From Experiment‐Driven to Theory‐ and Data‐Driven: A Computational Paradigm Shift in High‐Entropy Electrocatalyst Design

ABSTRACT

High‐entropy materials (HEMs) have emerged as promising electrocatalyst platforms because compositional diversity enables tunable electronic structures and abundant active sites. With rising demands in energy conversion and environmental applications, theory now plays a central role in HEM design, in particular density functional theory (DFT), molecular dynamics (MD), and machine learning (ML). Recent advances in computational strategies for elucidating mechanisms and selecting optimal compositions are synthesized. The shift from experiment‐driven studies to proactive, theory‐ and data‐driven discovery is highlighted, enabled by the integration of high‐throughput calculations with ML for efficient screening. Method limits and key challenges are assessed, including black‐box interpretability, modeling of disorder and coverage, and gaps between theoretical models and experimental conditions, and directions in workflow standardization, open databases, and reproducible benchmarks are outlined. Building on these elements, a compact DFT‐ML‐MD closed‐loop framework is proposed that links atomic‐scale energetics to device‐level metrics, with the aim of guiding the accelerated discovery and deployment of high‐activity, durable high‐entropy electrocatalysts for sustainable energy.

High‐entropy electrocatalysts open vast composition‐site spaces that resist trial‐and‐error discovery. This review traces the shift from experiment‐led interpretation to theory‐ and data‐driven design, and shows how DFT, ML, and MD integrate into a closed loop that links atomic energetics to device‐level metrics, guiding synthesis, benchmarking, and operando feedback for durable high‐entropy electrocatalysts.

1. Introduction

In the interdisciplinary context of renewable energy, environmental remediation, and resource conversion, materials design is fundamentally shifting from optimizing single‐performance metrics to achieving synergistic improvements across multiple performance criteria [1, 2, 3, 4, 5, 6]. This shift is particularly pronounced in catalytic materials, which must not only demonstrate high activity and selectivity but also maintain superior stability and adaptability under diverse reaction conditions [7, 8, 9, 10]. Such demands for outstanding performance across several key indicators necessitate greater structural tunability and functional programmability, prompting continuous exploration of highly designable material systems. While conventional unary or binary electrocatalysts often face activity‐stability trade‐offs and scaling‐relation limits for reaction intermediates, high‐entropy materials (HEMs), characterized by diverse elemental compositions, tunable electronic structures, and multiple active sites, provide a versatile platform that stabilizes single‐phase solid solutions, prevents phase segregation, and potentially breaks traditional scaling relationships [11, 12, 13, 14, 15].

HEMs are typically defined as single‐phase alloys or metal compounds comprising five or more principal elements, with configurational entropy ≥1.61 R, calculated by Equation 1 [16, 17, 18], which exhibit unique characteristics including high‐entropy effects [19, 20], lattice distortion effects [21, 22], sluggish diffusion effects [23, 24], and cocktail effects [25, 26], forming the four fundamental features underpinning their distinctive properties [27].

$$\mathrm{\Delta }{S}_{\mathrm{config}}=-R\sum _{i=1}^n{x}_{\mathrm{i}}\ln x_{\mathrm{i}}$$ (1)

where ΔS _config is the configurational entropy, R represents the ideal gas constant (8.314 J mol⁻¹ K⁻¹), and x _i represents the mole fraction of component i.

HEMs create a spectrum of tunable active sites and exhibit multi‐element synergistic effects that modulate surface electronic structure and intermediate binding energies. At the same time, lattice distortion and sluggish diffusion in HEMs confer enhanced stability and resistance to sintering, corrosion, and other deactivation pathways under reaction conditions. Within electrocatalysis, these traits have increasingly positioned HEMs as essential platforms for investigating the impact of entropy on catalytic performance [28, 29, 30]. Researchers have successfully developed high‐entropy alloys (HEAs) [31, 32, 33], oxides (HEOs) [34, 35, 36], and sulfides [37, 38, 39], demonstrating remarkable performance in critical electrochemical reactions such as the oxygen evolution reaction (OER) [40, 41, 42, 43], hydrogen evolution reaction (HER) [44, 45, 46, 47], and carbon dioxide reduction reaction (CO₂RR) [48, 49, 50, 51].

The advantages of HEMs also create design challenges: the composition and configuration spaces are vast, surface sites are heterogeneous, and binding energies form broad distributions. To navigate this landscape, theory‐driven approaches are essential. In particular, density functional theory (DFT)‐based first‐principles calculations can swiftly predict critical parameters of HEMs, including electronic structures, stability, active sites, and catalytic performances prior to experimental validation [52, 53, 54, 55]. Complementarily, molecular dynamics (MD) simulations provide valuable insights into the dynamic structural evolution of HEMs, elucidating the structural and performance changes occurring during catalytic processes [56, 57, 58]. Furthermore, integrating rapidly evolving machine learning (ML) and high‐throughput computational methods [59, 60, 61, 62], theoretical calculations facilitate more efficient exploration of the extensive compositional space of high‐entropy electrocatalytic materials. Table 1 compares the methods. These methodologies preemptively identify optimal material combinations for superior catalytic performance and inform experimental synthesis strategies, significantly enhancing research efficiency and success rates. Nevertheless, computationally driven design faces practical challenges, including substantial computational resource demands, limited database scale, and the necessity to balance prediction accuracy with realistic synthetic feasibility [63, 64, 65, 66].

