NMR calculations

NMR calculations are based on a given molecular geometry, which means that an experimental 3D structure must be available, or it has to be previously calculated. Because a rigid structure is used for the calculations, different chemical... 

Run your NMR calculations at the HF/6-31G(d) level here are the structures of the three molecules calculated at the B3LYP/6-31G(d) level ... 

In order to do so, you will need to perform Hartree-Fock NMR calculations using the 6-311+G(2d,p) basis set. Compute the NMR properties at geometries optimized with the B3LYP method and the 6-31G(d) basis set. This is a recommended model for reliable NMR predictions by Cheeseman and coworkers. Note that NMR calculations typically benefit from an accurate geometry and a large basis set. 

Cr CO t Bond Distance Experimental NMSt Results NMR Calculations... 

The relative accuracies of various model chemistries are discussed in more detail in Chapter 7 (page 146). Resource requirements for various models and calculation types are discussed in Chapter 6 (page 122). Recommended models for NMR calculations were discussed earlier in this work (pages 21 and 53). 

Determine the effect of basis set on the predicted chemical shifts for benzene. Compute the NMR properties for both compounds at the B3LYP/6-31G(d) geometries we computed previously. Use the HF method for your NMR calculations, with whatever form(s) of the 6-31G basis set you deem appropriate. Compare your results to those of the HF/6-311+G(2d,p) job we ran in the earlier exercise. How does the basis set effect the accuracy of the computed chemical shift for benzene ... 

According to a semiempirical study by Malar, the different polyphospholide anions have 86—101% aromaticities of that of the cyclopentadienide anion. Chesnut and Quin reported on the basis of GIAO NMR calculations using a triple-valence quality basis set that the phospholide anion s aromaticity is 63% that of the cyclopentadienide anion. The aromatic stabilization energy (ASE) obtained by Schley-er et al. from eq 2 (X = P ) was 90% that of the cyclopentadienide anion. 

Fig. 22. CCSD (tzp, spherical) optimized structures for the bridged and classical forms of the ethyl cation used in NMR calculations. (Reprinted with permission from Ajith Perera et a . (123). Copyright 1995 American Chemical Society.)...

The barriers to inversion of l-aryl-2,2-dimethylaziridines have been investigated422 by means of low-temperature NMR. Calculation of the Avalues involves observation of the coalescence temperature for the protons of the methyl groups. The process is accelerated by n conjugation of the nitrogen lone pair in the transition state, and accordingly the... 

Reference TMS <513C(calc) = 183.5 ppm, geometry (Cl) B3LYP/6-31G(d) NMR calculation SOS DFT PW91 (Perdew-Wang 91) IGLO IB. 

Kleinberg et al. (2005) and Takayama et al. (2005) show that NMR-log measurement of sediment porosity, combined with density-log measurement of porosity, is the simplest and possibly the most reliable means of obtaining accurate gas hydrate saturations. Because of the short NMR relaxation times of the water molecules in gas hydrate, they are not discriminated by the NMR logging tool, and the in situ gas hydrates would be assumed to be part of the solid matrix. Thus the NMR-calculated porosity in a gas-hydrate-bearing sediment is apparently lower than the actual porosity. With an independent source of accurate in situ porosities, such as the density-log measurements, it is possible to accurately estimate gas hydrates saturations by comparing the apparent NMR-derived porosities with the actual reservoir porosities. Collett and Lee (2005) conclude that at relatively low gas... 

As might be expected, NMR calculations that ignore electron correlation often give poor results, especially for molecules which typically require a correlated treatment in order to predict other properties accurately. For example, a good description of multiple bonds and lone pairs generally requires a correlated method. Thus, RHF NMR predictions for molecules such as CO and acetonitrile are poor (20). Furthermore, it has recently been shown that isotropic chemical shift calculations at the RHF level are unreliable for benzenium (21) and related carbenium ions which we often encounter in catalysis. 

Implicit in the above discussion was the assumption that the geometry of the molecules under study are also determined to sufficient accuracy. Thus, we generally also need correlated methods for the geometry optimizations prior to NMR calculations. Because many of the systems we study are large, we have found that density functional theory (DFT) methods are often very useful, providing the effects of electron correlation in a computationally expedient fashion. In the following we provide several examples that demonstrate the utility of NMR calculations in the interpretation of experimental studies in catalysis. 

The first two examples both involved the creation of cationic species on an acidic zeolite. In both cases we did not need to model the interaction of the cation with the zeolite framework good agreement was obtained with just calculation of the isolated cation. Apparently, the cation is not strongly perturbed by the presence of the zeolite. Such fortunate circumstances are rare. Here we show an example of how theoretical NMR calculations can help elucidate chemistry on a basic metal oxide surface, in particular, the adsorption of acetylene on MgO (26). For this study we needed to model the active sites of the catalyst, for which there are many possibilities. It is assumed the reactive sites are those in which Mg and O are substantially less coordinated than in the bulk. Comer sites are those in which Mg or O are three-coordinate, whereas Edge sites have four-fold coordination. These sites are where the strongest binding of the adsorbates are obtained. 

For our final example of theoretical NMR in catalysis, we again turn to carbenium ion chemistry. Here we study the formation of the isopropyl cation on frozen SbF5, a strong Lewis acid (27). In contrast to the studies presented earlier, with this system we were able to experimentally measure the chemical shift tensor. Because the full tensor is naturally obtained from NMR calculations, a comparison can readily be made. In addition, for the isopropyl cation we also studied the effect the medium (in this case, the charge balancing anion) had on the chemical shift tensor. 

We have shown several examples of how theoretical NMR calculations can be used in conjunction with experimental studies to further our understanding of catalysis. The agreement between the results of the two approaches is often excellent, and in all cases shown the agreement is sufficient to aid the interpretation of the chemistry. The synergy between the theoretical and experimental approaches provides benefits beyond what either approach could provide separately. We expect theoretical predictions of NMR data will become more widely used as both theorists and experimentalists gain a better appreciation of the methods. These techniques will... 

We refer the reader to the literature for details of the DFT-ZORA approach (14-16) and its application to NMR calculations (70). 

We use generalized gradient approximations (GGA) to the exchange-correlation (XC) functional of DFT for all NMR calculations that are reported here. All current dependent terms (28) in the XC functional are neglected. The M(CO)6 and [MO4]2-, M = Cr, Mo, W, calculations (7) employed the BP86 functional (29,30). All other calculations were performed with the PW91 GGA (57). 

Table I. Molecular Geometries used for Ab Initio NMR Calculations...

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