Molecular Orbital Approximation to Electron Coupled Interaction between Nuclear Spins

The general formulas obtained by Ramsey for the indirect second-order magnetic coupling of nuclear spins by electron spin and orbital magnetic moments in 1Σ molecules are used together with an antisymmetrized product of molecular spin orbitals to obtain a set of general equations for nuclear spin couplings which only involve (a) the individual molecular orbitals, and (b) rotationally invariant one and two electron space operators. By approximating the molecular orbitals with linear combinations of atomic orbitals quite tractable formulas are obtained for ``long-range'' nuclear spin-spin couplings, i.e., couplings between nuclei separated by two, three, or more bond lengths. The application of these formulas are illustrated by the development of an approximate formula for proton-proton coupling constants in terms of interproton bond orders, the application of this formula to methane, as well as some qualitative considerations of F19—F19 coupling constants in tetrafluoroethylene. In general nuclear spin couplings between protons not directly bonded to one another arises primarily through hyperfine interactions between protons and pairs of electron spins. In hydrocarbons long-range bond orders between protons, ηHH′, can be estimated from observed proton spin couplings by the equation, ηHH′2 = 0.5 × 10—2 JHH′ (in sec—1). In fluorocarbons (and probably many other substances) nuclear couplings are due to the combined effects of hyperfine electron orbital and electron spin interactions with F19 nuclei. Electron exchange effects are important for both two-electron spin and orbital contributions to nuclear coupling.