TABLE 1.

Comparison of DFT, MD, and ML in high‐entropy electrocatalyst research.

Met‐hod	Application scope	Scalability (size/throughput)	Accuracy	Computational cost	Limitations
DFT	Electronic structure, adsorption/free energies, reaction pathways, descriptor design	∼101–103 atoms; tens‐hundreds of candidates with high‐performance computing (HPC) [67, 68]	High for electronic structure and chemisorption on small‐medium cells [67, 68]	Very high; approximately cubic scaling with system size [67, 69, 70]	Sensitive to exchange‐correlation functional and self‐interaction; explicit constant electrode potential, solvation, and electric double layer (EDL) are non‐trivial; costly sampling of disorder/coverage [68, 71, 72]
MD	Thermal disorder; elemental segregation/reconstruction; diffusion; explicit solvent/interface dynamics	Classical MD: ∼103–106 atoms, ns‐µs; Ab initio molecular dynamics (AIMD): ∼102–103 atoms, ps‐ns [73, 74]	Moderate; captures structural dynamics and entropic effects [75]	Classical MD: moderate; AIMD: very high [75]	Classical MD is limited by force‐field quality/transferability; rare events and long times are hard to sample; electronic effects are absent unless using reactive force fields; AIMD is costly [73, 74, 76, 77]
ML	Surrogate modeling for adsorption/formation energies; high‐throughput composition/structure screening; pattern and descriptor discovery	Screens ∼104–106 candidates; easy parallelization [78, 79, 80]	Data‐dependent; can reach high predictive accuracy with high‐quality labeled data and appropriate features [78, 79, 80]	Low for prediction; training cost varies with dataset and model complexity [78, 79]	Requires high‐quality labeled data; limited extrapolation under domain shift; interpretability and uncertainty remain challenging [78, 79, 80]

This review emphasizes that research on high‐entropy electrocatalysts is undergoing a major paradigm shift—from experiment‐driven discovery toward genuinely theory‐ and data‐driven design [81, 82, 83]. Traditionally, experiment‐led workflows relied heavily on extensive trial‐and‐error and repeated testing; when confronted with the compositional and structural complexity of HEMs, such approaches are costly, time‐consuming, and often inefficient, making precise control and rapid design difficult [84, 85, 86]. In this context, theoretical calculations initially played only a supportive role, providing post hoc mechanistic insight into structures, properties, and catalytic pathways, and helping researchers rationalize experimental observations.

As sketched in Figure 1, recent advances in computational methodology, data science, and high‐throughput experimentation have progressively changed this situation. In Stage I (experiment‐driven), computation mainly assists experiments by interpreting active sites, reaction pathways, and adsorption behavior. In Stage II (theory‐guided coupling), prospective DFT/MD calculations and descriptor‐based models are used to pre‐screen compositions, surface terminations, and operating conditions, which are then refined through iterative feedback with experiments [87, 88, 89]. In Stage III (theory‐ and data‐driven design), classical theory is integrated with machine learning and high‐throughput screening to explore high‐dimensional composition‐structure spaces, identify hidden structure‐performance correlations, and close the design loop in a predictive, data‐driven manner [90, 91, 92]. Operationally, Stage II is defined by prospective pre‐experimental screening followed by experiment‐coupled refinement, whereas Stage III requires the explicit integration of machine learning or broader data‐driven high‐throughput workflows to enable predictive exploration of high‐dimensional design spaces. This evolution marks a fundamental shift in the role of computation in the HEMs field—from post hoc assistance to an a priori design engine that actively directs experimental efforts.

FIGURE 1.

Schematic of the paradigm shift in computational studies of high‐entropy electrocatalysts from mechanistic analysis to computation‐guided high‐entropy electrocatalyst design.

Overall, when coupled with experimental validation and feedback, a theory‐guided paradigm confers clear advantages for high‐entropy electrocatalysts, including reduced cost, improved efficiency, and enhanced predictive capability. This review focuses on how theory moves from a post hoc assistant to a genuine design engine for HEMs: a three‐stage paradigm (experiment‐driven, theory‐guided coupling, and theory‐ and data‐driven design) is formalized, representative case studies are mapped onto this framework, DFT, MD, and ML are integrated into a compact closed‐loop workflow that links atomic‐scale energetics to device‐level metrics and clarifies when each method is most appropriate, and theory‐experiment gaps and method‐specific limitations in high‐entropy systems are critically examined, thereby enabling the distillation of concrete design rules and workflow recommendations for future computation‐guided HEM discovery. Accordingly, Section 2 revisits Stage I (experiment‐driven, theory‐assisted studies), Section 3 highlights Stage II and Stage III case studies, and Section 4 discusses cross‐cutting challenges and the recommended integrated workflow. Collectively, this review aims to offer actionable guidance for the effective design, development, and deployment of high‐entropy electrocatalytic materials. In this context, the reaction‐specific modeling priorities discussed throughout this review are summarized in Table 2.

TABLE 2.

Reaction‐specific modeling priorities for high‐entropy electrocatalysts.

