Lattice constants from semilocal density functionals with zero-point phonon correction

Abstract

In a standard Kohn-Sham density functional calculation, the total energy of a crystal at zero temperature is evaluated for a perfect static lattice of nuclei, and minimized with respect to the lattice constant. Sometimes a zero-point vibrational energy, whose anharmonicity expands the minimizing or equilibrium lattice constant, is included in the calculation or (as here) used to correct the experimental reference value for the lattice constant to that for a static lattice. A simple model for this correction, based on the Debye and Dugdale-MacDonald approximations, requires as input only readily-available parameters of the equation of state, plus the experimental Debye temperature. However, due in particular to the rough Dugdale-MacDonald estimation of Grüneisen parameters for diatomic solids, this simple model is found to overestimate the correction by about a factor of two for some solids in the diamond and zinc-blende structures. Using the quasi-harmonic phonon frequencies calculated from density functional perturbation theory gives a more accurate zero-point anharmonic expansion (ZPAE) correction. The error statistics for the lattice constants of various semilocal density functionals for the exchange-correlation energy are however little changed by improving the ZPAE correction. The PerdewBurke-Ernzerhof generalized gradient approximation (GGA) for solids (PBEsol) and the revised TaoPerdew-Staroverov-Scuseria (revTPSS) meta-GGA, the latter implemented here selfconsistently in BAND, applied to a test set of 58 solids, remain the most accurate of the functionals tested, with mean absolute relative errors below 0.7% for the lattice constants. The most positive and most negative revTPSS relative errors tend to occur for solids where full nonlocality (missing from revTPSS) may be most important.

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

“…This assessment provides therefore a thorough overview of the performance which can be expected by the various functionals in different applications. Our results are in good agreement with previous similar assessments of meta-GGA functionals, [31,286,301,306,308,309,329,361,363] but we extend them to several different systems and properties as well as to model systems.…”

“…In this case nonempirical meta-GGAs performs better than PBE and similar to the best GGA (PBEsol). [31,308,309] However, all these functionals are not able to predict reasonable cohesive energies results in Refs. [26] and the SSCE8 results in Ref.…”

“…In any case, all meta-GGAs are worse than the simple PBE, in agreement with the results for the simple metals considered in Refs. [31] and [308]. Conversely, M06-L gives quite bad lattice constants for simple metals, see also Ref.…”

“…[306] However, for properties of bulk solids, revTPSS usually improves over TPSS. [30,[307][308][309][310][311][312][313] For further details about the revTPSS performance see Section 4.…”

Self-consistent meta-generalized gradient approximation within the projector-augmented-wave method

“…38 . Full phononspectrum estimates for about 60 solids will be available soon 59 . The experimental cohesive energies were corrected for the zero-point vibration energy 38,47 .…”