Heisenberg Exchange Interaction of Two Mn Atoms

A complete ab initio approximate Hartree-Fock calculation has been carried out on the ${\mathrm{Mn}}_2$ molecule at three internuclear distances, $R=4.5, 5.0, \mathrm{and} 5.5 a_0$. The theory of the Heisenberg exchange interaction, applied in an earlier paper to the nitrogen molecule at large $R$, is used to identify the Hartree-Fock configuration of lowest energy and to evaluate the effective exchange integral $J$. The Hartree-Fock energy has a minimum value with respect to separated atoms in a ${}_{}{}^9{}_{}{}^{}{\Sigma }_g_{}^{+}{}_{}{}^{}$ state. The exchange integral is small but negative, so a ${}_{}{}^1{}_{}{}^{}{\Sigma }_g_{}^{+}{}_{}{}^{}$ state of complex structure lies below this. The energy of this ${}_{}{}^1{}_{}{}^{}{\Sigma }_g_{}^{+}{}_{}{}^{}$ state has a minimum value of -0.79 eV, with respect to separated atoms, at $R=2.88\mathrm{}$ Å, neglecting the part of the net molecular correlation energy that is independent of spin. These two states are members of a closely spaced set with total spin $S^{\prime }=0, 1, 2, 3, 4$ coming from the coupling of spins $S=2\mathrm{}$ on each atom. The last occupied $\sigma$ orbital is of molecular form (bonding molecular orbital, doubly occupied) while the last $\pi$ and $\delta$ orbitals are localized and singly occupied. The existence of localized spin-coupled orbitals at equilibrium $R$ is very unusual for diatomic molecules, and this is the distinctive property of magnetic materials expected in the present theory.