The geometry structure, dissociation energy, vibrational frequencies, and low-lying spin-state energy spectrum of Mn2+ are investigated by using ab initio CASSCF/ECP10MDF, complete active space self-consistent field/atomic natural orbital basis sets CASSCF/ANO-s, CASPT2/ECP10MDF, and second-order perturbation theory with CASSCF reference function/atomic natural orbital basis sets CASPT2/ANO-s levels of theory. For the ground state the dissociation energy of 1.397 eV calculated at the CASPT2/ANO-s level supports Jarrlod's experimental value of 1.39 eV. The equilibrium bond length and vibrational frequency are 2.940 Å calculated at the CASPT2/ANO-s level of theory and 214.4cm−1 calculated at the CASSCF/ANO-s level of theory, respectively. On the basis of the mixed-valence model, the Heisenberg exchange constant J−71.2cm−1 and the double-exchange constant B 647.7cm−1 are extracted explicitly from the low-lying energy spectrum calculated at the higher levels of theory. The magnetic competition between the weaker Heisenberg exchange interactions and the stronger double-exchange interactions makes the ground state a 12g+ state, consistent with electron paramagnetic resonance experimental observation, which explains unusual magnetic properties of Mn2+, quite different from the antiferromagnetic ground state of Mn2 and Cr2. On the other hand, the results calculated at the higher levels of theory show the consistent antiferromagnetic Heisenberg exchange interactions between 3d−3d for Cr2, Mn2+, and Mn2.

The magnetic exchange interaction behavior and energy spectrum of low-lying spin states are investigated by using ab initio multireference configuration-interaction method for the representative binuclear transition-metal complexes fsNH3d5Crs m-OHdCrsNH3d5g5+ and fCl3FeOFeCl3g2−. Our calculations for the nonmodeling real title complexes found that under the appropriate basis sets and active space, ab initio method at multireference configuration-interaction level of theory is able to give accurate energy spectrum of low-lying spin states within reachable computation demand nowadays and the deviation of magnetic exchange interaction to Lande interval rule can be described by the biquadratic correction in terms of Heisenberg spin Hamiltonian. As a methodology comparison, density-functional theory combined with broken-symmetry approach provides an alternative yet efficient approach to produce accurate numerical results, but there are dependences on the particular chosen exchange-correlation functionals and system dependent. The spin population analyses at complete active space self-consistent-field level of the theory provide an instructively understanding and prediction for the magnetic interaction mechanism.