Nuclear Magnetic Resonance Volume 14

A Review of the Literature published between June 1983 and May 1984

By G. A. Webb

The Royal Society of Chemistry

Copyright © 1985 The Royal Society of Chemistry
All rights reserved.
ISBN: 978-0-85186-372-6

Contents

Chapter 1 Theoretical and Physical Aspects of Nuclear Shielding By Cynthia J. Jameson,
Chapter 2 Applications of Nuclear Shielding By G. E. Hawkes,
Chapter 3 Theoretical Aspects of Spin–Spin Couplings By A. Laaksonen,
Chapter 4 Applications of Spin–Spin Couplings By D. F. Ewing,
Chapter 5 Nuclear Spin Relaxation in Liquids and Gases By H. Weingärtner,
Chapter 6 Solid State N.M.R. By P. S. Belton, S. F. Tanner, and K.M. Wright,
Chapter 7 Multiple Resonance By H. C. E. Farlane and W. McFarlane,
Chapter 8 Natural Macromolecules By D. B. Davies,
Chapter 9 Synthetic Macromolecules By A. V. Cunliffe,
Chapter 10 Nuclear Magnetic Resonance of Living Systems By P. G. Morris,
Chapter 11 N.M.R. of Paramagnetic Species By K. G. Orrell,
Chapter 12 N.M.R. of Liquid Crystals and Micellar Solutions By O. Söderman,

CHAPTER 1

Theoretical and Physical Aspects of Nuclear Shielding

BY CYNTHIA J. JAMESON

1 Theoretical Aspects of Nuclear Shielding

A. Ab Initio Calculations. – As discussed in the previous volume of this series, calculations of shielding of nuclei of high atomic number have to be done with a relativistic theory. The detailed results of relativistic random phase approximation calculations described in a paper reviewed earlier are provided in tables for atoms and ions with closed 1s, 2p, 3p, 3d, 4p, 4d, and 5p shells. The tables include all ions in these sequences with nuclear charge up to Z = 56 and a representative selection of ions with 56 <Z ≤92.

Further applications are reported using the Individual Gauge for Localized (molecular) Orbitals (IGLO) method described earlier, which is essentially a coupled Hartree–Fock type of calculation but one in which different gauge origins are chosen for different localized molecular orbitals. The use of localized molecular orbitals allows the contributions to the total shielding to be partitioned into orbital contributions, so that the specific role played by the lone pairs on the atom in question and orbitals centred on neighbouring atoms can be discerned. In the most recent application, all shielding tensors are calculated with fairly good basis sets for N2, HCN, CO, C2 H2, CO2, NNO, OF2, O3, and FNO molecules. There is still some tendency to overestimate the paramagnetic term in several instances.

In addition to the values calculated at re, shown in Tables 1 and 2, shielding values have been calculated for configurations slightly displaced from the equilibrium one, from which one can calculate derivatives of nuclear shielding. For N2 and CO the nuclear shielding is calculated at two internuclear separations r0 and re, which values the authors unfortunately failed to include in their tables. For CO r0 = 1.1308 and re = 1.1283 Å, so we may calculate ([partial derivative]σC/[partial derivative]Δr)e = -600 p.p.m. Å-1 (which may be compared with the value obtained from temperature dependent chemical shift measurements in the gas phase taken to the zero pressure limit: -225 [+ or -] 45 p.p.m. Å-1) and ([partial derivative]σO/[partial derivative]Δr)e = 1200 p.p.m. Å-1). A similar value of r0 – re for N2 gives ([partial derivative]σN/[partial derivative]Δr)e = 1200 p.p.m. Å-1) = -1000 p.p.m. Å-1) (which may be compared with -775 [+ or -] 90 p.p.m. Å-1) from gas phase measurements). For ozone, the variation of the calculated 17O shielding ([partial derivative]σN/[partial derivative]Δr)e = 1200 p.p.m. Å-1) = -2.01 x 104 and – 1.89 x 104 p.p.m. Å-1 for the end and central oxygen respectively. The variation with angle is not obtained at the equilibrium bond length, nevertheless, ([partial derivative]σO/[partial derivative]Δα) = -600 and -1750 p.p.m. rad-1 at r = 1.2 Å for the end and central oxygen respectively. The authors also note that in O3 the paramagnetic contributions come mainly from the lone pairs on the respective oxygen atoms, unlike CO2 and NNO in which they result mainly from the bonds interacting with the antibonding π* and only a little from the lone pairs. Ozone appears to be an exceptional molecule. Experimental data in the zero pressure limit together with a good absolute shielding scale for 17O are essential in order to check the predictions of the theory. For 1H nuclei and for some 13C nuclei in these molecules, agreement with experimental shielding is quite good. However, for others, discrepancies between calculated and experimental values indicate that the paramagnetic contributions tend to be overemphasized by the theory.

