The following question, however, arise: Are the DFT results accurate enough? These data can then be integrated into existing thermodynamic data sets making them available to a broad range of applications. Nowadays, the generation of such end member thermodynamic data is possible in a relatively short time by using the density functional theory (DFT). This has the consequence that thermodynamic calculations including such end members suffer from missing accuracy. The experimental data basis is also poor for rare parageneses (e.g., minerals in calcium–aluminium-rich inclusions of primitive meteorites). Investigating the standard enthalpy of formation from the elements (Δ f H 298.15) and the standard entropy ( S 298.15) of mineral end members of geological and cosmochemical relevance is a prerequisite for reliable phase diagram calculations and still needed in many aspects: first, because such standard data of some mineral end members are derived from a limited number of experiments and largely missing for chemically more complex systems (e.g., Ti-containing end members of many solid solutions such as pyroxenes, micas, amphiboles) and, second, because there are important mineral solid solutions whose thermodynamic description needs data from end members which do not exist physically at all (e.g., Al-rich biotite end members). They, however, are still far better than enthalpy and entropy values obtained from estimation methods. For reactions with small reaction enthalpies (a few kJ/mol), the DFT errors are too large. The DFT-derived thermodynamic data are also accurate enough for computing the P–T positions of reactions that are characterized by relatively large reaction enthalpies (> 100 kJ/mol), i.e., dehydration reactions. They even suggest an improvement, because they agree with petrological observations concerning the coexistence of kyanite + quartz + corundum in high-grade metamorphic rocks, which are not reproduced correctly using internally consistent data sets. The DFT-based phase boundaries are comparable to those derived from internally consistent thermodynamic data sets. This is shown for the Al 2SiO 5 polymorphs. In the case of phase transitions, the DFT-computed thermodynamic data of involved phases turned out to be accurate and using them in phase diagram calculations yields reasonable results. The deviations from reference enthalpy and entropy values are in the order of several kJ/mol and several J/mol/K, respectively, from which the former is more relevant. These thermodynamic quantities were then transformed into standard enthalpies of formation from the elements and standard entropies enabling a direct comparison with tabulated values. kyanite, sillimanite, andalusite, albite, microcline, forsterite, fayalite, diopside, jadeite, hedenbergite, pyrope, grossular, talc, pyrophyllite, phlogopite, annite, muscovite, brucite, portlandite, tremolite, and CaTiO 3–perovskite. The internal energies and entropies of 21 well-known minerals were calculated using the density functional theory (DFT), viz.
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