Nuclear magnetic shielding theory

Recent Advances in Nuclear Magnetic Shielding Theory and Computational Methods... 

Jameson, C. J. Recent Advances in Nuclear Magnetic Shielding Theory and Computational Methods , in Modeling NMR Chemical Shifts, Gaining Insights into Structure and Environment (ACS Symposium Series 732) Facelli, J. C., Ed., ACS Washington DC, 1999, pp 1-23. 

III. Theory and Physical Models of Nuclear Magnetic Shielding... 

Theoretical bases of continuum models including their mathematical formulation and numerical implementation have already been discussed in the previous chapter of this book. We have therefore restricted our review to the environment effects on the NMR observables, without going into the theory of continuum models. This contribution is divided into five sections. After the Introduction, the definitions of the NMR parameters are recalled in the second section. The third section is focused on methodological aspects of the calculation of the NMR parameters in continuum models. The fourth section reviews calculations of the solvent effects on the nuclear magnetic shielding constants and spin-spin coupling constants by means of continuum models, and the final section presents a survey on the perspectives of this field. 

Another important extension of the theory concerns NMR chemical shift. Yamazaki et al. proposed a theory for computing the chemical shift of solvated molecules [17]. The nuclear magnetic shielding tensor o-x of a nucleus X can be represented as a mixed second derivative of the free energy A with respect to the magnetic field B and the nuclear magnetic moment mx ... 

Jensen, F. Basis Set convergence of nuclear magnetic shielding constants calculated by density functional methods, J. Chem. Theory Comput. 2008, 4, 719-727. 

A. Ligabue, S. P. A. Sauer, P. Lazzeretti, Gauge invariant calculations of nuclear magnetic shielding constants using the continuous transformation of the origin of the current density approach. 11. Density-functional and coupled cluster theory, J. Chem. Phys. 126 (2007) 154111. 

The expressions for the calculation of first- and second-order magnetic properties have been derived and implemented at the ZORA level [40-45] using density functional theory, and at the relativistic direct perturbation level of theory [38,39]. The fully relativistic theory of nuclear spin-spin coupling [80] and the theory of nuclear magnetic shieldings have been formulated by Pyykkd [81] and implemented at the extended Huckel level [82]. 

In order to demonstrate how a term proportional to arises in the relativistic theory, and to demonstrate how simple the relativistic theory really is, we will consider a textbook example the nuclear magnetic shielding tensor. In this case, we have... 

The GIAO method is used in conjunction with analytical derivative theory in this approach the magnetic field perturbation is treated in an analogous way to the perturbation produced by changes in the nuclear coordinates. In this framework, the components of the nuclear magnetic shielding tensor are obtained as ... 

Pulay, P. Hinton, J. F. Wolinski, K. "Efficient Imlementation of the GIAO Method for Magnetic Properties Theory and Application", Nuclear Magnetic Shieldings and Molecular Structure (NATO AST. Series C Mathematical and Physical Sciences, Vol. 386) Tossell, J. A., Ed., Kluwer the Netherlands, 1993, pp 243-262. 

In a later paper, Kromhout and Linder have reexamined the problem of calculating 0 and present a theory for calculating the London -van der Waals effect on nuclear magnetic shielding of closed shell atoms [205]. They also attempt to extend the theory to polyatomic molecules and derive two explicit expressions for the factor B in Eq. (3.24). The value of B is found to be proportional to the polarizability, a, of the atom under study, the total diamagnetic shielding constant for the closed shell atom and a function of the ionization... 

A comparison of the results for the electronic distortion theory with experiment [245 246] is difficult since especially the mean excitation energy is not easy to estimate with sufficient accuracy. Furthermore, no direct determinations of the nuclear magnetic shielding, relative to the free ions, of hydrated chloride, bromide or iodide ions have yet been performed (cf. Section 6.1). 

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