Nuclear Magnetic Resonance Volume 19

A Review of the Literature Published Between June 1988 and May 1989

By G. A. Webb

The Royal Society of Chemistry

Copyright © 1990 The Royal Society of Chemistry
All rights reserved.
ISBN: 978-0-85186-422-8

Contents

CHAPTER 1 Theoretical and Physical Aspects of Nuclear Shielding By Cynthia J. Jameson,
CHAPTER 2 Applications of Nuclear Shielding By I.P. Gerothanassis,
CHAPTER 3 Theoretical Aspects of Spin-Spin Couplings By Jens Oddershede,
CHAPTER 4 Applications of Spin-Spin Couplings By K. Kamienska-Trela and Z. Biedrzycka,
CHAPTER 5 Nuclear Spin Relaxation in Liquids By H. Weingärtner,
CHAPTER 6 Solid State N.N.R. By C.J. Groombridge,
CHAPTER 7 Multiple Pulse N.M.R. By L.Y. Lian,
CHAPTER 8 Natural Macromolecules By H.G. Parkes and D.B. Davies,
CHAPTER 9 Synthetic Macromolecules By Graeme Moad and R. Ian Willing,
CHAPTER 10 Conformational Analysis By C. Jones,
CHAPTER 11 Nuclear Magnetic Resonance of Living Systems By P.G. Morris,
CHAPTER 12 Oriented Molecules By C.L. Khetrapal, K.V. Ramanathan, and A. C. Kunwar,
CHAPTER 13 Heterogeneous Systems By T.K. Halstead,
AUTHOR INDEX, 525,

CHAPTER 1

Theoretical and Physical Aspects of Nuclear Shielding

BY CYNTHIA J. JAMESON

1 Theoretical Aspects of Nuclear Shielding

A. General Theory — The magnetic field dependence of nuclear magnetic shielding was predicted by Ramsey in 1970,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

Odd powers of B vanish because the magnitude of the shielding must be independent of the direction of the magnetic field. Earlier attempts to observe and calculate the magnitude of the field dependence of σ have been reviewed in Vol. 9 of this series. Instead of using fourth order perturbation theory, one could characterize the field dependence of a by a finite field calculation using several values of B which are chosen such that the contributions of higher powers of B to eq. (1) are negligible.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where σ(B) is evaluated at each value of B by taking

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

This finite difference method was applied by Boucekkine et al. to H- ion and the results are shown below, giving 1/6 τ = 2.25 x 10-13 T-2.

The limiting value [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] agrees with coupled Hartree-Fock calculations on H- ion. The method needs to be applied to a nucleus such as 59Co where τ(2) may be large enough to be observed experimentally.

The exact relativistic analogues of the non-relativistic hyperfine operators for the interaction of an electron with a nuclear spin have been derived. These relativistic operators are valid for spatially extended descriptions of both the nuclear charge and the nuclear magnetization. Further, the contributions to the hyperfine operator which are in addition to these relativistic terms have been derived. These theoretical developments provide the necessary foundation for the recently developed relativistic theory of nuclear magnetic shielding (see Vol. 13, this series for a review). For first and second row elements, relativity hardly affects the hyperfine structure but for atoms of higher nuclear charge there will be significant relativistic effects. Pyper’s theory has so far been used to calculate hyperfine structure components for atoms with one impaired electron. We look forward to applications of this theory to shielding of Pt, Hg, Tl, and Pb for which there are much experimental data to interpret.

Parity non-conservation leads to energy differences and intrinsic nuclear magnetic shielding differences between left and right isomers of a chiral molecule (see Vol. 17 of this series for a review). These effects become more important for high atomic numbers. Thus, a calculation of the difference in energy between left- and right-handed twisted ethylene-type molecules containing Pt and Pb had been carried out within a relativistic framework. Calculations performed with a relativistically parameterized extended Hückel method show a difference of a few mHz in the metal resonance frequency of enantiomers containing Pt or Pb. This is too small to observe. Even in highly twisted plumbylene (twist angle 65°) the intrinsic chirality of the electronic wavefunction is very small.

B. Ab Initio Calculations — A review of recent ab initio calculations of nuclear shielding has been published by Chesnut.

Calculations on some portion of the nuclear magnetic shielding surface are becoming more common. For example, the proton shielding in H2 has been calculated for R = 0.476 to 1.587 Å (Re = 0.741 Å). 13C and 17O shielding in CO have been reported for 0.8 – 1.25 Å (Re = 1.141 Å), and 13C shielding in CO32- ion at 1.24 – 1.315 Å (Re = 1.29 Å). The results confirm earlier conclusions about the shielding surface, that a is strongly R-dependent in diatomic molecules, and that derivatives of the shielding with respect to bond stretch are dominated by the shielding tensor component which is perpendicular to the bond. 17O shielding in H2BOBH2 at various B-O-B angles, 29Si and 17O in H3T-O-TH3 (T,T’ = Al, Si, P) as a function of T-O-T’ angle, provide models for exploring the well-established empirical linear relation between 29Si chemical shifts and T-O-T bond angles in zeolites and other silicates. We discuss this further under semiempirical calculations.