Reaction	Key factors	Suitable modeling level
Oxygen evolution reaction (OER)	*OH/*O/*OOH energetics across different local atomic environments; valence‐state flexibility; anodic reconstruction/segregation	DFT: ensemble thermodynamics; MD: reconstruction/segregation dynamics; ML: ensemble screening
Hydrogen evolution reaction (HER)	Site‐dependent *H binding; Volmer water‐dissociation barrier; bifunctional motifs on heterogeneous surfaces	DFT: site energetics/barriers; ML: motif screening; MD: interface dynamics
Oxygen reduction reaction (ORR)	*OH binding and 4e−/2e− selectivity across different surface sites; segregation‐shaped surface composition	DFT: pathway energetics; ML: selectivity screening; MD: segregation/dynamics
Carbon dioxide reduction reaction (CO2RR)	*CO/*COOH energetics across product‐selective local environments; cation/electric‐field effects at heterogeneous interfaces	DFT: adsorbate/interface energetics; MD: interface dynamics; ML: selectivity prediction
Nitrogen reduction reaction (NRR)	Probability of productive N2‐binding sites under bias; competition with HER	DFT: N2 adsorption/activation; ML: HER/NRR screening; MD: coverage dynamics

More fundamentally, high‐entropy electrocatalysts raise several questions that cannot be fully addressed by conventional catalyst models. In these systems, the catalytically relevant unit may be better understood as a dynamic ensemble of local motifs rather than as a single representative active site. Likewise, the nominal composition may not directly correspond to the true operando surface state because segregation, reconstruction, and coverage effects can continuously reshape the catalytically relevant interface. These features also limit the direct transfer of traditional descriptors developed for simpler materials, since catalytic behavior often depends on local‐environment‐sensitive interactions and site distributions. A further challenge is how to translate such site‐level energetics into experimentally measurable activity, selectivity, and stability. These questions define why high‐entropy electrocatalysts require not only faster screening, but also more realistic and multiscale computational design strategies.

2. Initial Stage of Theory‐Assisted Experiments: Mechanistic Exploration and Performance Interpretation

In this section, Stage I is highlighted, where computation mainly serves to interpret mechanisms and rationalize performance in experiment‐driven studies of high‐entropy electrocatalysts.

Due to the multi‐component nature and highly disordered structures, high‐entropy electrocatalysts exhibit exceptionally diverse physicochemical behaviors, significantly complicating a deep understanding of their catalytic mechanisms and structure‐property relationships [93, 94, 95]. In traditional catalytic systems, active centers, adsorption sites, and reaction pathways can typically be clearly identified through limited experimental techniques combined with theoretical analysis. However, the complex compositional tuning, atomic‐scale disorder, and diverse electronic structures inherent in high‐entropy materials mean that singular characterization approaches cannot fully elucidate their underlying catalytic mechanisms [53, 96, 97, 98]. Consequently, relying exclusively on experimental methods has become insufficient for comprehensively analyzing the microscopic mechanisms and controlling the performance of high‐entropy electrocatalysts.

In recent years, first‐principles calculation methods, especially density functional theory, have become essential theoretical tools for elucidating catalytic mechanisms and optimizing the performance of high‐entropy materials, due to their distinctive ability to quantitatively describe electronic structures, surface reactivity, and adsorption behavior at the atomic scale [99, 100, 101]. Concurrently, molecular dynamics simulations have demonstrated unique value in uncovering structural evolution under operational conditions, surface atom diffusion, elemental segregation, and dynamic stability of high‐entropy materials [102, 103]. MD simulations effectively track real‐time atomic movements and interfacial changes in complex high‐entropy systems during reactions, capturing structural reconstructions and physical mechanisms that are challenging to observe directly via experiments. By integrating with experimental observations, theoretical computations not only explain material performance but also guide the precise design and rational control of novel high‐entropy electrocatalysts, greatly expanding their application potential.

For consistency in the discussion that follows, the key electrochemical metrics and descriptors used throughout this review are summarized in Table 3.

TABLE 3.

Key electrochemical metrics and descriptors used in this review.

Term	Definition	High‐Entropy Consideration
Overpotential (η)	Extra potential is required beyond equilibrium.	May vary with reconstruction and local heterogeneity.
Half‐wave potential (E 1/2)	Potential at half of the limiting current, commonly used in ORR evaluation.	May broaden or shift with multiple active environments.
Turnover frequency (TOF)	Reaction events per site per unit time.	Often approximate because active sites are hard to define.
Faradaic efficiency (FE)	Fraction of charge forming the target product, commonly used for product‐selective reactions such as CO2RR and NRR.	Can be lowered by competing reactions or corrosion.
Mass activity	Kinetic current normalized by catalyst mass.	Depends on loading and catalyst utilization.
Specific activity	Kinetic current normalized by active surface area.	Depends on how electrochemical surface area (ECSA) is determined.
Tafel slope	Slope of η versus log (current density) in the Tafel region.	Reliable interpretation requires an appropriate linear region.
Adsorption free energy (ΔG ads)	Free‐energy change for intermediate adsorption on the surface.	Often better treated as a distribution in high‐entropy systems.
Free‐energy barrier/diagram	Barrier of an elementary step, or free‐energy profile of a reaction pathway.	Different local sites may exhibit different pathways and barriers.

As illustrated in Figure 2, DFT typically analyzes high‐entropy electrocatalysts by combining adsorption energetics and electronic‐structure descriptors. Adsorption energies of key intermediates (e.g., *OH, *O, *OOH, *H, or *CHO) on different local metal environments are converted into Gibbs free‐energy diagrams along the reaction coordinate, where the largest uphill step at the equilibrium potential defines the theoretical overpotential and the rate‐determining step. In parallel, density‐of‐states and charge–density‐difference plots link shifts in metal d states and O 2p states to stronger or weaker binding, providing a microscopic explanation for why certain high‐entropy sites are more active or selective than others.

