High-entropy materials for electrocatalytic applications: a review of first principles modeling and simulations

Figures & data

Table 1. Various developed software and the related basis set, functionals, and core potential.

Software	Basis set	Functionals	Core treatment
Gaussian^1	Gaussian basis	All functionals	Effective Core Potential
ORCA^2	Gaussian basis	GGA, meta-GGA, hybrid functionals	Effective Core Potential
Q-chem^3	Gaussian basis	LDA, GGA, and global hybrid functionals	Effective Core Potential
DALTON 2.0^4	Gaussian basis	LDA, GGA, hybrid functionals	Effective Core Potential
VASP^5	Plane wave	LDA, GGA, meta-GGA, and hybrid functionals	Ultrasoft pseudopotentials or projector-augmented wave potentials
CASTEP^6	Plane wave	LDA, GGA	Ultrasoft pseudopotentials / Nor-conserving pseudopotentials
ABINIT^7	Plane wave	LDA, GGA	Norm-conserving pseudopotentials
CP2K^8	Mixed Gaussian and plane waves	LDA, GGA, meta-GGA, hybrid functionals, and double-hybrid XC functionals	Pseudopotential, all-electron
WIEN 2K^9	The augmented plane wave plus local orbitals (APW + lo) method	LDA, GGA, meta-GGA, and hybrid functionals	Full potentials
DMol3^10	Numerical basis	LDA, GGA, B3LYP, meta-GGA, Hartree–Fock exact exchange	All-electron, elective Core potentials, all-electron relativistic, and semi-core pseudopotential
ADF^11	Slater basis	Numerical integration scheme	Frozen core approximation
Octopus^12	Numerical basis set, plane waves, and atomic orbitals	LDA, GGA	Optimized effective potential method (OEP)
LMTART^13	Atom centered local muffin-tin orbitals	LDA, GGA	Full potential
GPAW^14	Localized atomic orbitals and plane waves	LDA, GGA	Pseudopotential, all-electron

Notes: The websites of the software are listed as follows: 1. http://www.gaussian.com/; 2. https://orcaforum.kofo.mpg.de; 3. https://www.q-chem.com/; 4. https://www.daltonprogram.org/; 5. https://www.vasp.at/; 6. http://www.castep.org/; 7. https://www.abinit.org/; 8. https://www.cp2k.org/; 9. http://www.wien2k.at/; 10. https://wiki.fysik.dtu.dk/ase/ase/calculators/dmol.html; 11. https://www.scm.com/amsterdam-modeling-suite/; 12. https://octopus-code.org/wiki/Main_Page; 13. http://www.fkf.mpg.de/andersen/docs/lmtoart_programs.html; 14. https://wiki.fysik.dtu.dk/gpaw/.

Figure 1. (a) VCA models of FeCoNiCr, FeCoNiCrMn, and FeCoNiCrMnGe, respectively. Reprinted with permission from Ref. [42] Copyright 2011, Elsevier. (b) Crystal structure of PbSnTeSe HEA and Pb_0.99SnTeSe-Na_0.01 HEA. Reprinted with permission from Ref. [43] Copyright 2022, Elsevier. (c) CPA models for the equimolar ABCDE high-entropy alloys (HEAs). Reprinted with permission from Ref. [46] Copyright 2017, Creative Commons Attribution License (CC BY).

Figure 2. (a) Schematics for the supercell method. Reprinted with permission from Ref. [49] Copyright 2019, Elsevier. (b) 64-atom SQS used for DFT calculation with atomic species labeled. Reprinted with permission from Ref. [52] Copyright 2022, Elsevier. (c) Schematic representations of SQS and SSOS models for an HEA with FCC lattice. Reprinted with permission from Ref. [56] Copyright 2020, American Physical Society. (d) SLAE models for equiatomic BCC, FCC, and HCP HEAs. Reprinted with permission from Ref. [46] Copyright 2017, Creative Commons Attribution License (CC BY).

Figure 3. (a) Adsorption energy distributions. Reprinted with permission from Ref. [65] Copyright 2020, American Chemical Society. (b) Scaling relations on HEAs. Reprinted with permission from Ref. [70] Copyright 2020, Elsevier. (c) The heatmap for comparison of the strain effect on d-band center depth variations for the three low-index surfaces. Reprinted with permission from Ref. [73] Copyright 2020, Wiley-VCH GmbH. (d) Calculated charge-density difference of the P1 site for Co_0.6(VMnNiZn)_0.4PS₃. The red and blue regions refer to electron accumulation and depletion, respectively. Reprinted with permission from Ref. [83] Copyright 2022, American Chemical Society.

Figure 4. DFT calculation of FeCoNiCuPd HEA catalyst for alkaline HER. Reprinted with permission from Ref. [88] Copyright 2022, Elsevier.

Figure 5. (a) Free energy landscape and TDOS/PDOS plots for high entropy (oxy)hydroxides. Reprinted with permission from Ref. [91] Copyright 2022, Wiley-VCH GmbH. (b) DFT calculation of HEO catalyst for alkaline OER. Reprinted with permission from Ref. [92] Copyright 2022, Wiley-VCH GmbH.

Figure 6. (a) DFT calculation of HEAs for ORR. Reprinted with permission from Ref. [97] Copyright 2020, American Chemical Society. (b) Parameterization of the surface configurations and the activities of re-engineered compositions of the HEA IrPdPtRhRu. Reprinted with permission from Ref. [98] Copyright 2018, Elsevier.

Figure 7. (a) Schematic illustration of the rate-limiting factors in NH₃ decomposition. Reprinted with permission from Ref. [99] Copyright 2019, Springer Nature, Creative Commons Attribution License (CC BY). (b) Prediction of cathodic NRR activities for HEOs. Reprinted with permission from Ref. [104] Copyright 2022, Wiley-VCH GmbH.

