First - principles study of the inversion thermodynamics and electronic structure of Fe M 2 X 4 ( thio ) spinels ( M = Cr , Mn , Co , Ni ; X = O , S )

First-principles study of the inversion thermodynamics and electronic structure of FeM2 X4 (thio)spinels (M = Cr, Mn, Co, Ni; X = O, S) David Santos-Carballal,1,* Alberto Roldan,1,2 Ricardo Grau-Crespo,3 and Nora H. de Leeuw1,2,† 1Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom 2School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom 3Department of Chemistry, University of Reading, Whiteknights, Reading RG6 6AD, United Kingdom (Received 11 December 2014; revised manuscript received 17 March 2015; published 7 May 2015)