8.5. Selecting Appropriate Reference Systems

The ¹³C NMR results presented for 1,4-dimethylbenzene in the previous chapter involve tetramethylsilane (TMS) not only as the zero of the ¹H, ¹³C, and ²⁹Si NMR scales, but also as the reference system relative to which we compare the computed shielding values. Looking at these two compounds from a chemical point of view, we note that TMS is not neccesarily the best choice as a reference because (i) we compare C(sp²) hybridized carbon atoms in the 1,4-dimethylbenzene substrate with C(sp³) hybridized carbon atoms in the TMS reference, and (ii) we compare substrate and reference ¹³C atoms with a comparatively large chemical shift difference of 129.4 ppm. That both factors are of some importance in accurate ¹³C chemical shift predictions can be illustrated by switching from TMS to benzene (C₆H₆) as the reference molecule and using eq. (4) rather than eq. (5) for converting calculated shieldings to chemical shifts. When measured in CDCl₃, benzene displays a single signal in the proton-decoupled ¹³C NMR spectrum at +128.37 ppm. The chemical shifts of the C2 carbon atom in 1,4-dimethylbenzene and the carbon atoms in benzene thus differ by only 1.5 ppm, and both centers are of C(sp²) type. That this leads to a complete change in the predictive ability of ¹³C NMR chemical shift predictions can be seen graphically in Figure 8.5.1, where we employ the same levels of theory as already in Figure 8.4.1. The vertical axis for ¹³C NMR chemical shifts has been rescaled in this case to accomodate the fact that ALL predictions for the C2 center in 1,4-dimethylbenzene fall into a range of only one ppm. We also add the commonly assumed error for ¹³C NMR measurements of ±0.5 ppm as a faint gray bar just to indicate, that all computationally predicted ¹³C NMR chemical shifts fall into the experimental error range. While we may still feel most comfortable when using the largest possible and specifically optimized basis sets for NMR shielding calculations, the results in Figure 8.5.1 actually illustrate that highly accurate NMR shift predictions are possible even with DZP-quality basis sets when appropriate reference systems are selected.

Figure 8.5.1. ¹³C Chemical shift values calculated for the C2/C3/C5/C6 positions of 1,4-dimethylbenzene at RI-MP2/<basis> level of theory with ORCA using benzene (C₆H₆) as the reference. The experimentally measured ¹³C chemical shift for the C2 position in 1,4-dimethylbenzene is +129.4 ppm and that for benzene is +128.37 ppm in CDCl₃.

The selection of "appropriate" reference systems becomes more important in ³¹P NMR shift calculations, where the zero of the NMR scale is defined by 85% H₃PO₄ in water. What the molecular identity of this reference system is at this (high) concentration is not easily seen, and selection of water as a medium additionally complicates comparison to, for example, organophosphorus compounds in less polar solvents. One can, of course, simply ignore the apparent complexity and use phosphoric acid as the reference system in ³¹P shielding calculations. The results obtained for triphenylphosphane (PPh₃, a frequently used reagent and catalyst in organic synthesis) and its oxide are shown in Figure 8.5.2. In CDCl₃ solution PPh₃ displays a signal at -4.7 ppm in the proton-decoupled ³¹P NMR spectrum, often accompanied by a small amount of its oxide (OPPh₃) with a signal at +29.5 ppm.^[1] Gas phase shielding calculations at RI-MP2/pcSseg-2//M06-2X/def2-TZVPP level of theory performed with ORCA yield the results shown in Figure 8.5.2.

Figure 8.5.2. ³¹P Chemical shift values calculated for the phosphorus atom in PPh₃ and OPPh₃ relative to phosphoric acid as the reference system.

Application of eq. (5) predicts -8.8 ppm for PPh₃ and +19.3 ppm for its oxide OPPh₃. The significant offset for both signals towards more negative/less positive shift values may either indicate substantial differential solvent effects between the gas phase calculations, the water medium for phosphoric acid, and CDCl₃ for PPh₃ and its oxide. Or may also indicate that monomeric phosphoric acid is not a sufficiently good model for the 85% H₃PO₄ reference system. We can separate these two effects by selecting PPh₃ as the reference system with a known chemical shift value in CDCl₃ solution of -4.7 ppm, and applying eq. (4) for the prediciton of the chemical shift value for OPPh₃. As shown in Figure 8.5.2 this reduces the error for the shift prediction of OPPh₃ by close to 4 ppm. The predictive value of NMR chemical shift calculations can thus be enhanced very significantly by selecting a small set of reference compounds with closely similar chemical and spectroscopic properties as the system under investigation.^[2]
In order to make this strategy less dependent on the accuracy of a SINGLE analytical measurement, it is common place to select a small set of reference compounds with similar, but not necessarily identical spectroscopic properties (a focused library). This idea can be further extended by linear regression analysis of computed chemical shieldings for a larger dataset with the respective experimentally measured shift data. The slope and offset parameters of these correlations can then be used for the prediction of NMR chemical shifts of new compounds (or for the validation of NMR shift assignments of known compounds).^[3] The combination of shielding calculations with statistical analysis protocols has largely aided the ¹H and ¹³C NMR assignments of conformationally flexible compounds in organic chemistry.^[4]

References 
[1] C. Lindner, Y. Liu, K. Karaghiosoff, B. Maryasin, H. Zipse, "The Aza-Morita–Baylis–Hillman Reaction: A Mechanistic and Kinetic Study, Chem. Eur. J. 2013, 19, 6429−6434.
[2] J. Helberg, Y. OE, H. Zipse, "Mechanistic Analysis and Characterization of Intermediates in the Phosphane-Catalyzed Oligomerization of Isocyanates", Chem. Eur. J. 2018, 24, 14387–14391.
[3] M. W. Lodewyk, M. R. Siebert, D. J. Tantillo, "Computational Prediction of ¹H and ¹³C Chemical Shifts: A Useful Tool for Natural Product, Mechanistic, and Synthetic Organic Chemistry", Chem. Rev. 2012, 112, 1839–1862.
[4] N. Grimblat, M. M. Zanardi, A. M. Sarotti, "Beyond DP4: an Improved Probability for the Stereochemical Assignment of Isomeric Compounds using Quantum Chemical Calculations of NMR Shifts", J. Org. Chem. 2015, 80, 12526–12534.

last changes: 12.12.2024, Imon Mandal, and Hendrik Zipse, supported by the RTG 2610 on "Ion Pair Effects in Molecular Reactivity"
questions & comments to: zipse@cup.uni-muenchen.de