Computed 13C NMR Chemical Shifts via Empirically Scaled GIAO Shieldings and Molecular Mechanics Geometries. Conformation and Configuration from 13C Shifts

Accurate (rms error ∼3 ppm) predictions of 13C chemical shifts are achieved for many of the common structural types of organic molecules through empirical scaling of shieldings calculated from gauge including atomic orbitals (GIAO) theory with a small basis set and with geometries obtained from computationally inexpensive molecular mechanics methods. Earlier GIAO calculations are shown to be much better at predicting relative chemical shifts when density functional theory with the B3LYP hybrid functional is used to account for electron correlation, in comparison with Hartree-Fock calculations. The GIAO isotropic shieldings need to be empirically scaled to achieve good numerical agreement with experimental δC. GIAO calculations with different small basis sets are compared for a set of 38 model compounds containing C, H, O, and N with MMX and MM3 force fields and B3LYP/6-31G* optimizations providing the geometries. The best MM3-based results are obtained with B3LYP/3-21G(X,6-31+G*)/ /MM3 calculations in which the 3-21G basis set is augmented for heteroatoms with polarization and diffuse functions. The examples of the (E)and (Z)-2-butenes, axial and equatorial methylcyclohexanes, exoand endo-2-norbornanols, vulgarin and epivulgarin, and chair and twist-boat forms of 3R-hydroxy-2â-(4-morpholinyl)-5RH-androstan-17-one are examined to establish whether δpred values could determine the structure if only one of each pair of structures were available to provide experimental δC values. The δpred from B3LYP/3-21G(X,6-31+G*)//MM3 calculations are adequate for addressing questions of conformation and relative stereochemistry. Accurate prediction of 13C chemical shifts could become a tool that strongly complements if not rivals 1H-1H coupling constants, 1H-1H NOE measurements, and empirical chemical shift correlations for determination of conformations and configurations of organic molecules. 13C chemical shifts reflect structural features in a highly sensitive manner, but at present, most 13C chemical shift data that are reported are not used in a detailed analysis of structure. Schleyer, Gauss, and co-workers1 have suggested that the combination of high-level ab initio optimized geometries, theoretically computed NMR chemical shifts, and experimental NMR data provides a tool that can be routinely applied for structural elucidation and characterization of new compounds. Practical applications so far are most extensive in the areas of carbocations and boron compounds, where high-level ab initio methods including electron correlation are necessary to properly describe structure and bonding.1-3 Other studies oriented toward structure determination include an analysis of C84 fullerenes4 and studies relating to the conformation of the rhodopsin chromophore.5 Several studies have explored the challenging problem of predicting 13C shifts in amides and peptides.6 Applications of theoretically computed 13C chemical shifts to organic structure determination have not yet become routine, despite the apparent capability to predict shifts of 13C and other nuclei at a sufficient level of accuracy to allow practical applications. To achieve the goal of routine practical use, predicted 13C chemical shifts need to be accurate to within a Very few ppm for molecules in solution that include a wide Variety of functional groups and conformational characteristics. The predictions also need to be achieVed at modest computational cost. There have been some discouraging signs despite the great promise and demonstrated successes of the