Temperature-independent paramagnetism in closed-shell oxanions of first-row transition metals

Abstract

A consistent picture of the magnetism of the series of isoelectronic molecules VO^3–₄, CrO^2–₄ and MnO^–₄ is given by coupled Hartree–Fock theory. An external magnetic field induces a paramagnetic circulation around each nucleus that decreases in strength and extent from MnO^–₄ to VO^3–₄. The presence of low-lying empty orbitals derived from splitting of the partially occupied valence shell leads to a significant paramagnetic contribution to the total magnetizability. As the central charge falls, the bonding becomes more ionic, the metal–oxygen bond grows longer and the diamagnetic susceptibility increases in magnitude. At the same time, in Hartree–Fock theory, the virtual orbitals become more diffuse and the paramagnetic contribution falls: 160.7 au (1 au =e²a²₀/m_e≈ 7.891 04 × 10^–29 J T^–2) in MnO^–₄, which is about twice the estimated experimental value, 86.0 au in CrO^2–₄, which is 10% too high, and 80.8 au in VO^3–₄(no experimental value). As a result the anions change from ‘strongly’ paramagnetic to magnetically neutral; at the experimental bond lengths total magnetizabilities are 93.2 au in MnO^–₄(exp. 8.3), 13.6 au in CrO^2–₄(exp. 6.3) and –0.8 au in VO^3–₄. Lattice effects on the computed values are very small. Agreement with experiment is better at the SCF bond lengths. It is concluded that the Hartree–Fock model becomes more appropriate as the system becomes more ionic, and gives an accurate description of the magnetism in VO^3–₄.