Quantum-mechanical Hartree-Fock self-consistent-field study of the elastic constants and chemical bonding of MgF₂ (sellaite)

A periodic ab initio Hartree-Fock method (the program crystal) has been used to evaluate the total-electron-energy surface of MgF₂ (rutile-type tetragonal structure) as a function of crystal strain. Mg and F atoms are represented by 13 atomic orbitals in the form of contracted Gaussian-type functions. The equilibrium unit-cell edges and fluorine coordinates, the binding energy, and the six elastic constants C₁₁, C₁₂, C₁₃, C₃₃, C₄₄, and C₆₆ have been calculated. Inner strain was accounted for by relaxing the F-atom position for each lattice deformation applied, and contributed significantly to the C₄₄, C₆₆, and C₃₃ components. An average deviation of 8.0% is observed with respect to experimental elastic data. Classical two-body empirical calculations have been performed for the purpose of comparison. Energy bands, Mulliken electron populations, and charge-density maps are analyzed, and the chemical bonding is discussed, showing significant deviations from ionicity (z_Mg=1.80‖e‖).