FIGURE 2.

(a–d) DFT free‐energy diagrams and electronic‐structure analysis for OER on the high‐entropy spinel (Cr_0.2Mn_0.2Fe_0.2Ni_0.2Zn_0.2)₃O₄: (a) ΔG profiles at different metal sites; (b–d) DOS and charge–density differences for *OH, *O, and *OOH adsorption (yellow/blue: charge accumulation/depletion). Reproduced with permission [40]. Copyright 2022, Royal Society of Chemistry. (e–i) Mechanism, energy profiles, and PDOS for overall water splitting on FeCoNiWCuOOH@Cu: (e,f) OER and HER mechanisms; (g,h) free‐energy profiles; (i) PDOS of representative high‐entropy catalysts. Reproduced under the terms of the CC BY 4.0 license [105]. Copyright 2024, Wiley‐VCH. (j–l) Reaction pathways, free‐energy diagrams, and synergistic mechanism for EOR on PdAgSn/PtBi HEA catalysts: (j) reaction intermediates; (k) free‐energy diagrams for C1/C2 pathways at Pt and Pd sites on the (111) facet; (l) schematic of the synergistic enhancement. Reproduced with permission [106]. Copyright 2023, Wiley‐VCH.

For instance, recent studies demonstrated that the high‐entropy spinel oxide (Cr_0.2Mn_0.2Fe_0.2Ni_0.2Zn_0.2)₃O₄ exhibits outstanding OER activity, delivering a low overpotential of 295 mV at 10 mA cm⁻² with a Tafel slope of 53.7 mV dec⁻¹. DFT calculations performed in Vienna Ab initio Simulation Package (VASP) within the generalized‐gradient approximation using the Perdew–Burke–Ernzerhof (GGA‐PBE) functional for the exchange‐correlation interaction revealed that the enhanced activity originates from increased amounts of surface Ni^{3 +} sites, which facilitate metal‐oxygen electron transfer and significantly lower the reaction barrier (Figure 2a–d) [40]. Additionally, DFT investigations (spin‐polarized GGA‐PBE implemented in VASP) on a rare‐earth‐doped HEA, PtRuFeCoNiZn‐Ce/C, show that Ce doping induces surface electron delocalization and dipole formation, thereby lowering the adsorption energies of key intermediates and enhancing both HER and OER. Experimentally, this catalyst delivers ultralow overpotentials of 4 and 7 mV for HER (in 0.5 M H₂SO₄ and 1.0 M KOH, respectively) and 156 and 132 mV for OER (in 0.5 M H₂SO₄ and 1.0 M KOH, respectively) at 10 mA cm⁻²; a two‐electrode water electrolyzer assembled with this catalyst requires only 1.43 V to reach 10 mA cm⁻² [104].

The high‐entropy oxyhydroxide FeCoNiWCuOOH exhibits excellent OER/HER and overall water‐splitting performance in 1.0 M KOH. At 10 mA cm⁻², the OER and HER overpotentials are 200 and 18 mV, respectively, and the overall cell voltage is 1.40 V. The catalyst remains stable at 300 mA cm⁻² for 100 h in OER, 100 h in HER, and more than 1000 h for overall water splitting. Spin‐polarized DFT calculations using VASP with projector augmented wave (PAW), GGA using the PBE functional, and GGA+U with Löwdin‐orthogonalized projectors, indicate that the high‐entropy surface network substantially lowers the Gibbs free‐energy barriers, thereby reducing the theoretical overpotentials (Figure 2e–i) [105]. A Pd‐enriched‐core/Pt‐enriched‐shell HEA (PdAgSn/PtBi) showed high methanol oxidation reaction (MOR) and ethanol oxidation reaction (EOR) activity and durability, with MOR specific activity 4.7 mA cm⁻² and mass activity 2874 mA mg⁻¹ _(Pd+Pt), outperforming Pd/C and Pt/C by 1.7 (5.9) and 1.5 (4.8) times. DFT (Dmol3, GGA‐PBE, semi‐core pseudopotentials) attributes the enhancement to lattice strain and interfacial synergy that tune surface electronic structure and lower reaction barriers (Figure 2j–l) [106].

In the case of zirconium fluoride supported high‐entropy fluoride (HEF) catalysts, DFT calculations using the PAW method in VASP with the GGA‐PBE exchange‐correlation functional, and a special quasi‐random structure (SQS) model for the high‐entropy fluoride lattice, indicated that dynamically stable Ni‐Co redox pairs markedly lower the reaction barrier, leading to excellent OER activity (Figure 3a–d) [107]. Furthermore, the high‐entropy alloy nanoparticle catalyst Pt₁₈Ni₂₆Fe₁₅Co₁₄Cu₂₇ delivered outstanding HER and MOR performance, exhibiting an overpotential of 11 mV at 10 mA cm⁻² and mass activities of 10.96 A mg⁻¹ _Pt at −0.07 V vs. RHE for HER and 15.04 A mg⁻¹ _Pt for MOR in alkaline media. DFT calculations performed in CASTEP with GGA‐PBE, and Broyden–Fletcher–Goldfarb–Shanno (BFGS) geometry optimization indicate that rapid site‐to‐site electron transfer among multiple metallic sites underpins the high activity [108].

