Nuclear Magnetic Resonance: Volume 17

Excerpt. © Reprinted by permission. All rights reserved. Nuclear Magnetic Resonance Volume 17A Review of the Literature Published Between June 1986 and May 1987By G. A. WebbThe Royal Society of ChemistryCopyright © 1988 The Royal Society of ChemistryAll rights reserved.ISBN: 978-0-85186-402-0ContentsCHAPTER 1 Theoretical and Physical Aspects of Nuclear Shielding By Cynthia J. Jameson, CHAPTER 2 Applications of Nuclear Shielding By Mark J. Foster, CHAPTER 3 Theoretical Aspects of Spin - Spin Couplings By Jens Oddershede, CHAPTER 4 Nuclear Spin Relaxation in Liquids By H. Weingärtner, CHAPTER 5 Solid State N.M.R. By R. Dupree, CHAPTER 6 Multiple Pulse N.M.R. By D.L. Turner, CHAPTER 7 Natural Macromolecules By D.B. Davies, CHAPTER 8 Synthetic Macromolecules By A. Bunn, CHAPTER 9 Conformational Analysis By A. Gryff-Keller and P. Szczecinski, CHAPTER 10 Nuclear Magnetic Resonance of Living Systems By P.G. Morris, CHAPTER 11 Oriented Molecules By C.L. Khetrapal, B.S. Arun Kumar and S. Raghothama, CHAPTER 12 Heterogeneous Systems By T.K. Halstead, AUTHOR INDEX, 433, CHAPTER 1Theoretical and Physical Aspects of Nuclear ShieldingBY CYNTHIA J. JAMESONA. General Theory — The general concept of nuclear shielding in the presence of electromagnetic radiation is introduced by defining dynamic electromagnetic shielding tensors which describe the linear response in an external spatially uniform periodic electromagnetic field. The diamagnetic terms do not depend on the angular frequency, ω, of the electromagnetic radiation. The dynamic paramagnetic shielding tensor is a generalization of Ramsey's definition for the static property.The magnetic field induced by the electrons at nucleus I is expressed by Lazzeretti and Zanasi as follows:[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)The external magnetic field B is the real part of B0 exp(iωt). [??] is the partial derivative with respect to time. In the first term, σP is the dynamic paramagnetic shielding tensor,[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)Zn which L and MI involve the usual angular momentum operators [??]i (RI) centered on I and [??]i at the gauge origin.[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)and |a> and |j> are the time-independent perturbed states which are functions of B. o is the same as Ramsey's, and the [??]I(ω) term is called magnetoelectric shielding. Its physical meaning is shown in the equation; by taking the scalar diadic product with the time derivative of external electric field, one obtains the magnetic field induced at the nucleus. The terms in [??]P and λI, give the magnetic fields induced at the nucleus by a time-dependent magnetic field and an external electric field, respectively. λI(ω) is the analogous definition to σP(ω), except that L is replaced by -2mcR, R being [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. [??]P(ω) takes the imaginary part, whereas σP has the real part of the complex integrals MI|j>L|a> and [??]I takes the imaginary part, while λI has the real part of the complex integrals MI|j>R|a>. The generalized treatment shows fundamental relationships among the electromagnetic properties of molecules and the sum rules obeyed by them.The dispersion (dependence on ω) of the paramagnetic nuclear shielding in H2O has been calculated and found to be significant. For example, for 17O in H2O, in ppm, with the gauge origin at the center of mass,[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)a downfield shift of 184 ppm! This theory predicts a frequency dependence of the dimensionless chemical shifts in NMR spectroscopy, analogous to the frequency dependence (dispersion) of the electric dipole polarizabilities.Is there a possibility of measuring this dispersion of nuclear shielding by conventional NMR spectroscopy? The formalism developed by Lazzeretti and Zanasi is for a magnetic field B, which is the real part of B0 exp(iωt). In the NMR experiment