219 Research Article Received: 23 October 2009 Revised: 22 December 2009 Accepted: 30 December 2009 Published online in Wiley Interscience: 27 January 2010 (www.interscience.com) DOI 10.1002/mrc.2571 Empirical and DFT GIAO quantum-mechanical methods of 13 C chemical shifts prediction: competitors or collaborators? Mikhail Elyashberg, a Kirill Blinov, a Yegor Smurnyy, a Tatiana Churanova a and Antony Williams b* The accuracy of 13 C chemical shift prediction by both DFT GIAO quantum-mechanical (QM) and empirical methods was compared using 205 structures for which experimental and QM-calculated chemical shifts were published in the literature. For these structures, 13 C chemical shifts were calculated using HOSE code and neural network (NN) algorithms developed within our laboratory. In total, 2531 chemical shifts were analyzed and statistically processed. It has been shown that, in general, QM methods are capable of providing similar but inferior accuracy to the empirical approaches, but quite frequently they give larger mean average error values. For the structural set examined in this work, the following mean absolute errors (MAEs) were found: MAE(HOSE) = 1.58 ppm, MAE(NN) = 1.91 ppm and MAE(QM) = 3.29 ppm. A strategy of combined application of both the empirical and DFT GIAO approaches is suggested. The strategy could provide a synergistic effect if the advantages intrinsic to each method are exploited. Copyright c  2010 John Wiley & Sons, Ltd. Supporting information may be found in the online version of this article. Keywords: NMR; 13 C NMR; chemical shift prediction; GIAO; DFT; HOSE code; neural nets Introduction Different methods of 13 C NMR spectrum calculation have been developed over the years to provide a reliable choice for the most probable structural hypothesis, assist in the process of spectral signal assignment and to aid in the determination of stereochemistry for complex organic molecules. The first prediction algorithms were based on additive rules and referred to as an incremental method. They were intended for the empirical prediction of 13 C NMR chemical shifts and implemented in a series of programs. [1–4] The programs [5–9] utilizing a fragmental approach and HOSE codes [10] as well as efficient artificial neural net algorithms (NN) were developed. [11,12] These algorithms are based on empirical methods, run fully automatically and require no user intervention. As the programs were required by expert systems for the purpose of computer-aided structure elucidation (CASE), [13] they were implemented into the most advanced CASE systems. [14 – 16] Automated chemical shift prediction methods are under constant improvement. [17 – 19] Recently, it has been shown [18] that programs based on NN algorithms and additive rules are capable of predicting 13 C chemical shifts for diverse classes of organic molecules with a mean absolute error (MAE) value of 1.6 – 1.8 ppm and at a speed of 6000 – 10 000 shifts per second. Programs utilizing HOSE codes [7,9] provide similar or better accuracy. This approach also provides facilities which show all reference structures involved in a particular chemical shift calculation for a given atom. Visual analysis and comparison of atom environments in a reference structure and in the structure under investigation can be used to understand how the chemical shift was calculated. The shortcoming of these programs is that they are not very fast with the prediction speed varying between several seconds and tens of seconds depending on the size and complexity of a chemical structure. The prediction of 13 C chemical shifts using quantum-mechanical (QM) methods has become the focus of many researchers. There is extensive literature devoted to the development and application of different QM approaches. The discussion of all approaches is beyond the scope of this article which is focused on the GIAO approximation of the DFT approach which has been increasingly applied to NMR spectral calculations. The reason for wide applicability of the GIAO DFT calculations is the relatively low computational costs and the potential possibility to provide high enough accuracy to solve many problems for organic and analytical chemistry. Almost all practicing chemists use different modifications, most frequently the B3LYP functional variant of this method, when a QM prediction seems necessary. The important advantage of this approach is that it takes into account electron correlation effects. Additional consideration is given to electron correlation by perturbation theory. The calculation of shielding constants at MP2 level (perturbation theory of second order) is available, but these computations are too time-consuming and this is the reason why they are applied only to small molecules. There is an N 3 dependence in computational time for the DFT approach and N 5 for MP2, where N is the number of basis functions. The ∗ Correspondence to: Antony Williams, Royal Society of Chemistry, US Office, 904 Tamaras Circle, Wake Forest, NC 27587, USA. E-mail: tony27587@gmail.com a Advanced Chemistry Development, Moscow Department, 6 Akademik Bakulev St, 117513 Moscow, Russian Federation b Royal Society of Chemistry, US Office, 904 Tamaras Circle, Wake Forest, NC 27587, USA Magn. Reson. Chem. 2010, 48, 219–229 Copyright c  2010 John Wiley & Sons, Ltd.