various quantum mechanical methods for predicting chemical shifts. Several methods used with ab initio calculations are now available for calculating nuclear shieldings, such as the GIAO (gauge including atomic orbitals),7 IGLO (individual gauge for localized orbitals),3,8 CSGT (continuous set of gauge transformations),9 X Abstract published in AdVance ACS Abstracts, September 15, 1997. (1) Bühl, M.; Gauss, J.; Hofmann, M.; Schleyer, P. v. R. J. Am. Chem. Soc. 1993, 115, 12385. (2) Recent leading references: (a) Bühl, M.; Schleyer, P. v. R. J. Am. Chem. Soc. 1992, 114, 477. (b) Onak, T.; Diaz, M.; Barfield, M. J. Am. Chem. Soc. 1995, 117, 1403. (c) Olah, G. A.; Head, N. J.; Rasul, G.; Prakash, G. K. S. J. Am. Chem. Soc. 1995, 117, 875. (d) Siehl, H.-U.; Müller, T.; Gauss, J.; Buzek, P.; Schleyer, P. v. R. J. Am. Chem. Soc. 1994, 116, 6384. (e) Perera, S. A.; Bartlett, R. J.; Schleyer, P. v. R. J. Am. Chem. Soc. 1995, 117, 8476. (f) Siehl, H.-U.; Fuss, M.; Gauss, J. J. Am. Chem. Soc. 1995, 117, 5983. (g) Nicholas, J. B.; Xu, T.; Barich, D. H.; Torres, P. D.; Haw, J. F. J. Am. Chem. Soc. 1996, 118, 4202. (h) Rauk, A.; Sorensen, T. S.; Maerker, C.; Carneiro, J. W. de M.; Sieber, S.; Schleyer, P. v. R. J. Am. Chem. Soc. 1996, 118, 3761. (3) Kutzelnigg, W.; Fleischer, U.; Schindler, M. In NMR Basic Principles and Progress; Diehl, P., Fluck, E., Günther, H., Kosfeld, R., Seelig, J., Eds.; Springer-Verlag: Berlin, 1991; Vol. 23, p 165. (4) Schneider, U.; Richard, S.; Kappes, M. M.; Ahlrichs, R. Chem. Phys. Lett. 1993, 210, 165. (5) (a) Wada, M.; Sakurai, M.; Inoue, Y.; Chûjô, R.Magn. Reson. Chem. 1992, 30, 831. (b) Wada, M.; Sakurai, M.; Inoue, Y.; Tamura, Y.; Watanabe, Y. J. Am. Chem. Soc. 1994, 116, 1537. (c) Wada, M.; Sakurai, M.; Inoue, Y.; Tamura, Y.; Watanabe, Y. Magn. Reson. Chem. 1995, 33, 453. (d) Houjou, H.; Sakurai, M.; Asakawa, N.; Inoue, Y.; Tamara, Y. J. Am. Chem. Soc. 1996, 118, 8904. (6) (a) Jiao, D.; Barfield, M.; Hruby, V. J. Magn. Reson. Chem. 1993, 31, 75. (b) de Dios, A. C.; Pearson, J. G.; Oldfield, E. Science (Washington, D.C.) 1993, 260, 1491. (c) de Dios, A. C.; Oldfield, E. Chem. Phys. Lett. 1993, 205, 108. (d) de Dios, A. C.; Pearson, J. G.; Oldfield, E. J. Am. Chem. Soc. 1993, 115, 9768. (e) de Dios, A. C.; Oldfield, E. J. Am. Chem. Soc. 1994, 116, 5307. (f) Sulzbach, H. M.; Schleyer, P. v. R.; Schaefer, H. F., III J. Am. Chem. Soc. 1995, 117, 2632. (g) He, Y.; Wu, D.; Shen, L.; Li, B. Magn. Reson. Chem. 1995, 33, 701. (7) (a) Ditchfield, R.Mol. Phys. 1974, 27, 789. (b) Rohling, C. M.; Allen, L. C.; Ditchfield, R. Chem. Phys. 1984, 87, 9. (c) Wolinski, K.; Hinton, J. F.; Pulay, P. J. Am. Chem. Soc. 1990, 112, 8251. (8) (a) Kutzelnigg, W. Isr. J. Chem. 1980, 19, 193. (b) Schindler, M.; Kutzelnigg, W. J. Am. Chem. Soc. 1983, 104, 1360. (9) Keith, T. A.; Bader, R. F. W. Chem. Phys. Lett. 1993, 210, 223. 9483 J. Am. Chem. Soc. 1997, 119, 9483-9494 S0002-7863(97)00112-1 CCC: $14.00 © 1997 American Chemical Society and LORG (localized orbitals, local origin)10 methods. The need for accurate geometries has been emphasized repeatedly, leading to the practice of performing geometry optimizations at high levels of ab initio theory, often with electron correlation included.1-3,12 Such an approach can be quite expensive computationally, especially since many candidate structures for an organic molecule of even modest size can often be identified through simple consideration of possible conformations or through a systematic conformational search. Recent studies also show that electron correlation contributions should be included to obtain the most accurate shielding tensors.13 For example, significant improvements in chemical shift predictions