NMR chemical shielding

The routine calculation of NMR chemical shifts using quantum chemical methods has become possible since the introduction of local gauge-origin methods, which provide a solution to the gauge-origin problem within approximated schemes. In our formulation, we use gauge-including atomic orbitals 

For example, in many systems, we found the GIAO-HF method to yield H-NMR chemical shifts with an accuracy of typically 0.2-0.5 For other nuclei the inclusion of correlation effects can become more impor-The computation at the GIAO-DFT level is closely related. NMR chemical shifts are calculated as second derivatives of the energy with respect to the external magnetic field B and the nuclear magnetic spin m of a nucleus N  

The equation shows that, similar to the calculation of vibrational frequencies, the response of the one-particle density matrix to a perturbation is necessary, which is in the case of NMR shieldings the magnetic field B,. Therefore, the CPSCF equations need to be solved for the perturbed one-particle density matrices (short P ). In the context of NMR shieldings, the computational effort of conventional schemes scales cubically with molecular size. 

To reduce the scaling behavior for the calculation of response properties, we focus in the following on a reformulation of the CPSCF equations in a density matrix-based scheme, so that the scaling of the computational effort can be reduced to linear for systems with a nonvanishing HOMO-LUMO gap. 

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Theoretical calculation of NMR chemical shifts is usually done by first considering the electronic current density which is induced by the external magnetic field. Once this current has been calculated the chemical shift can be obtained by application of the Biot-Savard law, which describes the magnetic field created by it. The strength of this field at the position of an atom represents the NMR chemical shielding of this atom. 

This shows that the second and further solvation shells still have a non-negligible effect on NMR chemical shielding constants through the long-range electrical field they create. The approximation of an isolated molecular cluster in vacuo is valid for large clusters only this eventually makes determination of the shieldings of all protons computationally much more expensive than the fully periodic ab initio calculation. 

Hyperpolarizabilities Magnetic dipole moment Magneticsusceptibility NMR chemical shielding... 

It could appear interesting to apply Chestnut s approximate infinite-order perturbation-theory prescription for isotropic NMR chemical shieldings (25) in order to extrapolate our HF//MP2 and MP2//MP2 results to higher orders of perturbation theory. However, due to the feet that reference MP3-GIAO and MP4-GIAO results are not available, even for C6H5F, we did not feel that the use of ratios, derived from MPn-GIAO calculations on smaller moleules, would be sufficiently well justified. 

The experimentally determined dependence of the Rb NMR chemical shielding on ionic distance is shown in Figure 9A. Upon initial inspection, it can be seen that the halides form three parallel lines. The dependence of the 87Rb shielding on the Rb-X distance is linear for all three halides. The slopes are very similar to each other (about 400 ppm/A), indicating that the sensitivity of the shielding to interionic distance is probably a property of Rb and is independent of the identity of the halide and the other cation. The three halides form three separate but parallel lines due to an offset caused by changing the identity of the halide. 

Ab initio calculations of 29Si and 13C NMR chemical shielding tensors have been used as an aid in the interpretation of experimental results aimed at elucidating the role of alkoxyalkylsilanes as external electron donors in Ziegler-Natta catalysis of propene. The results support a model in which dialkoxydialkylsilanes are loosely attached to two adjacent magnesium ions on the surface of magnesium chloride, but trialkoxyalkylsilanes are attached primarily by only one magnesium ion. 

Ab Initio Calculations of 31P NMR Chemical Shielding Anisotropy Tensors in Phosphates The Effect of Geometry on Shielding... 

In the past fifty years, the NMR Chemical Shielding have evolved from corrections to the measurement of nuclear magnetic moments as quoted from Ramsey s 1950 original papers (Phys. Rev. 77, 567 and 78, 699), to one of the most important tools for structural elucidation in many branches of chemistry. There are no simple relationships between molecular structure and chemical shifts. Their dependence on the molecular electronic and geometrical structure can be derived via complex quantum mechanical equations. 

This volume was developed from the second international symposium on NMR chemical shifts. This meeting was organized by the editors at the 216th National Meeting of the American Chemical Society, Boston, Massachusetts, August 23-26,1998, and was cosponsored by the ACS Divisions of Computers in Chemistry and Physical Chemistry. The symposium included four extended lectures by Jameson, Ando, Oldfield, and Nicholas, which are included in this volume as Chapters 1-4, respectively. These lectures provide a convenient review of the current state of the art in the calculation of the NMR chemical shielding (Jameson, Chapter 1), and its application to different areas of chemistry polymers (Ando), biomolecules (Oldfield), and catalysis (Nicholas). 

P. B. Karadakov and K. Morokuma, ONIOM as an efficient tool for calculating nmr chemical shielding constants in large molecules, Chem. Phys. Lett., 317 (2000) 589-596. 

The now wide-spread use of solid state NMR techniques such as magic angle spinning (MAS) led to a need for calculations of NMR parameters such as chemical shifts and quadrupole coupling constants. A notable achievement this century has been the development of a method to calculate NMR chemical shielding in periodic solids. This will be described in the following section along with developments in the calculation of other properties. 

D. Chesnut and B. Rusiloski, A study of NMR chemical shielding in water clusters derived from molecular dynamics simulations, J. Molec. Struct. (THEOCHEM), 314 (1994), 19-30. 

Influence of stacking interactions on NMR chemical shielding tensors in benzene and formamide homodimer as studied by HF, DFT and MP2 calculations81... 

The goal of the present work is to obtain a consistent structural model for a microemulsion system. In particular, we are interested in carrying this model down to the molecular level so that the intermolecular effects which are responsible for the stability of these systems can be elucidated. We have studied the system consisting of water, SLS and MMA with and without n-hexanol or n-pentanol. We have determined the phase boundaries of the isotropic microemulsion and Lj phases and determined how these are affected by surfactant concentration and alcohol chain length. Measurements were also made of the vapor pressure of MMA over these systems to determine the concentration of MMA in the water surrounding the microemulsion droplets. From these data, the energetics of transfer of the MMA from aqueous to micellar solution were determined. Finally, a 1,C NMR chemical shielding study was performed to find how the MMA and the alcohol were distributed within the microemulsion. 

Zhang, Y., Oldfield, E. Solid-state 31P NMR chemical shielding tensors in phosphonates and bisphosphonates A quantum chemical investigation. J. Phys. Chem. B 2004,108,19533 40. 

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