Quantum-mechanical Hartree-Fock self-consistent-field study of the elastic constants and chemical bonding of ${\mathrm{MgF}}_2$ (sellaite)

A periodic ab initio Hartree-Fock method (the program crystal) has been used to evaluate the total-electron-energy surface of ${\mathrm{MgF}}_2$ (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 ${\mathit{C}}_{11}$,${\mathit{C}}_{12}$, ${\mathrm{C}}_{13}$,${\mathit{C}}_{33}$,${\mathit{C}}_{44}$, and ${\mathit{C}}_{66}$ have been calculated. Inner strain was accounted for by relaxing the F-atom position for each lattice deformation applied, and contributed significantly to the ${\mathit{C}}_{44}$,${\mathit{C}}_{66}$, and ${\mathit{C}}_{33}$ 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 (${\mathit{z}}_{\mathrm{Mg}}$=1.80‖e‖).