NMR shielding constant

Chemical shifts are reported in parts per million (ppm) and are the difference between screening constants in the molecule and that in a reference molecule such as tetrameth-ylsilane (TMS) for proton and C NMR spectra. The chemical shift 5, of nucleus i is defined by 

Many standard quantum-chemistry programs allow calculation of NMR shielding constants and spin-spin coupling constants. 

Calculations of proton chemical shifts that used several common density functionals and basis sets on a test set of compounds together with Unear scaling of the results recommended WP04/cc-pVDZ(rms error 0.115 ppm, m = 1.020, ft = 31.84), WP04/6-31G (rms error 0.12 ppm, m = 1.033, ft = 32.02), B3LYP/6-31G (rms error 0.13 ppm. 

One can use calculated NMR shielding constants and /h h values to help assign the structure of a new compound by seeing which of several possible structures has a calculated spectrum in good agreement with the observed one. 

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Malkin, V. G., Malkina, O. L., Salahub, D. R., 1993, Calculations of NMR Shielding Constants by Uncoupled Density Functional Theory , Chem. Phys. Lett., 204, 80. 

In the first, quantum mechanics can be used to calculate the NMR coupling constant between two nuclear spins in the molecular environment or the NMR shielding constant. Jensen [8] in Chapter 10 of the reference provides a comprehensive introduction to the methods for calculating these molecular properties. The NMR coupling constant, KAB, is related to the second derivative of the energy with respect to the internal magnetic moments, /u, arising from the nuclear spin of the two atoms, A and B. 

Table 1.29Si NMR shielding constants a and chemical shifts 6 in ppm and their localized contributions for SiX4 (I) and XSifNH (II)...

Case58 investigated the effect of ring currents on NMR shielding constants by means of the DFT calculations. The studied rings included the ones commonly found in proteins and nucleic acids. The shielding constants were calculated for methane molecule placed in several positions relative to the ring. The calculations provided data needed to derive structural parameters from measured chemical shifts in proteins and nucleic acids. 

The second kind of NMR isotope effect has its origin in the mass differences between isotopes. In NMR mass effects show up as isotopic differences in NMR shielding constants and coupling constants. Their theoretical rationalization is... 

Table 5. The NMR shielding constant and shielding polarizabilities of the xenon atom calculated at the Hartree-Fock level using the Drrac-Coulomb Hamiltonian (SR + SO), its spin-free version (SR) as well as the non-relativistic Levy-Leblond Hamiltonian. The shielding constant is given in ppm and shielding polarizabilities in ppm/(au field2) (1 a.u. field = 5.14220642X 10" V...

The experience gained in these studies has been invaluable for the development of the BERTHA molecular code much of the material of the present article was first presented in [29] and [30], together with applications to the study of magnetic and hyperfine interactions in atoms and small molecules, NMR shielding constants for H2O and NH3, and P-odd interactions in chiral molecules such as CHBrClF. A detailed study of the water molecule [31] examined the convergence of the DHF and DHFB calculations with a series of uncontracted correlation consistent basis sets due... 

J. Mason, Conventions for the reporting of nuclear magnetic shielding (or shift) tensors suggested by participants in the NATO ARW on NMR shielding constants at the University of Maryland, College Park, July 1992. Solid State Nud. Magn. Reson., 1993, 2,285-288. 

Because of the difficulty in evaluating the paramagnetic contribution, ab initio calculations of NMR shielding constants are few in number and limited to rather small molecules. Jaszunski and Sadlej used a variational perturbation approach with an ab initio SCF wave function of H20 and found aH = 28.3 ppm. [M. Jaszunski and A. J. Sadlej, Theor. Chim. Acta, 27, 135 (1972).] The known proton screening constant in H2 is 26.6 ppm,6 and gaseous H20 shows a proton chemical shift of 3.6 ppm relative to gaseous H2 hence the experimental H20 proton shielding constant is 30.2 ppm. 

The NMR shielding constant external magnetic field at the nucleus by the presence of electrons. 

In experimental practice the isotropic NMR shielding constant a is replaced by the NMR chemical shift 8 and the spin-spin coupling constant JKL is used instead of the reduced spin-spin coupling constant Kkl. 

Solvent effects on nuclear magnetic properties are well known, and have been studied for a long time. Both the NMR shielding constant and the nuclear spin-spin coupling constant depend on the electronic structure of the whole system. This means that both are sensitive to the weak intermolecular interactions between solute and solvent molecules. 

The possibility of calculating 33S NMR shielding constants has made it possible to obtain a better insight into the origin of substituent effects on 33S NMR in 2-substituted ethanesulphonates.35 Sulphur isotropic absolute shielding... 

As a further example on the use of the PE scheme, we discuss the calculation of NMR shielding constants for molecules in solution. More specifically, we will focus on the case of pyridine in water solution [44], The NMR calculations presented here are based on the use of the PBEO functional combined with the 6-311++G(2d,2p) basis set. The PE-DFT results for the NMR... 

C. van Wiillen and W. Kutzelnigg, Chem. Phys. Lett., 205, 563 (1993) W. Kutzelnigg, C. van Wiillen, U. Fleischer and R. Franke, in Proceedings of the NATO Advanced Workshop on The Calculation of NMR Shielding Constants and Their Use in the Determination of the Geometric and Electronic Structures of Molecules and Solids, 1992. 

This model approximation is known as the cluster approach. The fragment extracted from a zeolite framework is terminated with hydrogen atoms. Such method has been used with success for the estimate of properties such as frequencies of vibration, NMR shielding constants, or reactivity. Another mandatory reason of the use of this method was the too heavy computational cost to simulate larger systems. 

Fig. 4.6. Comparison of calculated - Si NMR shielding constants and experimental Si chemical shifts (8exp) for SiF and other silicon compounds (after Tossell and Lazzeretti, 1986 see text for discussion).

Table 4.16. Calculated Si NMR shielding constants for HjSiCOHij and the oligomers (H SilnO, n = 2—4...

Tossell, J. A., and P. Lazzeretti (1987a). Ab initio calculation of oxygen nuclear quadrupole coupling constants and oxygen and silicon NMR shielding constants in molecules containing Si-O bonds. Chem. Phys. 112, 205-12. 

The mixed derivative of an external and an internal magnetic field (nuclear spin) is the NMR shielding constant, [Pg.127]

Properties depending on the response to electric and/or magnetic fields such as optical properties and NMR shielding constants have only been implemented relatively recently. A way to calculate electrical polarization in periodic solids, for example, was only found in the 1990s. 

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