FIGURE 3.

(a–d) OER mechanisms and energetics on zirconium fluoride‐supported high‐entropy fluorides: (a) adsorbate evolution on Co‐based HEF, highlighting OOH formation via O─O coupling; (b) potential‐dependent OER pathway on Ni‐based HEF; (c,d) free‐energy diagrams on Co‐HEF (1.23 V vs. RHE) and Ni‐HEF (≈1.50 V vs. RHE). Reproduced under the terms of the CC BY 3.0 license [107]. Copyright 2025, Royal Society of Chemistry. (e–g) Structure, electronic states, and energetics of high‐entropy layered perovskite with exsolved core–shell nanoparticles for CO₂ electrolysis: (e) potential‐energy profiles on SrFeO_3‐δ (SFO) (222), RP‐SFO (110), and RP‐SFO@FeO (420) surfaces; (f) total DOS of key C‐bonding sites; (g) charge–density differences for CO₂ adsorption. Reproduced with permission [109]. Copyright 2023, Wiley‐VCH. (h–l) Atomic/electronic structure, d‐band center, and HER energetics of Pt‐modified high‐entropy rare‐earth oxides: (h) 3D contour plots of bonding/antibonding orbitals near the Fermi level; (i) PDOS; (j) comparison of d‐band centers; (k) site‐resolved PDOS for Pt and rare‐earth cations; (l) ΔG _*H, water‐dissociation barriers, and H₂‐evolution free‐energy diagrams. Reproduced with permission [110]. Copyright 2024, American Chemical Society.

Recently, a catalyst composed of a high‐entropy perovskite Pr_0.8Sr_1.2(CuFe)_0.4Mo_0.2Mn_0.2Nb_0.2O_4‐δ loaded with in situ exsolved CuFe@FeOx core–shell nanoparticles was used as the SOEC cathode for CO₂ electrolysis, delivering a current density of 1.95 A cm⁻² at 1.5 V and maintaining excellent stability for 200 h at 0.75 A cm⁻² and 800°C in pure CO₂ (Figure 3e–g) [109]. DFT calculations (VASP, PBE‐GGA with PAW, D3 vdW correction, and GGA+U with U−J = 4.0 eV for Fe) indicated that oxygen‐vacancy‐rich FeOx shells markedly expand the triple‐phase boundary (TPB), thereby enhancing CO₂ adsorption, activation, and dissociation kinetics and boosting both activity and durability.

Pt‐modified high‐entropy rare‐earth oxide Pt‐(LaCeSmYErGdYb)O delivered ultralow overpotentials of 12, 57, and 77 mV to reach 100 mA cm⁻² in 0.5 M H₂SO₄, 1.0 M KOH, and 1.0 M PBS, respectively; it also sustained 400 mA cm⁻² at 60°C for 100 h with a mass activity of 37.7 A mg⁻¹ _Pt and a turnover frequency of 38.2 s⁻¹ at 12 mV (Figure 3h–l) [110]. DFT calculations using CASTEP with the GGA PBE functional showed that strong interactions between Pt and the rare‐earth oxide support optimize the electronic structure and the adsorption of key intermediates, thereby enhancing HER activity.

Similarly, subnanometer HEA nanowires PtRuNiCoFeMo achieved a mass activity of 6.75 A mg⁻¹ _(Pt+Ru) and a specific activity of 8.96 mA cm⁻² for HOR, while maintaining performance in the presence of 1000 ppm CO (Figure 4a–g) [111]. DFT calculations using CASTEP with the GGA PBE functional indicate that strong multi‐metal interactions tune the adsorption of protons and hydroxyl groups, thereby enhancing HOR kinetics. Moreover, studies on high‐entropy alloys containing interstitial oxygen (HEA‐O) show that interstitial O atoms act as electronic buffers, reshaping the local electronic structure of catalytically active metals and thereby enhancing both stability and activity. DFT calculations performed in VASP within the GGA using the PBE functional, after screening 100 random initial geometries and fully optimizing the lowest‐energy bulk model, corroborate that interstitial O stabilizes charge distribution and beneficially tunes adsorption energetics [112].

FIGURE 4.

(a–g) Atomic/electronic structure and HOR energetics of subnanometre HEA nanowires: (a) top view of the optimized HEA SNWs (Pt, Ni, Co, Fe, Mo, Ru); (b) 3D electronic distribution near the Fermi level; (c, d) Partial density of states (PDOS) and site‐resolved PDOS; (e, f) H and OH binding energies on HEA SNWs/C versus Pt(111) and PtRu(111); (g) HOR free‐energy profiles on HEA SNWs/C, Pt(111), and PtRu(111). Reproduced under the terms of the CC BY 4.0 license [111]. Copyright 2021, Springer Nature. (h–l) Machine‐learning‐guided analysis of active sites and elemental distributions in high‐entropy sulfide electrocatalysts: (h) DFT + ML + MC + oxidation workflow; (i) spatial distribution of Co, Cr, Fe, Mn, Ni in FeCoNiCrMnS₂ nanoparticles; (j) elemental‐affinity network; (k) volcano plot of element‐dependent glycerol‐oxidation sites; (l) coordination‐element fractions for Cr/Ni and Co phases for average and elite active sites. Reproduced with permission [113]. Copyright 2023, Elsevier.

