-correlation functional. Many attempts on improving the oldest one, the local-density approximation (LDA) [3, 4], have been undertaken in the past, but these attempts were not always successful. During the past two decades, however, considerable progress has been made and thus various approximate functionals, which remedy the main failures of LDA, are now available. For example, functionals such as PW91 [5], PBE [6], or BLYP [7, 8], belonging to the generalized-gradient approximation (GGA) class, are known to strongly improve the atomiza- tion energies of the molecules, but to give barrier heights for various prototypical chemical reactions which are not accurate. Better results for these barriers can be obtained by means of the so-called hybrid functionals (among which B3LYP [9, 10] is probably the most famous one), where a fraction of the exact exchange is combined with an approximate functional in order to describe the whole exchange and correlation of the system. In this case, the increased precision of the results is paid in terms of an increased computational cost and of a more difficult implementation in the computer programs. Most solid-state codes, for example, do not allow one to perform calcula- tions using hybrid functionals. A common practice in searching for new approximate functionals is to choose an analytical expression having some desirable features and to determine the parameters entering this expression by fitting some set of reference data (the so-called ‘‘training set’’). If the training set is sufficiently large, this procedure assures good perfor- mances of the functional for a wide class of systems. A well-known functional obtained in such a way is B3LYP. The parameters which determine the mixing of exact and approximate exchange, as well as of local and nonlocal correlation, were obtained by optimizing the results V. Tognetti  C. Adamo Laboratoire d’Electrochimie et de Chimie Analytique, UMR 7575, Ecole Nationale Supe ´rieure de Chimie de Paris, 11 rue P. et M. Curie, 75231 Paris Cedex 05, France P. Cortona (&) Laboratoire Structure, Proprie ´te ´ et Mode ´lisation des Solides, UMR 8580, Ecole Centrale Paris, Grande Voie des Vignes, 92295 Cha ˆtenay-Malabry, France e-mail: pietro.cortona@ecp.fr 123 Theor Chem Account (2009) 122:257–264 DOI 10.1007/s00214-008-0503-y