Charge-ordered insulating state of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Fe</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>from first-principles electronic structure calculations

The charge-ordered insulating state of ${\mathrm{Fe}}_{3}$${\mathrm{O}}_{4}$ below the Verwey transition temperature has been studied by the modified local density approximation with Coulomb interaction correction method. The charge ordering is found to be a stable solution with an energy gap value of 0.34 eV (the experimental value is 0.14 eV) in contrast to a uniform metallic state given by the standard local spin-density approximation. The calculated effective intersite Coulomb interaction is well screened (V=0.18 eV). It was shown that the change in electrostatic potential associated with the transition to a completely disordered state can close an energy gap leading to a metallic state. \textcopyright{} 1996 The American Physical Society.