Figure 8. (a) Theoretical catalysis results for the HEA, select pure TMDCs and silver. Reprinted with permission from Ref. [106] Copyright 2021, Wiley-VCH GmbH. (b) Comparison of adsorption characteristics of HEA. Reprinted with permission from Ref. [107] Copyright 2021, Springer Nature, Creative Commons Attribution License (CC BY).

Wang S, Xiong J, Li D, et al. Comparison of two calculation models for high entropy alloys: virtual crystal approximation and special quasi-random structure. Mater Lett. 2021;282:128754. doi:10.1016/j.matlet.2020.128754

 Web of Science ®Google Scholar

Raphel A, Vivekanandhan P, Rajasekaran AK, et al. Tuning figure of merit in Na doped nanocrystalline PbSnTeSe high entropy alloy via band engineering. Mater Sci Semicond Process. 2022;138:106270. doi:10.1016/j.mssp.2021.106270

 Web of Science ®Google Scholar

Tian F. A review of solid-solution models of high-entropy alloys based on ab initio calculations. Front Mater. 2017;4:1–10. doi:10.3389/fmats.2017.00036

 Web of Science ®Google Scholar

Ikeda Y, Grabowski B, Körmann F. Ab initio phase stabilities and mechanical properties of multicomponent alloys: a comprehensive review for high entropy alloys and compositionally complex alloys. Mater Charact. 2019;147:464–511. doi:10.1016/j.matchar.2018.06.019

 Web of Science ®Google Scholar

Kim G, Diao H, Lee C, et al. First-principles and machine learning predictions of elasticity in severely lattice-distorted high-entropy alloys with experimental validation. Acta Mater. 2019;181:124–138. doi:10.1016/j.actamat.2019.09.026

 Web of Science ®Google Scholar

Sorkin V, Tan TL, Yu ZG, et al. Generalized small set of ordered structures method for the solid-solution phase of high-entropy alloys. Phys Rev B. 2020;102:174209. doi:10.1103/PhysRevB.102.174209

 Web of Science ®Google Scholar

Pedersen JK, Batchelor T, Bagger A, et al. High-entropy alloys as catalysts for the CO2 and CO reduction reactions. ACS Catal. 2020;10:2169–2176. doi:10.1021/acscatal.9b04343

 Web of Science ®Google Scholar

Pedersen JK, Batchelor T, Yan D, et al. Surface electrocatalysis on high-entropy alloys. Curr Opin Electrochem. 2021;26:100651. doi:10.1016/j.coelec.2020.100651

 Web of Science ®Google Scholar

Wu T, Sun M, Huang B. Probing the irregular lattice strain-induced electronic structure variations on late transition metals for boosting the electrocatalyst activity. Small. 2020;16:2002434. doi:10.1002/smll.202002434

 Web of Science ®Google Scholar

Wang R, Huang J, Zhang X, et al. Two-dimensional high-entropy metal phosphorus trichalcogenides for enhanced hydrogen evolution reaction. ACS Nano. 2022;16:3593–3603. doi:10.1021/acsnano.2c01064

 PubMed Web of Science ®Google Scholar

Wang S, Xu B, Huo W, et al. Efficient FeCoNiCuPd thin-film electrocatalyst for alkaline oxygen and hydrogen evolution reactions. Appl Catal B. 2022;313:121472. doi:10.1016/j.apcatb.2022.121472

 Web of Science ®Google Scholar

Zhang L, Cai W, Bao N, et al. Implanting an electron donor to enlarge the d–p hybridization of high-entropy (oxy)hydroxide: a novel design to boost oxygen evolution. Adv Mater. 2022;34:2110511. doi:10.1002/adma.202110511

 Web of Science ®Google Scholar

Tang L, Yang Y, Guo H, et al. High configuration entropy activated lattice oxygen for O2 formation on perovskite electrocatalyst. Adv Funct Mater. 2022;32:2112157. doi:10.1002/adfm.202112157

 Web of Science ®Google Scholar

Jin Z, Lyu J, Zhao Y, et al. Rugged high-entropy alloy nanowires with in situ formed surface spinel oxide as highly stable electrocatalyst in Zn-air batteries. ACS Mater Lett. 2020;2:1698–1706. doi:10.1021/acsmaterialslett.0c00434

 Google Scholar

Batchelor T, Pedersen J, Winther S, et al. High-entropy alloys as a discovery platform for electrocatalysis. Joule. 2018;3:834–845. doi:10.1016/j.joule.2018.12.015

 Web of Science ®Google Scholar

Xie P, Yao Y, Huang Z, et al. Highly efficient decomposition of ammonia using high-entropy alloy catalysts. Nat Commun. 2019;10:4011. doi:10.1038/s41467-019-11848-9

 PubMed Web of Science ®Google Scholar

Sun Y, Yu L, Xu S, et al. Battery-driven N2 electrolysis enabled by high-entropy catalysts: from theoretical prediction to prototype model. Small. 2022;18:2106358. doi:10.1002/smll.202106358

 Web of Science ®Google Scholar

Cavin J, Ahmadiparidari A, Majidi L, et al. 2D high-entropy transition metal dichalcogenides for carbon dioxide electrocatalysis. Adv Mater. 2021;33:2100347. doi:10.1002/adma.202100347

 Web of Science ®Google Scholar

Mori K, Hashimoto N, Kamiuchi N, et al. Hydrogen spillover-driven synthesis of high-entropy alloy nanoparticles as a robust catalyst for CO2 hydrogenation. Nat Commun. 2021;12:3884. doi:10.1038/s41467-021-24228-z

 PubMed Web of Science ®Google Scholar