Nuclear Spin–Spin Coupling

BY K. G. R. PACHLER

1 Introduction

The arrangement of material in this chapter adheres closely to the pattern developed by the previous Reporter. Section 3, which reports correlations between coupling constants and other parameters, has been added since it was found difficult to accommodate most of its contents under other headings. Some sections of a compound-oriented nature have been omitted as well as the section 'Experimental Advances'. Sections 4 — 6 have been subdivided in accordance with the proposals made in the Introduction to Chapter 2 in Volume 4 of this series. Sub-headings to the section on long-range couplings have been dictated by the available material.

The nomenclature used in this chapter conforms as far as possible with earlier Reports on coupling constants. The term 'long-range coupling' is often differently understood. This report classifies couplings as directly bonded, geminal, and vicinal, or one-bond, two-bond, and three-bond couplings, respectively, and refers to all couplings over more than three bonds as long-range. 'Through-space coupling' is written in quotation marks since it is — in the Reporter's opinion — an ill-defined term, the use of which should be discouraged.

Standard abbreviations and symbols have been used extensively and the reader is referred to the list at the beginning of this volume for definitions.

2 Theoretical Work

A. Ab Initio Calculations. — Sänger and Voitländer have given a detailed account of their variational calculations of coupling constants in HD using a nonsingular contact operator. The principle of the calculations has been described in a previous Report (Vol. 4, p. 68). Numerical results obtained by minimizing (i) the total second-order energy, (ii) the self-coupling energy only, and (iii) the hetero-coupling energy only deviate considerably. Pyykkö, however, has pointed out that the use of a Blinder operator, supposed to reduce the singularities of the δ-function of the FC operator, gives no improvement in the calculation of second-order energies. In particular, in the calculations of Sänger and Voitländer the hetero-coupling energy, which is proportional to J, depends on the self-coupling energy, explaining the divergence in Voitländer's numerical results. Sänger and Voitländer have subsequently repeated their calculations with a modified 'Ansatz' which allowed an independent variation of short-range (nuclear dimensions) and long-range (atomic dimensions) terms. The results do not depend on the short-range part. Consistent hetero-coupling energies are obtained for all three approaches and 1J(DH) (39 Hz) agrees reasonably well with the experimental value of 42.94 Hz. Rayez-Meaume and Hoarau have reported calculations which avoid the problems associated with the δ-function of the FC operator by introducing terms which cancel the singularities arising in the first-order perturbation equation. Results on the HD molecule obtained with a minimal Slater basis set are of the right order of magnitude. Calculations with larger basis sets are in progress.

Kowalewski et al. have calculated (H,H) coupling constants for several small molecules considering the FC term only. Their perturbation calculations use eight different sets of contracted GTO's with large configuration interaction and include all singly and doubly excited triplet states. The results are analysed in view of contributions from various occupied and virtual orbitals. Configuration interactions are important for couplings over two bonds, but have little influence on vicinal couplings. Numerical agreement with experimental values is poor. Discrepancies are attributed to the neglect of other coupling mechanisms (SD or OB) and of vibrational effects. A subsequent paper on vibrational effects in ammonia, however, has indicated these to be small though couplings varied strongly with the HNH angle. The effect of bond-angle variations has been discussed in relation to experimental results on RNH2 compounds.

Barbier et al. have calculated geminal (H,H) and (C,H) coupling constants in saturated hydrocarbons with a double-perturbation method including electron correlation. Quasi-localized orbitals have been obtained from minimal basis sets of STO's with exponents optimized for CH4. Calculations on methane, ethane, and propane gave very similar results. Increasing the HCH angle in methane resulted in a decrease of the absolute value of 2J(HH). Introduction of electronegative substituents also decreased [absolute value of 2J(HH)] due to changes in the carbon hybridization and the two-centre integrals.

Albrand et al. have performed MO SCF calculations using contracted GTO's of V(PP) in four conformations of P2H4. FC, SD, and OB terms have been included, the first term being dominant. The value of 1J (PP) increases rapidly from – 283.03 Hz in the eclipsed conformation to +10.92 Hz in the staggered form with a dihedral angle of 180°. The angular dependence is mainly due to changes in the FC term. Sign and magnitude of the experimentally measured coupling in diphosphine agree well with the coupling calculated for the stable gauche-conformation.

Oddershede, Jørgensen, and Beebe have proposed a self-consistent time-dependent Hartree-Fock scheme based on a Green's function approach as an economic alternative to configurational interaction for introducing electron correlation into second-order properties. FC contributions to the coupling constant in HD, using a basis set of 14 optimized STO's, have been calculated on various levels of approximation. The J(DH) value obtained by the SPPA method (self-consistent polarization propagator approximation) agrees reasonably well with the experimental result and the best-to-date ab initio calculation by Kowalewski et al. The remaining discrepancy is attributed to the use of a limited basis set.

Similar calculations of 1J (FH) in the HF molecule indicate that large numbers (> 55) of particle-hole excitations (equivalent to states in an SOS approach) have to be included to reach convergence in J. Introduction of electron correlation did not affect the convergence but improved the numerical value of J(FH).

Pyykkö et al. have used a spectral-density function to calculate spin-spin coupling constants. Reference 12 reports calculations for XH4 hydrides. The X — H bond is described in terms of a simple LCAO model using a hydrogen atomic orbital...