Eigenvalue-type equations for Löwdin-Amos-Hall spin-paired (corresponding) orbitals are developed to provide an alternative to the standard spin-polarized Hartree-Fock or Kohn-Sham equations in dealing with broken-symmetry (BS) states. To derive paired orbitals for different spins (PODS) equations there has been applied Adams-Gilbert "localizing" operator approach. The PODS equations contain different operators for different spins the eigenvectors of which are paired orbitals associated with the same eigenvalue for each pair. Preliminary applications to simple systems show viability of this approach. Although the spectrum of possible applications of the PODS equations seems to be quite wide, they would be especially useful for obtaining and analyzing the S(z) = 0 BS solutions for the systems with antiferromagnetic structure.
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