Density Functional Calculations DOI: 10.1002/ange.200801843 Sources of Error in DFT Computations of C  C Bond Formation Thermochemistries: p !s Transformations and Error Cancellation by DFT Methods** SusanN.Pieniazek,FernandoR.Clemente,andKendallN.Houk* Quantum mechanical methods based on Kohn–Sham Density Functional Theory (DFT) [1] are currently the most used methods in computational chemistry. In particular, the hybrid density functional B3LYP [2] enjoys a vast popularity in the chemistry community, but there is increasing evidence about the limitations of this functional. The good performance of the ubiquitous B3LYP/6-31G(d) model chemistry has been suggested to result from error cancellation. [3, 4] In a recent Highlight in Angewandte Chemie, [5] Schreiner reviewed current research about limitations of DFT methods. Exam- ples of problematic areas include calculations of enthalpies of formation of long-chain and branched hydrocarbons, [6] hydro- carbon reaction energies, [7] and calculation of electrocyclic reactions. [8] In our study of Diels–Alder reactions of halofur- ans, [9] errors in B3LYP caused us to resort to high accuracy CBS-QB3 calculations. Despite the alarming reports [4, 10] about large errors in DFT energetics, little effort has been made to identify sources of error. Studies have shown that B3LYP is insufficient in the prediction of isomer relative energies of hydrocarbon and other main group element containing molecules. [10–12] The work of Schleyer et al. [13] identified systematic errors of DFT methods in the evaluation of the stabilizing 1,3-alkyl-alkyl interactions (protobranching) that exist in linear, branched, and most cycloalkanes, but not in methane and ethane. Grimme has provided a theoretical explanation based on the inability of DFT to compute medium-range correlation. [11] In related examples, increasing DFTerrors have been found with increasing hydrocarbon system size for the isomers with the largest number of single bonds and small rings. [14] As a result of the reported problems in energy evalua- tions, and the plethora of, apparently similar, existing DFT methods, chemists are facing uncertainty in their application to research problems, often relying on a fortunate error cancellation. Method development, on the other hand, should obviously benefit from the identification of problematic areas in fundamental transformations of interest in chemistry. To bridge the chemistry community and the field of functional development, the aim of this work is to provide insight into the combined sources of errors present in C  C bond forming reactions. In particular, Diels–Alder reactions are decom- posed into contributions from the basic structural features involved in these C C bond-forming reactions. The energetics of the ten Diels–Alder reactions I–V in Scheme 1 have been computed [15] with the high-accuracy CBS-QB3 [16] and G3 [17] methods. The results are given in Table 1. These reactions involve acyclic and cyclic dienes, and ethylene and acetylene dienophiles. All reactions involve the conversion of p to s bonds from either alkene or alkyne reactants, as well as changes in branching, hyperconjugation interactions, and strain. The errors in these hydrocarbon Diels–Alder reaction energetics using a number of popular hybrid DFT func- tionals [18] and the wave-function-based SCS-MP2 [19] method are shown in Figure 1. Double-z (6-31 + G(d,p)) and triple-z (6-311 + G(2df,2p)) basis sets have been used (Figure 1a and b, respectively). The double-z results emphasize the practical aspect of the study as this type of basis sets is widely used in calculations of large systems. For the set of reactions in Scheme 1, all methods have mean absolute deviations (MADs) ranging from 2–8 kcal mol 1 (double-z) or 1–12 kcal Scheme 1. Cycloadditions involving ethylene and acetylene as dieno- philes. [*] Dr. S. N. Pieniazek, Dr. F. R. Clemente, Prof. Dr. K. N. Houk Department of Chemistry and Biochemistry, University of California Los Angeles, CA 90095-1569 (USA) Fax: (+ 1) 310-206-1843 E-mail: houk@chem.ucla.edu [**] We are grateful to the National Science Foundation and the Partnerships for Advanced Computational Infrastructure (PACI) for the financial support of this research. The computations were performed on the UCLA Academic Technology Services (ATS) Hoffman Beowulf cluster. Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/anie.200801843. Zuschriften 7860 # 2008 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Angew. Chem. 2008, 120, 7860 –7863