Diamagnetic contributions to the nuclear spin–spin coupling constants of several small molecules. An application of Monte Carlo integration methods to molecular one-electron properties

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Abstract
A numerical Monte Carlo integration procedure has been developed for calculation of J1a, the diamagnetic contribution to the nuclear spin–spin coupling constant from an arbitrary molecular charge density. The method is applied first to the HD molecule where several previous values of JHD1a are refined and corrected. A test of Brillouin’s theorem for this unusual sum of one‐electron operators is made and the extensive cancellations from different regions of space are examined in detail. Values of J1a are then given for HF, BF, CO, and HCN. It appears that J1a may be the one‐electron property most sensitive to the quality of the wavefunction which has been considered to date. Monte Carlo integration may be employed for the calculation of one‐electron properties when alternatives to analytic integral evaluation are sought.

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