Heisenberg exchange enhancement by orbital relaxation in cuprate compounds

We calculate the Heisenberg exchange J in the quasi-2D antiferromagnetic cuprates La ₂CuO ₄, YBa ₂Cu ₃O ₆, Nd ₂CuO ₄ and Sr ₂CuO ₂Cl ₂. We apply all-electron (MC)SCF and non-orthogonal CI calculations to [Cu ₂O ₁₁] ^18-, [Cu ₂O ₉] ^14-, [Cu ₂O ₇] ^10- and [Cu ₂O ₇Cl ₄] ^14- cluster in a model charge embedding. The (MC)SCF triplet and singlet ground states are well characterized by Cu ²⁺ (d _{x²- y²}) and O ^2-. The antiferromagnetic exchange is strongly enhanced by admixing relaxed (MC)SCF triplet and singlet excited states, in which a single electron is transferred from the central O ion to Cu. We ascribe this effect to orbital relaxation in the charge transfer component of the wavefunction. Close agreement with experiment is obtained.