can be achieved over Hartree-Fock SCF calculations through the use of the GIAO MP2 method.1 Density functional theory (DFT) provides a lower cost alternative to the more traditional electron correlation techniques such as the Moeller-Ploesset (MPn) methods.14 However, a recent comparison by Cheeseman, Trucks, Keith, and Frisch of models for calculating NMR shielding tensors found that, for GIAO calculations, the root-mean-square (rms) error in calculated 13C shifts for a set of small molecules was 11.1 ppm at the HartreeFock 6-31G* level and 12.5 ppm with a DFT method, the B3LYP hybrid functional.15 Unfortunately, errors at >10 ppm are not Very attractiVe to chemists for most practical applications, as discussed below. In their study, geometries for the set of model compounds were optimized at the B3LYP/6-31G* level. The DFT GIAO predictions did improve to an rms error of 4.2 ppm with the large B3LYP/6-311+G(2d,p)//B3LYP/631G* basis set while the HF GIAO predictions with the same basis set remained at the same large size of rms error. Apparently based on this study, the user’s reference for the Gaussian 94 software indicates that the DFT methods do not provide systematically better NMR results than HF.16 Calculations at the HF 6-31G*//B3LYP/6-31G* level have been recommended as the minimum model for NMR calculations, but the larger basis set with DFT was considered preferable.15,17 In this paper, we reevaluate the study of 13C chemical shift calculations carried out by Cheeseman and co-workers in order to point out that, after empirical scaling, their B3LYP/6-31G* GIAO predictions are much more successful than reported.15 More importantly, we now report that accurate (rms error ∼3 ppm) predictions of 13C chemical shifts can be achieved for many of the common structural types of organic molecules through the use of scaled shieldings calculated from GIAO theory with a small basis set and on the basis of geometries obtained from computationally inexpensive molecular mechanics methods. GIAO calculations with different small basis sets are compared for a new set of model compounds oriented toward organic functional groups and for which the MMX18 and MM319 force fields as well as B3LYP/6-31G* optimizations are used to provide geometries. We also examine the capability of empirically scaled GIAO shieldings obtained with MM3 geometries to satisfy the demands involved with determining structural stereochemistry. Scaling of GIAO Absolute Isotropic Shieldings. Absolute shieldings predicted by ab initio methods tend to approach experimental values with increased size of the basis set and are often improved by inclusion of correlation corrections.1,7c,15 The increased success depends partly on the direct effect of improved shielding calculations and partly on the indirect effect of improved molecular geometries when optimized at higher levels of theory.1 The paper by Cheeseman et al. noted that shieldings from the GIAO method tended to converge more smoothly toward experimental values than the CSGT method as the basis set was increased.15 Pulay and co-workers also noted the smooth convergence and that relative shieldings were reproduced well by the GIAO method, although there were some large discrepancies between predicted and observed absolute shieldings.7c Most studies of theoretical shieldings either compare experimental absolute shieldings to calculated absolute shieldings or compare experimental chemical shifts to chemical shifts calculated from absolute shieldings by subtraction of a calculated reference. In a review chapter on shielding theory and on the IGLO method in particular, Kutzelnigg, Fleischer, and Schindler noted the inherent problem of using