Electronic structure and vibrational spectra of magnetite

The electronic structure, crystal structure and infra-red conductivity of magnetite have been calculated using hybrid density functional methods. The crystal structure was calculated using a conjugate gradient method and atomic coordinates were obtained while freezing lattice parameters at experimental values or by simultaneously allowing lattice parameters and atomic coordinates to relax. Atomic coordinates obtained when lattice parameters were frozen at experimental values are in excellent agreement with values from x-ray and neutron scattering data. The best agreement with experiment is obtained when a B3LYP hybrid functional is used. Phonon modes at the F point of the Brillouin zone were calculated using a frozen phonon method. All computed phonon eigenfrequencies were real when experimental lattice parameters were used, but when phonons were calculated using the fully relaxed structure there was one imaginary phonon frequency. When frequencies from the calculation which used experimental lattice parameters are rescaled, there is agreement between the low temperature infra-red conductivity predicted using these phonon modes and experiment.