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INTRODUCTION AND SUMMARY
Mineralogists and geophysicists need to understand and predict the properties of solids and liquids at normal and especially at high pressures and temperatures. For example, they need to know the equilibrium structure, equation of state, phase transitions, and vibrational properties of solids, and the interatomic or intermolecular interaction needed for a molecular dynamics study of liquids (Stixrude et al. 1994; Soederlind and Ross 2000; Karki et al. 2001; Alfè et al. 2002; Steinle-Neumann et al. 2004; Sha and Cohen 2006; Carrier et al. 2007). This information, in sufficient detail, is not always available from experiment. Increasingly, it comes from the simple first-principles Kohn-Sham density functional theory (Kohn and Sham 1965; Parr and Yang 1989; Dreizler and Gross 1990; Perdew and Kurth 2003; Perdew et al. 2009a). Often the ground-state version of this theory suffices, since the electrons can stay close to their ground state even when the nuclear motion is thermally excited; there is however also a temperature-dependent version of the theory (Mermin 1965).
In Kohn-Sham density functional theory, the exact ground-state density and energy of a many-electron system can be found by solving selfconsistent one-electron Schroedinger equations for the orbitals or one-electron wavefunctions. Many different methods of solution are available in many different standard computer codes, which tend to agree when carefully applied. The required computational effort is much less than in approaches that employ a many-electron wavefunction. In practice, one term in the energy as a functional of the electron density, the exchange-correlation energy, must be approximated. Although this term is often a relatively small part of the total energy, it is “nature’s glue,” responsible for most of the binding of one atom or molecule to another. Simple and computationally undemanding semilocal approximations are accurate enough for …