NMR absolute shieldings

In table 6 the absolute shielding constants for several molecules, obtained at the PBE and PBEO level of theory, are reported. This first set has already been taken as a benchmark in a previous NMR study [82]. Some statistical parameters, including overall absolute mean deviation, max deviation and mean deviation for C and N shieldings, are also included in the same table. 

Let us first analyze the results for in terms of the different hybridizations of the carbon atom. From the data reported in the table, it is apparent that both the PBE and PBEO methods generally provide reliable resirlts for chemical shieldings of sp carbons. Furthermore the PBEO results are closer to the experimental values than both MP2 and B3LYP methods. For instance the PBEO value for the carbon atoms in ethane is 194 ppm, whereas the PBE value is 191 

In summary, the PBEO absolute shieldings for the carbon atoms are of remarkable quality for all the hybridizations and chemical enviroments considered here. In particular the mean absolute deviation for the PBEO model (4.6 ppm) is lower than that provided by the MP2 approach (6.0 ppm) and by the HF method (7.9 ppm). So, the PBEO functional represents an improvement over conventional quantum mechanical approaches, whereas the B3LYP model (and all the other current functionals) remains essentially at the same level as the HF method [82]. 

Our set of molecules allows also some analysis of N absolute shieldings. In particular, it is remarkable that already the PBE functional gives results closer to experiment than the B3LYP values, and a further improvement is obtained when going to the PBEO model. In contrast, an excessive shielding is obtained by the MP2 method and just the opposite occurs at the B3LYP level. 

Absolute isotropic shielding constants (a, ppm) computed at various theoretical levels for C, N and O. Density functional values are computed using the 6-311+G(2d,p) basis set and 6-31 lG(d,p) geometries. Nuclei are labelled from left to right. 

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Spin-Orbit/Fermi Contact Effects. While scalar relativistic effects seem to be sufficient for some systems like the metal carbonyls of Table I (even though it has been speculated (9) that spin-orbit might improve the agreement with experiment even further), there are other cases where this is not the case. We have chosen as an example the proton NMR absolute shielding in hydrogen halides HX, X = F, Cl, Br, I (7,9), Figure 1. This series has also been studied by other authors (34-38), and it may well be the most prominent example for spin-orbit effects on NMR shieldings and chemical shifts. 

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