a calculated shielding for a reference compound in predicting chemical shifts.3 Any error in the calculated shift for the single point of the reference compound will be reflected in all of the derived shifts, although subtracting the reference can also compensate for a general discrepancy in the magnitude of the predicted absolute shieldings. Another possibility is that the relative order of shifts could be predicted accurately, but the shifts might need scaling in order to provide a good match with experimental shifts. This need for scaling appears to be present in the GIAO shielding calculations reported by Cheeseman et al.15 The rms error of 12.5 ppm for 13C chemical shifts that was found in GIAO predictions at the B3LYP/6-31G*//B3LYP/631G* level is worse than the 11.9 ppm rms error for GIAOcalculated shifts at the HF 6-31G*//B3LYP/6-31G* level.15 However, it was also noted that the 6-31G* results deviate on both sides of the experimental values, while the B3LYP/6-31G*predicted chemical shifts all deviate in one direction from the experimental values. It was not reported, however, that the deviations appear to increase with the magnitude of the chemical shifts, i.e., that the error is systematic and could be compensated for by empirical scaling. Our approach in this paper is to use linear regression data to provide empirical scaling for theoretical isotropic shieldings in order to achieve more closely the level of predictive accuracy needed for practical applications of computed 13C shifts. In a recent review, Chesnut demonstrated excellent correlations for isotropic shieldings obtained in Hartree-Fock GIAO calculations with both 1H and 13C experimental shielding data.20 In particular, he showed the improvement in rms error that could be achieved by using slope-corrected shieldings in the case of (10) Hansen, A. E.; Bouman, T. D. J. Chem. Phys. 1984, 82, 5035; 1989, 91, 3552. (11) Chesnut, D. B.; Phung, C. G. J. Chem. Phys. 1989, 91, 6238. (12) Nuclear Magnetic Shieldings and Molecular Structure; Tossell, J. A., Ed.; Kluwer Academic: Dordrecht, The Netherlands, 1993. (13) (a) Gauss, J. Chem. Phys. Lett. 1992, 191, 614. (b) Gauss, J. J. Chem. Phys. 1993, 99, 3629. (c) Gauss, J. Chem. Phys. Lett. 1994, 229, 198. (d) van Wüllen, C. J. Chem. Phys. 1995, 102, 2806. (e) Ziegler, T.; Schreckenbach, G. J. Phys. Chem. 1995, 99, 606. (14) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (b) Becke, A. D. Phys. ReV. A: At. Mol. Opt. Phys. 1988, 38, 3098. (c) Kohn, W.; Sharn, L. J. Phys. ReV. 1965, 140, A1133. (d) Ziegler, T. Chem. ReV. 1991, 91, 651. (e) Pople, J. A.; Gill, P. M. W.; Johnson, B. G. Chem. Phys. Lett. 1992, 199, 557. (f) Parr, R. G.; Yang, W. Density Functional Theory of Atoms and Molecules; Oxford Press: Oxford, 1989. (15) Cheeseman, J. R.; Trucks, G. W.; Keith, T. A.; Frisch, M. J. J. Chem. Phys. 1996, 104, 5497. (16) Frisch, M. J.; Frisch, Æ.; Foresman, J. B. Gaussian 94 Users Reference (Revision D.1 and Higher); Gaussian Inc.: Pittsburgh, 1996; p 109. (17) Foresman, J. B.; Frisch, Æ. Exploring Chemistry with Electronic Structure Methods, 2nd ed.; Gaussian Inc.: Pittsburgh, 1996; pp 21, 53, 104. (18) (a) Gajewski, J. J.; Gilbert, K. E.; McKelvie, H. In AdVances in Molecular Modeling; Liotta, D., Ed.; JAI Press: Greenwich, CT, 1990; Vol. 2. (b) PCMODEL, V.6.0, Serena Software: Box 3076, Bloomington, IN. (19) (a) Allinger, N. L.; Yuh, Y. H.; Lii, J.-H. J. Am. Chem. Soc. 1989, 111, 8551, 8566, 8576. (b) MM3(94), Tripos, Inc.: St. Louis, MO. (20) Chesnut, D. B. In ReViews in Computational Chemistry; Lipkowitz, L. B., Boyd, D. B., Eds.; VCH: New York, 1996; Vol. 8, Chapter 5. 9484 J. Am. Chem. Soc., Vol. 119, No. 40, 1997 Forsyth and Sebag