Energetics, structure, and compressibility of NaF determined by the periodic Hartree–Fock method

Abstract

Basis set development methods for molecular cluster calculations were used to develop basis sets for periodic ab initio calculations of the energy-dependent properties of ionic crystals. Two extended, Gaussian basis sets for closed-shell sodium and fluorine ions were developed to compare with two minimal basis sets in calculating the crystal structures, enthalpies of formation, and high-pressure compression behavior of the B1 and B2 phases of NaF. Accurate calculation of the energy-dependent properties to within experimental error required the use of the larger, extended basis sets. Enthalpies of formation for NaF–B1 at 0 K and 1 bar were calculated to be between −921 and −929 kJ/mol, which agrees well with an experimental value (−927±10 kJ/mol) estimated from calorimetric data. For the B1 phase, the zero-pressure bulk modulus was calculated to be between 0.485 and 0.499 Mbar, as compared to the measured value of 0.464±0.062 Mbar. The calculated molar volume at zero pressure agrees to within 0.1% of the experimental value. For the B2 phase, the zero-pressure bulk modulus was nearly the same as that for the B1 phase, ranging from 0.494 to 0.517 Mbar. However, this calculated bulk modulus for the B2 phase was considerably smaller than the experimental value of 1.03±0.19 Mbar estimated from high-pressure compression measurements. Our calculations also suggest the V02/V01 of the B2 phase is nearer to 0.871–0.895 than to the experimental estimate of 0.811. The compression curves for both phases agreed, for the most part, with the experimental data to within the experimental error. The calculated pressure for the NaF B1/B2 transition is between 0.26 and 0.29 Mbar, slightly higher than the averaged experimental value (0.23±0.03 Mbar) but within a pressure range where both phases metastably coexist along the compression curve. The calculated volume change accompanying the phase transition (−10.1%) is in good agreement with experimental data (−10.4%). The apparent discrepancies between the zero-pressure bulk modulus and the compression curves of the B2 phase are shown to be related to the range of molar volumes used in deriving the zero-pressure properties from an equation of state.