Of particular note, a direct glycerol fuel cell based on FeCoNiCrMnS₂ delivered a peak power density of 50.1 mW cm⁻² with formate selectivity over 80% (Figure 4h–l) [113]. To rationalize this performance, density functional theory in combination with Monte Carlo (MC) and machine learning was employed. A high‐dimensional neural network potential (HDNNP) trained on spin‐polarized PBE within GGA, together with Monte Carlo identity‐swap sampling, enabled large‐scale exploration of thermodynamically favored configurations. The calculations indicate that Ni and Co serve as the primary active sites, while Cr and Mn modulate the local electronic structure and the distribution of adsorption energies, thereby enhancing overall activity. Although machine learning was involved, it was used here primarily for post hoc mechanistic interpretation and performance attribution rather than prospective screening. This example is therefore classified as Stage I, while also illustrating how such combined methods can lay methodological groundwork for later data‐driven design.

Another study of the AgAuCuPdPt high‐entropy alloy combined Monte Carlo‐molecular dynamics (MC/MD) revealed pronounced surface segregation relevant to CO₂RR [114]. Ag enriches the outermost layer, Au preferentially occupies subsurface regions, Pt remains largely in the bulk, while Cu and Pd adopt intermediate, near‐surface distributions—thereby increasing the number and diversity of Ag‐centered surface sites and the heterogeneity of adsorption environments. Simulations employed an embedded‐atom method (EAM) in LAMMPS at 1200 K for low‐index slabs (100), (110), (111), (211) (exchanges restricted to the top six layers) and for nanoparticles (∼2.6–2.7 nm, ∼6 × 10³ atoms; full‐atom exchanges), indicating segregation within ∼1 nm of the surface. These results underscore that explicit treatment of segregation/reconstruction should precede activity modeling to obtain realistic active‐site ensembles and more reliable catalytic predictions.

As mentioned above, contemporary theory‐assisted studies of high‐entropy electrocatalysts predominantly use plane‐wave DFT (GGA‐PBE/PAW, with frequent DFT+U and dispersion corrections), 400–600 eV cutoffs and Γ/Monkhorst‐Pack meshes on slab‐plus‐vacuum models; disorder is treated via SQS/cluster expansion or local‐motif sampling, solvation/potential via implicit media and the computational hydrogen electrode, and kinetics via microkinetics. MD complements DFT by tracking segregation/reconstruction (increasingly with ML interatomic potentials), while ML surrogates (e.g., Gaussian Process Regression, CGCNN) accelerate screening across vast composition‐site spaces. Key limitations persist: functional selection bias; fixed‐charge treatments that miss double‐layer/constant‐potential effects; incomplete sampling of configurations, coverages, and dynamics; and uncertain translation from site energetics to device‐level metrics. Emerging remedies include constant‐potential/grand‐canonical DFT with improved solvation, uncertainty‐aware ranking, ML‐accelerated configurational averaging and active learning, microkinetic‐transport coupling under device‐relevant constraints, and synthesizability/phase‐stability filters with multi‐objective criteria (activity, durability, cost). Together, these developments establish the methodological foundation from which later predictive design strategies emerge.

Beyond its methodological role, the key conceptual advance of Stage I is that it recasts high‐entropy electrocatalysts not as uniform surfaces with a few representative active sites, but as heterogeneous ensembles of local motifs with distributed adsorption energetics and evolving surface states [115, 116]. Recent theory‐assisted studies increasingly show that catalytic behavior in these systems is governed by environment‐dependent binding strengths and motif‐specific electronic interactions, rather than by a single optimal site or a simple descriptor inherited from conventional catalysts. This perspective is uniquely important for high‐entropy materials, in which compositional disorder, local configurational diversity, and surface segregation or reconstruction are intrinsic features that directly shape the population of catalytically relevant sites under working conditions [117]. However, because most Stage I models still simplify operando surface populations and motif statistics, the link between distributed site energetics and macroscopic catalytic response remains only partially resolved. These unresolved issues define the central bottlenecks of Stage I and, more importantly, provide the rationale for the emergence of Stage II and Stage III strategies, where motif‐aware screening, uncertainty‐aware learning, and more explicit treatment of disorder and dynamics become essential for predictive design.

3. Transition of Research Paradigm: From Computational Validation to Active Design

Building on the theory‐assisted case studies discussed in Section 2, this section focuses on the progression from Stage II (theory‐guided coupling) to Stage III (theory‐ and data‐driven design) in high‐entropy electrocatalyst research.

As sketched in Figure 1, the computational paradigm shift can be understood in three stages. In Stage I (experiment‐driven), computation plays mainly a post hoc, theory‐assisted role: DFT and MD are used to rationalize experimentally observed phenomena such as reaction pathways, active‐site distributions, and adsorption behaviors at the microscopic level [118, 119, 120]. This is particularly important for high‐entropy systems, where the intrinsic multi‐component nature and structural disorder make it difficult for purely experimental approaches to fully elucidate catalytic mechanisms, and atomic‐scale simulations provide critical mechanistic insight and performance interpretation for experiment‐led studies [121, 122, 123]. The following subsections therefore focus on Stage II (theory‐guided coupling) and Stage III (theory‐ and data‐driven design), where computation begins to pre‐screen compositions and operating conditions and ultimately becomes a primary driver for proposing and optimizing high‐entropy electrocatalysts.