The coupled Hartree–Fock and the self-consistent configuration interaction (SCF-CI) methods have been applied to the H2O, H3O+, and OH- systems. In the SCF-CI scheme, both the unperturbed zeroth order wavefunction and the first order wavefunction are expanded in all singly and doubly excited singlet configuration state functions. 1H shieldings in H2O, H3O+,and OH- are respectively 29.3, 20.7, and 41.4 p.p.m. with the SCF-CI method; 17O shielding values are respectively 295.8, 330.4, and 231.1 p.p.m. The CHF method gives somewhat smaller shieldings for both 1H and 17O. Theory predicts that the 1H and 17O resonance signals shift in opposite directions in the series H3O+, H2O, OH-. Comparison with experiment is not straightforward since no gas-phase data in the zero-pressure limit are available, nor are there any spin-rotation constants measured in a molecular beam or in the gas phase. Condensed phase chemical shifts cannot easily be corrected for H3Q+-solvent (or OH- -solvent) interactions and for the contributions from counterions and H2O molecules in the hydration sphere. From the spin-rotation constant, 1H shielding in the H2O molecule is 30.052 [+ or -] 0.015 p.p.m. With an estimated gas-to-liquid shift, the approximate value for 17O shielding in the H2O molecule is 334 [+ or -] 15 p.p.m. These are to be compared with the theoretical values of 29.3 p.p.m. and 295.8 p.p.m., respectively. Other calculated values for shielding in H2O were reviewed in Volume 12 of this series. In this connection, P. Lazzeretti has kindly brought attention to this reporter’s error in the comparison of the off-diagonal components for 1H shielding in that volume. When the different directions of the axes used by the authors are properly taken into consideration, after the transposition and change in sign, the two sets of numbers can be compared. The σxz and σzx components are -8.97 and -10.12 p.p.m. by Höller and Lischka’s calculations, to be compared with -8.872 and -10.247 p.p.m. by Lazzeretti and Zanasi. The agreement is excellent.

Another CI approach to the calculation of nuclear shielding involves a sum over states (SOS-CI). This perturbation technique considers all singly excited configurations and, at the same time, introduces doubly excited configurations in a restricted way. Application of this method to several molecules gives mixed results.

For the compounds HN=NH, HP=NH, HP=PH and HAs=AsH, there is a strong geometrical dependence of the paramagnetic term in the shielding of all nuclei. The N or P nucleus in the trans isomer is less shielded than in the cis. The 1H in the trans is less shielded than in the cis isomer for hydrogens bonded to N; the reverse is true for hydrogens bonded to P. In all cases, the N and P nuclei are deshielded relative to the bare nucleus. Unfortunately, there are no experimental values to compare with. Related molecules with various substituents replacing H are known; for example, (SiMe3)3 C — As=As — C(SiMe3)3 is a stable molecule. In the diazenes, diphosphenes, and phosphazenes, (RN=NR’, RP=PR’, RN=PR’) the N and P nuclei are drastically deshielded relative to NH3 and PH3, respectively, which agrees qualitatively with the theoretical results. However, observed relative shieldings in cis and trans isomers for R, R’ ≠ H go in the opposite direction to that predicted by the calculations. The authors attribute this to substituent effects.

The effect of an external electric field on nuclear shielding is usually calculated in a multiple perturbation scheme, involving the magnetic field, the nuclear moment, and the electric field. A simple approach to this problem is suggested, in which only the paramagnetic shielding term is included. For nucleus A in a diatomic molecule AB at internuclear separation R, with the internuclear vector along the direction of the electric field, E:

[MATHEMATICAL EXPRESSION OMITTED] (1)

in which

σ(0)A(R) = const(ab) (2)

σ(1)A(R) = const[- ac + μ1(R)/b] (3)

σ(2)A(R) = const[- ac(1/e2ZA)(dμ1/dR) – 2μ1(R)c + μ2(R)b] (3)

where

a = μ0(R) – eZBR (5)

b = ZB/R2 + (1/e2ZA)(d W0/d R) (6)

c = (1/e2ZA)(dμ0/dR) + (1/e) (7)

and const stands for a factor involving only fundamental constants. Note that all of the contributions are expressible in terms of dW0/dR, (the derivative of the adiabatic potential in the absence of an electric field), the dipole moment μ of the molecule, and its derivatives with respect to bond extension:

[MATHEMATICAL EXPRESSION OMITTED] (8)

Here, μ0, μ1, and μ2 can be identified as the permanent dipole moment in the absence of the field, the longitudinal polarizability (α[parallel]), and the longitudinal first and second hyperpolarizabilities of the molecule in a field along the direction of the internuclear axis, and dμ0/dR, dμ1/dR, and [dμ2/dR, are the derivatives with respect to bond extension.

The equations (1)–(4) depend on the adoption of a magnetic vector potential with the gauge origin at the centre of gravity of the electron cloud of the molecule. Equation (2) is a generalized form of the formula of Chan and Das. The advantage of the simple approach is that the effects of an external electric field on the nuclear shielding are expressed entirely in terms of other molecular properties, which are functions of the internuclear separation. Further equations (1)–(4) can be expressed in terms of Re(E), the equilibrium internuclear distance itself depends on the electric field) and the derivatives [MATHEMATICAL EXPRESSION OMITTED] and [MATHEMATICAL EXPRESSION OMITTED] quantities which may be obtained directly from experiment or from ab initio calculations which do not involve the perturbation by external fields. This method is applied by the authors to 1H in H2, HF, HCl, HBr, and HI and the agreement with experiment is reasonable for the paramagnetic terms in the absence of an electric field: -6.3, -86.6, -119.5, -226.8, -305 p.p.m. (calculated), to be compared with -5.8, -79.7, -110.9, -21 4.0, -283 p.p.m. (experimental). There are no experimental values for the shielding terms which are linear and quadratic in the electric field, which are also calculated. It should be noted that this method calculates only the paramagnetic term. There are contributions due to the effects of the electric field on the diamagnetic term in the shielding as well.

