Effectiveness of smearing and tetrahedron methods: best practices in DFT codes

Abstract

Density functional theory (DFT) codes are commonly treated as a ‘black box’ in high-throughput screening of materials, with users opting for the default values of the input parameters. Often, non-experts may not sufficiently consider the effect of these parameters on prediction quality. In this work, we attempt to identify a robust set of parameters related to smearing and tetrahedron methods that return numerically accurate and efficient results for a wide variety of metallic systems. The effects of smearing and tetrahedron methods on the total energy, number of self-consistent field cycles, and forces on atoms are studied in two popular DFT codes: the Vienna ab initio Simulation Package and Quantum Espresso. From nearly 40 000 computations, it is apparent that the optimal smearing depends on the system, smearing method, smearing parameter, and k-point density. The benefit of smearing is a minor reduction in the number of self-consistent field cycles, which is independent of the smearing method or parameter. A large smearing parameter—what is considered large is system dependent—leads to inaccurate total energies and forces. Blöchl’s tetrahedron method leads to small improvements in total energies. When treating diverse systems with the same input parameters, we suggest using as little smearing as possible due to the system dependence of smearing and the risk of selecting a parameter that gives inaccurate energies and forces.

Machine Learning Based Electronic Structure Predictors in Single-Atom Alloys: A Model Study of CO Kink-Site Adsorption across Transition Metal Substrates

“…Prior to relaxation, the adsorbate was placed on top of the TM atom at the kink site in a “vertical” configuration as indicated in Figure a . The Brillouin zone was integrated using the Gaussian smearing method at parameter value of 0.1 eV and a k -point mesh of 5 × 5 × 1, with the vertical direction out of the vicinal plane having the least number of k -points . Due to the large number of structures in the data set, in the present study we did not consider the effects of spin polarization and the zero-point vibrational energy, which requires significantly more computational resources.…”

Thermodynamic properties calculations of Cu‐based species

“…A larger smearing parameter used in calculations, which leads to higher thermodynamic values. [47][48][49] The lower smearing values might lead to a closer resemblance to ground-state energies and, hence, lower thermodynamic values.…”

“…Smearing refers to the occupation of electronic states according to a smooth distribution function, usually the Fermi‐Dirac distribution, to mitigate numerical issues arising from finite Brillouin zone sampling and system characteristics. A larger smearing parameter used in calculations, which leads to higher thermodynamic values 47–49 . The lower smearing values might lead to a closer resemblance to ground‐state energies and, hence, lower thermodynamic values.…”

Constant potential energetics of metallic and semiconducting electrodes: A benchmark study on 2D materials

“…DOS broadenings are intrinsically introduced when allowing non-integer occupations for electronic states, which is necessary for numerical reasons to obtain converged energetics and forces for metals or metalized semiconductors at finite k-point resolution. [51][52][53][54] In principle, realistic temperature-related broadening effects are obtained when Fermi-Dirac occupations are used in combination with a room temperature smearing width σ = k B T ∼ 25 meV. 50 However, it is common practice to use other occupation functions that can exhibit smaller artifacts at larger-than-roomtemperature smearings at the expense of introducing unphysical electronic entropy contributions or non-unique Fermi levels.…”