The so-called mixed method of Flament et al., reviewed in Vol. 18 of this series, has provided the best results yet for CO and H2O in comparison with experiment. The recent results for 13C and 17O in CO are shown in Table 1 and 2, and compared with other ab initio calculations.

In this method both electron correlation and gauge effects are taken into account in a two-step calculation (1) The electronic ground state 10) is obtained by an SCF calculation (using HONDO), followed by configuration interaction (using CIPSI). (2) The perturbed state is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where the gauge factor [??] is a function of the electronic coordinates. This factor absorbs the effects of gauge changes, assures gauge-invariance at any basis set size. The operator [??] introduces the magnetic perturbation for a given choice of gauge, is a sum over all terms involving states generated by all mono-, di-, and tri-excited determinants which are orthogonal to |0> and which interact with it by means of the paramagnetic shielding operators [??] and [??]N/rN3. Step (2) involves solving a system of linear equations. As with otherab initiomethods, satisfactory values of shielding require calculations with large basis sets. One conclusion of Flament et al. is that a good value for σe can be achieved only with inclusion of electron correlation. As can be seen in Table 1 and 2, their results are closer to experiment than the results from other ab initio methods applied to CO.

GIAO (Gauge-Including Atomic Orbitals) and IGLO (Individual Gauge for Localized Molecular Orbitals) are variants of the CHF (Coupled Hartree Fock) approach which unlike the conventional CHF which uses a single unique gauge origin for the calculation of a nuclear shielding, use different gauge origins for different orbitals explicitly by means of an experimental gauge factor. Like the LORG (Localized Orbital Local Origins) method, these variants succeed in removing an overall gauge dependence of the calculated results for any size basis set and in damping the contributions from distant core electrons. Satisfactory results still require large basis sets, of course.

Conventional CHF calculations of the shielding of all nuclei in CX and XCY molecules (X, Y = O, S, Se) have been reported by Jokisaari, Lazzeretti, and Pyykkö. These are compared with their results from semi-empirical REX calculations in the same molecules and also for (X, Y = Te). In Tables 3,4,5 and 6, their ab initio results are compared with other ab initio calculations and with experiment.

Other 33S calculations are in SF4 molecule, giving [??] = 292.7 ppm by conventional CHF compared to [??] = 128.7 ppm by IGLO. There is no experimented shift to compare with. There are also conventional CHF calculations for 17O in NO3-, CO32-, and BO33-, [??] = -19.3 ppm (-112.1 ppm expt), 182.1 ppm (115.9 ppm expt), emd 239.1 ppm respectively. The experimental data are based σ(17OH2, l) = 307.9 ppm on the 17O absolute shielding scale and σ(H2O, l) – σ(NO-3) = 420 ppm and σ(H2O, l) – σ(CO32-) = 192 ppm. In both cases the calculations give a too shielded 17O, that is, the paramagnetic term is not large enough. There are intermolecular effects included in the experimental values, and these are usually deshielding effects. Thus, the real discrepancies between calculation and experiment may not be as large as they seem.

29Si nuclear shielding calculations can now be compared with experiment using the recently published absolute shielding scale (discussed in Section 2E). The GIAO method has been used to calculate Si shielding tensors in 28 silicon compounds. Some of these are compared to previous ab initio calculations in Table 7.

While the IGLO results have reasonably good agreement with experiment, the other calculations still have deviations of 50 to 100 ppm for most species except SiH4. Clearly the basis sets used, e.g., 6-31G*,55 are inadequate for this property. These results also show why it is necessary to establish absolute shielding scales. While GIAO calculations at the 6-31G* level appear to reproduce the trends in the 29Si chemical shifts in the system of related fluorosilanes, SiHnF4-n, quite well, the absolute shieldings all differ from experiment by about 50 ppm. In the early days of shielding calculations a discrepancy of only 50 ppm out of an absolute shielding of 450 ppm was quite good. As we have seen in this chapter, in the past few years, theoretical results have been improving dramatically. The IGLO results for Si have come sufficiently close to SiH4 and SiF4 experimental data in the gas phase that it now becomes necessary to look at SiH3F, SiH2F2 and SiHF3 under the same experimental conditions in order to see how good the IGLO results really are. These results are plotted in Fig. 1. Corrections for the intermolecular effects on the latter three compounds are expected to bring the experimental results closer to theory. It should be noted that the use of sufficiently large basis sets are essential for the success of any of these methods. A discussion of the minimum requirements for second row atoms is given by Fleischer et al.