With rapid advances in theoretical methodologies, data science, and modeling techniques, computation has progressed from this passive role to an active engine that guides experiments. In Stage II (theory‐guided coupling), prospective DFT/MD calculations and descriptor‐based models are used to pre‐screen compositions, surface terminations, and treatment conditions, which are then refined through iterative experimental feedback loops [124, 125, 126]. In Stage III (theory‐ and data‐driven design), classical theory (DFT, MD) is integrated with machine learning and high‐throughput experimentation to explore high‐dimensional compositional spaces, identify hidden structure‐performance correlations, and close the design loop in a data‐driven manner [28, 127, 128]. The case studies in this section are organized following these three stages, moving from post hoc mechanistic interpretation to theory‐guided optimization and finally to fully computation‐driven discovery of high‐entropy electrocatalysts.

3.1. Theory‐Guided Computational Design

For example, spin‐polarized DFT (VASP, GGA‐PBE with D3 and DFT+U under implicit solvation) predicts Fe–Co–Ni–Cu–Rh high‐entropy clusters anchored on N‐doped graphene to be highly active for oxygen reduction reaction (ORR), OER, and CO₂RR [129]. A representative motif, CoNiCuRh@FeN₄, shows overpotentials of ≈0.37 V for ORR and OER and 0.24 V for CO₂→CO; FeNiCuRh@CoN₄ reaches ≈0.35 V for CO₂→CH₃OH. The high‐entropy cluster electronically modulates the M‐N₄ center, enhancing charge transfer and stabilizing key intermediates, thereby improving activity and stability.

For the Co–Cu–Fe–Mo (oxy)hydroxide catalyst, spin‐polarized DFT (VASP, PBE‐PAW) on a CoOOH(012) slab with Co‐site substitution was used to screen adsorption configurations and barriers of key OER intermediates, yielding a “top‐level” design strategy for high‐entropy electrocatalysts. The CHE calculations predicted CoCuFeMoOOH to have the lowest theoretical overpotential (≈0.32 V, versus ≈0.51 and 0.89 V for CoCuMoOOH and CoFeMoOOH), although the absolute values overestimated experiment by ∼0.1–0.6 V. Experiments confirmed this ranking, and CoCuFeMoOOH delivered the best OER performance, with an overpotential of 199 mV at 10 mA cm⁻², a Tafel slope of 48.8 mV dec⁻¹ in 1 M KOH, and stable operation for 72 h (Figure 5a–d) [130]. Further studies introduced an electron donor (such as Ag) to high‐entropy (oxy)hydroxides (Cu–Co–Fe–Ag–Mo), thereby enlarging the metal‐oxygen d‐p hybridization and enhancing OER activity (Figure 5e–h) [42]. Notably, this work for the first time proposed metal‐oxygen d‐p hybridization as a quantitative descriptor for catalytic activity in high‐entropy (oxy)hydroxides. DFT results showed that all metal sites, including those in Ag nanoclusters, were activated, with Ag sites exhibiting the lowest overpotential (η ≈ 0.34 V), which is ≈0.12 V higher than the experimental η ₁₀ of 218 mV. Accordingly, the fabricated Ag‐modified high‐entropy (oxy)hydroxide (Ag@CoCuFeAgMoOOH) delivered a low overpotential of 270 mV at 100 mA cm⁻² and a small Tafel slope of 35.3 mV dec⁻¹, together with good electrochemical stability, confirming the synergistic effect between electron donors and high‐entropy matrices as well as the performance benefits provided by the electron donor.

FIGURE 5.

(a–h) Electronic structure, adsorption energetics, and OER free‐energy landscapes of high‐entropy oxyhydroxides: (a) adsorption geometries of intermediates on CoOOH and multi‐component Co‐based oxyhydroxides; (b, e, f) free‐energy diagrams at 0 V (including CoCuFeAgMoOOH and Ag@CoCuFeAgMoOOH); (c, d, g, h) DOS/PDOS and charge‐density differences. Reproduced with permission [42, 130]. Copyright 2022, Wiley‐VCH. (i–p) Structure evolution and DFT‐guided NO₃ ⁻RR catalyst design of Pt‐based high‐entropy intermetallics: (i–k) ΔH _mix‐driven structural evolution of Pt_0.8Fe_0.2Co_0.2Ni_0.2Cu_0.2, including schematic structural change, pairwise ΔH_mix values, and XRD patterns at different annealing temperatures; (l–p) Atomic‐scale ordering, electronic structure, nitrate adsorption, and HER energetics of Pt‐based high‐entropy intermetallics: (l) ordering degree versus annealing temperature; (m) PDOS for three HEIs; (n) NO₃ ⁻ adsorption sites and ΔE_NO3 on the [110] facet; (o) HER Gibbs free‐energy diagrams; (p) ΔE_*H at stable sites. Reproduced with permission [131]. Copyright 2024, Wiley‐VCH.

