Automated coordination corrected enthalpies with AFLOW-CCE

Rico Friedrich, Marco Esters, Corey Oses, Stuart Ki, Maxwell J. Brenner, David Hicks, Michael J. Mehl, Cormac Toher, and Stefano Curtarolo

Phys. Rev. Materials 5, 043803 – Published 15 April 2021

Abstract

The computational design of materials with ionic bonds poses a critical challenge to thermodynamic modeling since density functional theory yields inaccurate predictions of their formation enthalpies. Progress requires leveraging physically insightful correction methods. The recently introduced coordination corrected enthalpies (CCE) method delivers accurate formation enthalpies with mean absolute errors close to room temperature thermal energy, i.e., $\approx 25$ meV/atom. The CCE scheme, depending on the number of cation-anion bonds and oxidation state of the cation, requires an automated analysis of the system to determine and apply the correction. Here, we present AFLOW-CCE—our implementation of CCE into the AFLOW framework for computational materials design. It features a command line tool, a web interface, and a Python environment. The workflow includes a structural analysis, automatically determines oxidation numbers, and accounts for temperature effects by parametrizing vibrational contributions to the formation enthalpy per bond.

Received 7 January 2021
Accepted 22 March 2021

DOI:https://doi.org/10.1103/PhysRevMaterials.5.043803

Physics Subject Headings (PhySH)

Electronic structure First-principles calculations Thermodynamics

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Rico Friedrich ^1,2,3, Marco Esters^1,2, Corey Oses ^1,2, Stuart Ki^1,2, Maxwell J. Brenner^1,2, David Hicks ^1,2, Michael J. Mehl ^1,2, Cormac Toher ^1,2, and Stefano Curtarolo ^2,4,*

¹Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA
²Center for Autonomous Materials Design, Duke University, Durham, North Carolina 27708, USA
³Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany
⁴Materials Science, Electrical Engineering, Physics and Chemistry, Duke University, Durham, North Carolina 27708, USA

^*stefano@duke.edu

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Vol. 5, Iss. 4 — April 2021

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Figure 1
User interfaces. (a) Example command—here for perovskite ${CaTiO}_{3}$ —for the AFLOW-CCE command line tool. The input structure file (here test.POSCAR), precalculated DFT formation enthalpies per cell, and functionals are given via the options --get_cce_corrections < test.POSCAR, --enthalpies_formation_dft=-63.452,-72.084,-72.412, and --functionals=PBE,LDA,SCAN, respectively. The structure can be in any format recognizable by AFLOW, such as VASP POSCAR [48], Quantum Espresso [56], FHI-AIMS [57], ABINIT [58], ELK [59], and CIF [60]. Oxidation numbers for all atoms can be provided as a comma separated list as input using --oxidation_numbers=ox_num_1,ox_num_2,.... (b) When executed, the output includes the CCE corrections and formation enthalpies at both 298.15 and 0 K. If no DFT formation enthalpies are given, an estimate for the formation enthalpy at 298.15 K based on experimental values per bond (CCE@exp, blue) [1] is calculated according to Eq. (3). (c),(d) Example command/output when determining oxidation numbers for the structure in test.POSCAR. (e),(f) Example command/output when determining cation coordination numbers for the structure in test.POSCAR. (g) The web interface yields the cation coordination numbers, oxidation numbers, and CCE corrections for the structure provided in the field “Input POSCAR.” If DFT formation enthalpies per cell are provided, the output also includes the CCE formation enthalpies. (h) Example Python script using the AFLOW-CCE Python environment. Similar to the command line, functionals, enthalpies_formation_dft, and input oxidation_numbers are optional arguments for the get_corrections method. The results are returned as a dictionary.
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Figure 2
Oxidation number algorithm. Schematic representation of the algorithm to determine oxidation numbers $α$ of a compound with $n$ species. The part of the algorithm for determining cation oxidation numbers (inside the black dashed box) is first applied making use of the preferred oxidation numbers for all species. If no successful assignment is achieved, it is employed a second time after checking for mixed-valence compounds using all known oxidation states (Table 1). The oxidation numbers of more electronegative cation species are iterated faster than the more electropositive ones. Three dots indicate proceeding equivalently for all further cation species. For multianion systems, atoms identified as additional anions during the structural analysis are excluded when assigning cation oxidation numbers.
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Figure 3
Corrections for different temperatures. (a) For 298.15 K, the CCE corrections to the DFT formation enthalpies are fitted to experimental room temperature formation enthalpies resulting in room temperature corrections. (b) For 0 K, first the thermal contribution deduced from a quasiharmonic Debye model [51] is subtracted from experimental values, resulting in estimates for 0 K formation enthalpies. CCE corrections fitted to these values yield 0 K corrections.
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Figure 4
Validating 0 K predictions. Deviations of (a) DFT formation enthalpies and (b) CCE 0 K predictions from experimental 0 K formation enthalpies from NIST-JANAF [21]. For ${Al}_{2} {SiO}_{5}$ , the results for both the kyanite (k) and andalusite (a) structures are depicted.
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