The magnetic and electronic structure of vanadyl pyrophosphate from density functional theory

We have studied the magnetic structure of the high symmetry vanadyl pyrophosphate ((VO)₂P₂O₇, VOPO), focusing on the spin exchange couplings, using density functional theory (B3LYP) with the full three-dimensional periodicity. VOPO involves four distinct spin couplings: two larger couplings exist along the chain direction (a-axis), which we predict to be antiferromagnetic, J_OPO = -156.8 K and J_O = -68.6 K, and two weaker couplings appear along the c (between two layers) and b directions (between two chains in the same layer), which we calculate to be ferromagnetic, J_layer = 19.2 K and J_chain = 2.8 K. Based on the local density of states and the response of spin couplings to varying the cell parameter a, we found that J_OPO originates from a super-exchange interaction through the bridging -O-P-O- unit. In contrast, J_O results from a direct overlap of 3dx² - y² orbitals on two vanadium atoms in the same V₂O₈ motif, making it very sensitive to structural fluctuations. Based on the variations in V-O bond length as a function of strain along a, we found that the V-O bonds of V-(OPO)₂-V are covalent and rigid, whereas the bonds of V-(O) ₂-V are fragile and dative. These distinctions suggest that compression along the a-axis would have a dramatic impact on J_O, changing the magnetic structure and spin gap of VOPO. This result also suggests that assuming J_O to be a constant over the range of 2-300 K whilst fitting couplings to the experimental magnetic susceptibility is an invalid method. Regarding its role as a catalyst, the bonding pattern suggests that O₂ can penetrate beyond the top layers of the VOPO surface, converting multiple V atoms from the +4 to +5 oxidation state, which seems crucial to explain the deep oxidation of n-butane to maleic anhydride.