IGLO calculations of 13C shifts in proposed structures of C4H7+, C4H42+, and C4Me42+ ions are said to favor a puckered rather them planar structure for the latter two, and a cyclobutyl rather than a cyclopropylcarbinyl structure for the former. However, by itself, better agreement of chemical shifts with one structure compared to another does not necessarily constitute sufficient proof, even when calculated chemical shifts differ by about 50 ppm. First of all, the optimized geometry for the isolated ion may not be accurate enough for the ion in solution. Since the shielding is very sensitive to geometry (for 13C nuclei, shielding changes of several hundred ppm per Angstrom are common), the calculated values for the two different structures could both be in error by unknown amounts. Even when the geometry is well-known experimentally with bond lengths good to 10-4 Å, agreement between experimental and calculated shielding could be no better than the examples in Table 1. Secondly, the rovibrational averaging corrections may not be small. These could be large when, as reported, the potential surface in the vicinity of the stationary points is extremely flat. In most cases these corrections are deshielding (although not enough information is available for ionic species). Thirdly, the intermolecular effects on the shielding have not been taken into account. These could be very important in the case of ionic species. If, as is usually the case, the intermolecular effects and rovibrational corrections are both deshielding, then one should seek agreement with a less positive chemical shift than the experimentally observed shift instead of seeking a perfect match with one of the calculated values. This method of proof of a structure is especially tenuous when only DZ (double zeta) basis sets are employed, as in one example. It is also unfortunate when reported calculations give only chemical shifts rather than the calculated shielding, especially when the calculated reference value used to convert the calculated shieldings to chemical shifts is not reported.

A computationally efficient new implementation of the LORG method (reviewed in Vol. 16, this series) has been reported. In this modification, the paramagnetic response to a magnetic field is obtained by means of an iterative method for large sets of linear equations instead of the previously described direct Hermitian diagonalization of the matrix (A-B) which include the terms in the two-electron integrals over the MOs. The new implementation has been shown to be more computer time-efficient and also makes no more demands in terms of computer memory than closed-shell SCF MO calculations on the molecule. As an example, all the 13C shielding tensors for 2-norbomenone have been calculated. The results for the isotropic shielding are shown in Figure 2. It should be expected that rovibrational corrections together with intermolecular corrections will adjust all points towards the right (that is, the experimental values in CDCl3 solution are deshielded compared to the isolated rigidgeometry molecule). In this light, the LORG calculations are in best agreement with experiment for the most shielded environments of carbons 1, 3, 4, and 7, somewhat better than for the less shielded environments of carbons 2, 5, and 6. These results are encouraging. The overall computational effort in obtaining all the shieldings in this molecule is found to be comparable to obtaining a second order Moller-Plesset (MP2) energy for the same system.

The DNA bases are molecules of comparable size to 2-norbomenone. IGLO calculations have been reported for the 8-11 heavy nuclei in each of the cytosine, thymine, uracil, adenine, and guanine molecules. All the 13C and 14,15N shielding tensors and magnetic susceptibilities, as well as the shifts in the 13C and 14,15N NMR spectra upon protonation have been calculated by Schindler. The directions of the principal axes of the shielding tensors are characteristic of the C or N nuclear site type. The most shielded component ou is perpendicular to the molecular plane (except for CH3 and NH2 sites, of course, for which they are along the C-CH3 or the C- NH2 bond). Of the two in-plane components for the C=O carbons the σ22 axis is pointed roughly towards the center of the ring whereas for the =CH carbons the σ33 axis is pointed towards the center of the ring. The N shielding tensors have σ22 directed into the ring for pyridine-like N sites, while this direction corresponds to σ33 for the pyrrole-like sites. Comparisons with experiment is problematic due to complete lack of gas phase or oriented molecule data. Chemical shifts in solution (in DMSO) are available for 13C, nitrogen shifts are available only for adenine. Nitrogen NMR data are available for the corresponding nucleosides, but these have unknown shifts from the bases themselves. Furthermore, pyrrol e-type and pyridine-type nitrogens are known experimentally to have intermolecular effects which are of opposite sign. Schindler also found that pyridine-like sites and pyrrole-like sites have different basis set dependencies. There have been earlier calculations on these pyrimidine and purine bases, using the GIAO method, but the basis sets used were rather small, leading to unreliable results. Typically, the isotropic shieldings obtained earlier are more shielded (poorer results for paramagnetic terms) than the IGLO results; the tensor components are more widely deviating than the isotropic averages. This is not unexpected for it has been shown that individual tensor components from small basis set calculations are generally unreliable. Schindler has found that polarization functions on atoms other them H are absolutely necessary for calculations of shielding. Experimental shielding tensor components for 13C, N, and 17O in these molecules in solid Ar at 4-20 K would be very helpful in assessing the quality of these IGLO calculations.

(Continues…)Excerpted from Nuclear Magnetic Resonance Volume 19 by G. A. Webb. Copyright © 1990 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
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