Orthogonal- and nonorthogonal-orbital methods in the theory of magnetism

The effective spin Hamiltonian is obtained in the Dirac-van Vleck form by the method of nonorthogonal atomic orbitals with an estimate of virtual interatomic transitions. The equivalence of the orthogonal- and nonorthogonal-orbital methods is demonstrated for a bounded configurational interaction, with an accuracy to quadratic terms in the overlap integral.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 12, No. 3, pp. 59–67, March, 1969.In conclusion the author thanks B. V. Karpenko for formulating the problem, for consultation, and for discussions.