Electron Correlation and the Nuclear Spin–Spin Coupling Constant. II. The Generalized Product Approximation with Intergroup Configuration Interaction

A generalization of a number of existing theoretical descriptions of contact nuclear spin–spin coupling is presented in terms of a density matrix formalism and the generalized product approximation. The recognition of distinct groups such as bonds, $\sigma$ electrons, or $\pi$ electrons by this method permits a simplification of the discussion of many electron systems, but for an adequate description of spin coupling in many cases in which there is more than one group, it is essential to introduce intergroup configuration interaction. The resulting theoretical expressions provide a generalization of those descriptions which use second‐order perturbation theory and do not invoke the approximation of a “mean excitation energy” in the second‐order perturbation sum. The applicability of the method is demonstrated for cases in which the groups are described by both molecular‐orbital and valence‐bond (VB) wavefunctions. Using VB wavefunctions, specific π‐electron coupling constant results are reported for fragments of the butadiene and allene molecules. In the generalized product approximation, each of these fragments is described in terms of two groups of four electrons. Although considerably less computational effort is required by this method, the calculated results are in substantially good agreement with previous results based on eight‐electron VB calculations. With the computational simplification provided by the generalized product approximation, theoretical results are obtained for the π‐electron coupling between protons separated by from two to nine bonds in octatetraene.