Orbital-free extension to Kohn-Sham density functional theory equation of state calculations: Application to silicon dioxide

Abstract

The liquid regime equation of state of silicon dioxide SiO2 is calculated via quantum molecular dynamics in the density range 5 to 15 g/cc and with temperatures from 0.5 to 100 eV, including the α-quartz and stishovite phase Hugoniot curves. Below 8 eV calculations are based on Kohn-Sham density functional theory (DFT), above 8 eV a new orbital-free DFT formulation, presented here, based on matching Kohn-Sham DFT calculations is employed. Recent experimental shock data is found to be in very good agreement with the current results. Finally both experimental and simulation data are used in constructing a new liquid regime equation of state table for SiO2.

Quantum molecular dynamics of warm dense iron and a five-phase equation of state

“…While the simple Thomas-Fermi approximation has been used successfully at very high temperatures there is significant loss of accuracy at lower temperatures [13]. Recently we have developed and applied an approach correcting the Thomas-Fermi approximation through an additional density gradient term which is determined by matching Kohn-Sham calculations at lower temperatures [14]. This then allows for extension through very high temperatures.…”

“…Using the approach described in Ref. [14] we performed gradient corrected orbital-free DFT calculations. Here the free energy is given by standard Thomas-Fermi approximation plus a gradient correction coefficient of varying strength given by λ,…”

Multiphase aluminum equations of state via density functional theory

“…It is this approach we use in this work, for which the development and implementation details may be found in Ref. 24. However, unlike in that work, here we found the coefficient of the gradient term to be negligibly small, and so we have effectively performed for aluminum Kohn-Sham calculations up to temperature of 6 eV and Thomas-Fermi calculations above that.…”

“…While the simple Thomas-Fermi approximation has been used successfully at very high temperatures, there is significant loss of accuracy at lower temperatures 23 . Recently we have developed and applied an approach correcting the Thomas-Fermi approximation, F T F ,through an additional density gradient term in which the leading coefficient, λ is determined by matching Kohn-Sham calculations of the pressure at lower temperatures of 5-10 eV 24 ,…”

Thermodynamic properties of LiD under compression with different pseudopotentials for lithium

“…However this approach is applicable only at relatively high temperatures [13]. Both methods appeal to experiment to verify the quality of calculations [12,14]. That is why it is reasonable to use reliable experimental data as a gage to reveal the influence of inner electronic shells to thermodynamic properties.…”