Methods for Chemical Shift Calculations

In principle, a chemical shift calculation represents a perturbation theory, because of the presence of an external field Bz and magnetic moments due to the dipole character of nuclei. Therefore, perturbations to the Hamiltonian and the wave function have to be considered. The next important point is that the origin of the vector potential Az is not fixed due to the relation Bz = rot Az- Any change of the gauge origin Rq should not change any measurable observable. Therefore, a gauge transformation of the wave function 1%) and Hamilton operator h is essential 

Another major point in which the theoretical methods differ is the quantum chemical approach to solve the operator equation of the Hamilton operator itself. The most important schemes are Hartree-Fock self consistent field (HF-SCF), density functional theory (DFT) and multi-body second order perturbation theory (MP2). Different combinations have been established, so for instance GIAO-SCF, GlAO-DI I, (,IA()-MI 2, or DF I-IGLO. Most precise measurements on small systems were done with coupled cluster methods, as for instance GIAO-CCSDT-n.  

The bond polarization theory is a semi-empirical approach applied within the 

According the Ramsey expression, the chemical shift tensor can be consi- 

The correlation coefficient obtained from the parameter calibration is J = 0.994 with a standard deviation of SD = 7.2 ppm. If the parameters 

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More recently, solid-state NMR has seen enormous progress in absolute structure detennination of solids, and methods have been introduced that complement the more traditional powder diffraction methods based on X-rays or neutrons. Many recent studies have also shown that plane wave DFT calculations can accurately reproduce measured NMR chemical shifts in solids. This complementary approach has been used to vaUdate and refine a number of crystal structures [38 2], The DFT structure validation requires a structural starting point for chemical shift calculations, so therefore it must be coupled with CSP methodology for generation of such candidates. 

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 ... 

Answer Chemical shift calculations for nanoscale semiconductors by DFT methods and comparison with experimental results have recently appeared [140], and while quite challenging hold much promise. 

K. Wolinski, J. F. Hinton and P. Pulay, Efficient implementation of the gauge-independent atomic orbital method for NMR chemical-shift calculations. J. Am. Chem. Soc., 1990, 112,8251-8260. 

C NMR spectra are recorded for a low molecular weight atactic PP dissolved in a variety of solvents over a broad temperature range [293 - 393 K). Comparison of chemical shifts calculated via the y effect method with the observed resonances, whose relative chemical shifts are solvent independent, permits their assignment to most of the methyl heptad, methylene hexad, and methine pentad stereosequences. Agreement between observed and calculated chemical shifts requires y effects, he., upfield chemical shifts produced by a gauche arrangement of carbon atoms separated by three bonds, of ca. - 5 ppm for the methyl and methine carbons and ca. - 4 ppm for the methylene carbons. 

Although there have been many published reports of chemical shift calculations neglecting electron correlation, it is well established that electron correlation is important for carbenium ions, triple bonds, and other systems sensitive to correlation. Currently, Gauss MP2 method (distributed as part of ACES II) (85) is the most extensively validated methodology for carbenium ion chemical shift calculations. 

Fifolt [ 130] reported this chemical shift additivity method for fluorobenzenes in two deuterated solvents d6 acetone and d6 dimethyl sulfoxide (DMSO) Close correlations between experimental and calculated fluorine chemical shifts were seen for 50 compounds Data presented in Table 18 result from measurements in deuterochloroform as (he solvent [56] Fluorine chemical shifts calculated by this additivity method can be used to predict approximate values for any substituted benzene with one or more fluorines and any combination of the substituents, to differentiate structural isomers of multisubstituted fluorobenzenes [fluoromtrotoluenes (6, 7, and 8) in example 1, Table 19], and to assign chemical shifts of multiple fluorines in the same compound [2,5 difluoroamline (9) in example 2, Table 19] Calculated chemical shifts can be in error by more than 5 ppm (upfield) in some highly fluonnated systems, especially when one fluonne is ortho to two other fluorines Still, the calculated values can be informative even in these cases [2,3,4,6-tetrafluorobromobenzene (10) in example 3, Table 19]... 

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