A solid-state hybrid density functional theory study of Prussian blue analogues and related chlorides at pressure

The variations with pressure in the structural, electronic and magnetic properties of a series of Prussian blue analogues (PBAs) K I M II [Cr III (CN) 6 ] (M = V II , Mn II and Ni II ) and associated isomorphous chlorides K I M II Cr III Cl 6 are investigated within a series of solid-state hybrid density functional calculations. The sensitivity of the computed properties to the choice of Hamiltonian is tested by application of functionals containing 35%, 65% and 100% admixtures of Fock exchange. Magnetic coupling constants ( J ) are obtained at a range of cell volumes ( V ), with fits of the Bloch relationship ( , ε typically 3–4) yielding exponents ε in the ranges 5.16–6.34, 8.48–12.07 and 4.00–4.51 for the antiferromagnetic (AF) V II Cr III - , ferrimagnetic (FI) Mn II Cr III - and ferromagnetic (FO) Ni II Cr III PBAs, respectively; and 3.33–4.99, 1.86–3.09 and 1.65–3.28 for the AF V II Cr III - , FO Mn II Cr III - and FO Ni II Cr III chlorides, respectively. The Mn II Cr III PBA range encloses the high values ε∼9–10 obtained in a recent joint experimental and theoretical study, and it is suggested that this strong magnetostructural effect arises due to the presence of competing AF and FO interactions in this material. Estimates of the spin ordering temperatures derived from the combination of the 35%-functional couplings with a mean field approach are in good agreement with experiment in the V II Cr III and Ni II Cr III PBAs, but are too low in the Mn II Cr III system. The variations with pressure in the structural parameters, charges and spin moments are also detailed, the PBA and chloride energy–volume data yielding bulk moduli in the ranges 39–53 and 36–50 GPa, respectively. Finally, the energies governing CN – ligand isomerization are estimated and successfully interpreted in terms of a simple crystal field stabilization model.