[en] Expressions appropriate for the evaluation of the hyperfine splitting in ferric-hemoglobin hydroxide have been derived in the Hartree-Fock approximation using ''giant'' multielectron molecular-orbital wave functions formed as linear combinations of atomic orbitals of the constituent atoms and the molecular orbitals of the OH^- complex incorporating overlap effects. Core orbitals as well as valence orbitals have been considered. The relevant multicenter matrix elements have been evaluated accurately by means of the analytical expressions which we have derived by employing a general closed-form expression developed previously for the coefficients of the expansion of a Slater orbital from one center onto the other. Various calculated electric field gradient components have been analyzed separately in terms of the valence and the core orbitals of the central ion (iron) interacting with the orbitals of the other constituent atoms and the complex OH^-. One finds that the ''local'' and ''distant'' parts of the field gradient due to OH^- nearly cancel one another and, consequently, produce negligible effect on the hyperfine splitting of iron. The nitrogens of the porphyrin plane contribute dominantly to the splitting. Other surrounding atoms contribute less and their influence decreases rapidly as their distance from the central ion increases. On combining various contributions, the calculated hyperfine splitting comes out to be 1.44 + 0.16 mm/sec, which agrees excellently with the experimental splitting 1.57 mm/sec observed by Lang and Marshall. The results from the present calculations have been compared with those obtained by Weissbluth and Maling employing semiempirical treatment on a porphyin-hydroxide model compound. Their estimate is found to give negative sign to the splitting in contrast with our result. Sources of disagreement have been pointed out. Positive hyperfine splitting in ferric-hemoglobin compounds is predicted