GIAO theory

The GIAO-MP2/TZP calculated 13C NMR chemical shifts of the cyclopropylidene substituted dienyl cation 27 show for almost all carbon positions larger deviations from the experimental shifts than the other cations 22-26. The GIAO-MP2/TZP method overestimates the influence of cr-delocalization of the positive charge into the cyclopropane subunit on the chemical shifts. Electron correlation corrections for cyclopropylidenemethyl cations such as 27 and 28 are too large to be adequately described by the GIAO-MP2 perturbation theory method and higher hierarchies of approximations such as coupled cluster models are required to rectify the problem. 

Recently, ab initio shielding calculations based on well-established theories, IGLO (individual gauge for localized orbitals)9, GIAO (gauge including atomic orbital)10 and LORG... 

The structure of a natural product hexacyclinol, a polycyclic endoperoxide, was reassigned on the basis of calculated chemical shifts (HF-gauge-independent atomic orbital (GIAO) level of theory) <2006OL2895>. 

There has been much recent progress in the application of density functional theory (DFT) to the calculation of shift tensors, and several methods are presently available. The sum-over-state (SOS) DFT method developed by Malkin et al. (70) does not explicitly include the current density, but it has been parametrized to improve numerical accuracy. Ziegler and coworkers have described a GIAO-DFT method (71) that is available as part of the Amsterdam density functional package (72). An alternate method developed by Cheeseman and co-workers (73) is implemented in Gaussian 94 (74). 

Schleyer and coworkers have shown35 that in order to use effectively the IGLO/NMR approach to structure elucidation, it is necessary to employ high-level optimized geometries (e.g. at the correlated MP2/6-31G or DFT levels of theory) in order to obtain best agreement between computed and experimental chemical shifts. Early GIAO-SCF... 

Over the years, several computational methods have been developed. The variational theory can be used either without using experimental data other than the fundamental constants (i.e., ab initio methods) or by using empirical data to reduce the needed amount of numerical work (i.e., semiempirical data methods). There are various levels of sophistication in both ab initio [HF(IGLO), DFT GIAO-MP2, GIAO-CCSD(T)] and semiempirical methods. In the ab initio methods, various kinds of basic sets can be employed, while in the semiempirical methods, different choices of empirical parameters and parametric functions exist. The reader is referred to reviews of the subject.18,77... 

Also shown in Figure 2 are the GIAO-MP2/tzp/dz values of the isotropic 13C chemical shifts. The predicted chemical shift for C2 and C3 is 255.3 ppm, which compares to the experimental value of 250 ppm. For C2, theory predicts a chemical shift of 152.8 ppm, whereas the experimental value is 148 ppm. The CH2 carbons are predicted to have isotropic chemical shifts of 50.0 ppm which compare to the measured values of 33 ppm. Finally, the methyl carbons have theoretical values of 28.9 ppm, whereas the experimental chemical shifts are 24 ppm. In all cases the theoretical values are downfield of the experimental chemical shifts. The differences are generally =5 ppm, with the exception of C3. The source of this larger difference is not clear. Still, the agreement is sufficient to verify the presence of the 1,3-dimethylcyclopentyl carbenium ion within the zeolite. 

To compare with the experimental NMR data, the 13C isotropic chemical shifts of all of the acetylide and vinylidene complexes were calculated. These systems were too large for us to be able to do chemical shift calculations at the MP2 level. We thus used the GIAO method at the RHF level. Fortunately, the RHF level of theory appears to be adequate for these complexes. We used a mixed basis set for the GIAO, with tzplarge+ on C, tzplarge on H, tzp on the Mg and O associated with the adsorbed species, and dzp on the remaining Mg and O (26). 

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