The computation of Karplus equation coefficients and their components using self-consistent field and second-order polarization propagator methods

The Karplus equation has been investigated by ab initio computation of the spin-spin coupling constants for a series of rotated ethane geometries. The couplings have been calculated at the self-consistent field (SCF) level as well as using the second-order polarization propagator approximation (SOPPA) and the second-order polarization propagator approximation with coupled cluster singles and doubles amplitudes (SOPPA(CCSD)) and have been compared with results of previous calculations. The four principal components of the coupling constants rather than just the Fermi-contact have been calculated, and the common supposition that the Fermi-contact term is totally dominant has been confirmed. The derivatives of the orbital paramagnetic and orbital diamagnetic terms are significant but opposite in sign for the case of this rotation in ethane. It is found that the coefficients in the Karplus equation are largely overestimated at the SCF level, whereas the SOPPA(CCSD) results are in good agreement with coefficients derived from experimental coupling constant data or the results of multi-configurational self-consistent field (MCSCF) calculations. It is further observed that extending the Fourier series in the Karplus equation to include cos(3θ) and cos(4θ) terms neither significantly improves the quality of the fit nor significantly changes the values of the other coefficients. In order to simulate the Abraham and Pachler equation, calculations varying the nuclear charge on hydrogen have been performed. These will allow an abstract but flexible prediction of the effect of electronegative substituents.