A recently developed method of non-empirical wave-function calculation is applied to the calculation of ESR hyperfine coupling constants. In particular the effect of d orbitals on the computed values of these constants is investigated for I%$--and H2S'. In this note, we wish to report the use of the "mixed basis" method developed by the authors and outtlined elsewhere [l], for the evaluation of nuclear hyperfine coupling constants and to investigate the effect of d orbitals on these constants. The calculation of spin coupling constants (both ESR and NMR) from approximate moiecular wave-functions is known to depend very strongly on the integral approximations used; for example, CNDO type calculations for o radicals give erratic agreement with experiment [2]. In a perturbation expression for spin coupling constants in x racucals, these quantities are easily seen to depend on the Coulombic interaction between transition spin densities, i.e. in an orbital basis on exchange integrals, and so the magnitude of the calculated coupling constant will depend criticaily on (a) whether or not all the integrals appear in the approximate method and (b) the relative accuracy of these small integrals. Clearly the CNDO method which neglects large numbers of exchange integrals cannot be expected to yield reliable estimates of spin dependent properties. This 1s seen if the calculation of the ESR coupling constants is performed by the "open shell SCF followed by CI (singly excited)" method, say, for the planar methyl radical. Such a calculation predicts zero nuclear coupling constants for both the protons and the heavy atom, since every exchange integral (avia! x*) vanishes due to the CNDO approximation of setting the relevant atomic integrals to zero. The