  Eigenvalue-type equations for Lowdin-Amos-Hall spin-paired (corresponding)
orbitals are developed to provide an alternative to the standard spin-polarized
Hartree-Fock or Kohn-Sham equations. Obtained equations are non-canonical
unrestricted Hartree-Fock-type equations in which non-canonical orbitals are
fixed to be biorthogonal spin-paired orbitals. To derive paired orbitals for
different spins (PODS) equations there has been applied Adams-Gilbert
localizing operator approach. PODS equations are especially useful for
treatment of the broken-symmetry solutions for antiferromagnetic materials.