Maps of nuclear magnetic shielding density, showing the values of the nuclear shielding density function in a plane (not necessarily a molecular plane), especially in a 3-D perspective view, permit visualization of the regions of molecular space where shielding or deshielding effects arise. Such maps are plotted for 1H shielding in benzene molecule, calculated by the CHF method, using a very large basis set (198 contracted gaussians). The pictures unequivocally demonstrate that the immediate region surrounding a proton is largely responsible for its nuclear shielding. Deshielding effects arise almost entirely from the nearest carbon and the C — H bond, and there is no appreciable deshielding contribution from the region of the C — C bonds. Thus, the maps fully explain the observed deshielding of 1H in benzene in terms of local contributions, in terms of C and C — H magnetic anisotropy. This supports Musher’s localized model for the interpretation of proton shifts in aromatic compounds, and suggests the ring current model as physically incorrect. A topological description of the electron current density field in molecules in an external homogeneous magnetic field is presented for the many-electron current density and also for its one-electron (orbital) components. The description is applied to the magnetically induced current densities in the cyclopropenyl cation. This qualitative description involves identification of domains of physical space associated with vortices and is presented with the possible application to the distinction between local and nonlocal effects in electronic properties of molecules. Its utility remains to be seen.

The 31P in deoxyribonucleoside monophosphates tends to be less shielded for those systems having large values of 3J(PH) to 3′ and 5′ protons, which indicates a dependence of the 31P shielding on the torsion angles about the P — O ester bond. Calculations on a model compound (dimethylphosphate anion) for different values of the torsion angles about the P—O ester bond and different orientations of the methyl groups, show that both types of conformational parameters affect the value of 31P shielding. The highest shielding is obtained when the methyl groups are staggered with respect to the P — O bond, the least shielding for the eclipsed arrangement.

B. Semi-empirical Calculations. – Average bond lengths tend to increase with increasing temperature as a result of anharmonic vibrations and centrifugal distortion. The same intramolecular dynamics tend to result in longer average bond lengths when one of the atoms involved in the bond is replaced by a lighter one. Nuclear shielding varies with these changes in molecular geometry. This is the basis for the observation of a temperature dependence of nuclear shielding in the gas phase at the zero-pressure limit, and the observation of a mass dependence of nuclear shielding (the n.m.r. isotope shift). Interpretation of these experiments require nuclear shielding calculations for molecular configurations slightly displaced from the equilibrium one. These nuclear shielding values form a surface in configuration space which correspond to the global minimum in the potential energy surface, and the rovibrational average over the surface leads to the observed thermal average shielding. Some calculations are reported for portions of the shielding surfaces of B, C, N, F, P, and Si nuclei in the following molecules: BF3 , CF4, SiF4, NF3, PF5, CH4, and PH3. One important finding is that in every case the variations in bond length and bond angle lead to neglibible changes in the diamagnetic shielding contributions. Thus, the paramagnetic terms are responsible for δσ/δΔr)e and ([partial derivative]σ/[partial derivative]Δα)e. Although other more accurate calculations of [partial derivative]σ/[partial derivative]Δr)e have been carried out for diatomic molecules, the methods used normally do not allow the separate contributions to be identified when gauge-dependent orbitals are used. These semi-empirical calculations show that the nuclear shielding decreases with increasing internuclear separation in these polyatomic molecules. This is consistent with all previous calculations for a variety of nuclei in diatomic molecules and in H2O. Thus far, only Li nuclear shielding in LiH has been found to increase with increasing bond length.

The variation of N and P shielding as the pyramidal bond angle is changed in NH3, NF3, PH3, and PF3 is also reported. Except for a previous calculation of ([partial derivative]σ/[partial derivative]Δα)e in H2O, this aspect of nuclear shielding has not been previously explored. The N and P shielding decreases with the increasing bond angle in NH3, NF3, and PH3, P shielding increases with increasing bond angle in PF3. These results are consistent with earlier approximate calculations of P shielding in PZ3-type molecules, in which the electronegativity of Z was arbitrarily varied and the variation of P shielding with bond angle changes direction as the electronegativity of Z increases. Unfortunately, these recent calculations cannot easily lead to conclusions about the bond angle deformation contributions to the thermal average shielding. While the increase of the bond length with temperature is fairly well established experimentally and theoretically, the thermal average bond angle is not so well known, it may be greater or less than the equilibrium bond angle.

(Continues…)Excerpted from Nuclear Magnetic Resonance Volume 14 by G. A. Webb. Copyright © 1985 The Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
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