Moreover, regarding Pt‐based high‐entropy intermetallic (HEI) catalysts for the electrochemical reduction of nitrate (NO₃ ⁻RR) to ammonia (NH₃), the multi‐site synergy mechanism was elucidated for the first time (Figure 5i–p) [131]. DFT calculations (spin‐polarized, VASP with GGA‐PBE and PAW) and atomic‐scale structural analysis revealed that cooperative adsorption among multiple metallic sites effectively decreased the reaction barriers and markedly improved both Faradaic efficiency (FE) and cycling stability. The rate‐determining *NO → *NOH step showed a maximum free‐energy barrier of ∼0.23 eV (≈0.23 V), which is only ∼0.07 V smaller than the experimental potential (−0.30 V vs. RHE) for nearly quantitative NH₃ production, indicating good agreement between theory and experiment. Accordingly, quinary Pt_0.8Fe_0.2Co_0.2Ni_0.2Cu_0.2 HEI nanoparticles on N‐doped mesoporous carbon delivered over 97% NH₃ FE and sustained over 20 cycles under both acidic and basic conditions.

Another example is plasma‐regulated 2D high‐entropy oxide (HEO) arrays for the hydrogen evolution reaction (Figure 6a–d) [132]. Spinel‐type FeNiCoMnVO_x nanosheet arrays were grown on conductive substrates and treated with Ar plasma to create oxygen vacancies and activate multiple metal sites. DFT calculations indicated that introducing a single oxygen vacancy (HEO_(x‐1)) moves the hydrogen adsorption free energy toward a near‐thermoneutral value (ΔG _H ≈ 0.34 eV), consistent in trend with the experimentally observed low HER overpotential, although the simple ΔG _H descriptor still underestimates the absolute activity. Experimentally, the optimized Ar‐15‐FeNiCoMnVO_x delivered an overpotential of 81 mV at 10 mA cm⁻², a Tafel slope of 88 mV dec⁻¹, and stable operation for 100 h in 1.0 M KOH.

FIGURE 6.

(a–d) DFT‐optimized structures and HER energetics of FeNiCoMnVO_x high‐entropy oxides: view of the H‐adsorbed surfaces, models with one and two surface oxygen vacancies, and corresponding HER free‐energy diagrams. Reproduced with permission [132]. Copyright 2022, Elsevier. (e–g) OER modeling on IrRuO_x and IrRu‐HEO: reaction pathway models, Gibbs free‐energy diagrams, and PDOS. Reproduced with permission [133]. Copyright 2024, Elsevier. (h–k) Site‐specific electronic/energetic analysis of NiFeCrVTi‐based high‐entropy alloys: schematic elemental distribution and H₂O adsorption on Ni‐HEA‐30; projected d‐orbital DOS for Ni, Fe, and Cr; adsorption free energies of H₂O/H and rate‐determining steps at different sites. Reproduced with permission [134]. Copyright 2023, Wiley‐VCH.

In another study focused on RuIrFeCoNi high‐entropy oxides, DFT calculations (PBE‐GGA) were systematically used to analyze the influence of individual metallic elements on the electronic structure and the adsorption energies of OER intermediates. The results revealed that multimetallic synergistic effects can effectively downshift the d‐band center and optimize the adsorption of key intermediates such as *OH, thereby lowering the energy barrier for the OER (Figure 6e–g) [133]. Although the calculated limiting overpotential (∼0.73 V) substantially exceeded the experimental value, the DFT trends correctly captured the activity enhancement of the high‐entropy oxide. Guided by these theoretical insights, the synthesized rutile‐type (RuIrFeCoNi)O₂ high‐entropy oxide prepared via molten‐salt oxidation not only significantly reduced the noble‐metal content, but also exhibited an overpotential of 261 mV at 10 mA cm⁻² and outstanding cycling stability, maintaining 1.73 V at 1 A cm⁻² over 100 h during proton exchange membrane (PEM) water electrolysis.

Furthermore, through high‐throughput computational pre‐screening prior to synthesis, researchers rapidly prioritized a promising NiFeCrVTi composition and then fabricated the corresponding high‐entropy alloy via laser etching (Figure 6h–k) [134]. While not yet an explicitly data‐driven workflow, this study already reflects the broader shift toward more predictive and computationally proactive high‐entropy electrocatalyst discovery. From this perspective, the case also hints at how pre‐synthetic computational screening can begin to incorporate considerations of compositional accessibility and phase stability. This material demonstrated excellent HER performance in seawater, delivering an overpotential of 55.9 mV at 10 mA cm⁻² with a Tafel slope of 47.3 mV dec⁻¹. DFT calculations (spin‐polarized PBE‐PAW) indicated that incorporating Cr enhances water‐molecule adsorption, while precise electronic‐structure modulation optimizes H binding at Ni sites. Although the calculated barrier for the rate‐determining step (∼0.10 eV) still overestimates the required driving force compared with experiment, it captures the enhanced activity and corrosion resistance.

It is also worth noting that spinel‐type high‐entropy oxides show lattice strain from elemental mixing that is pivotal to OER performance (Figure 7a–e) [135]. Combined DFT (VASP, PBE‐PAW with DFT+U) and experiments indicate that compositional mixing plus lattice strain broaden the adsorption‐energy distribution at active sites and lower the limiting overpotential to ∼0.29 V, in close agreement with the experimental overpotential (∼307 mV at 10 mA cm⁻²) and enabling durable operation over 168 h.

FIGURE 7.

(a–e) Theoretical modeling and activity prediction of spinel high‐entropy oxides for OER: (a) schematic HEO active site; (b) relative mixing enthalpy of different active sites; (c) OER volcano heatmap based on *O/*OH binding; (d) distribution of Cr/Co/Fe‐type active sites versus overpotential; (e) predicted activity trends from explicitly calculated *OOH. Reproduced under the terms of the CC BY 4.0 license [135]. Copyright 2023, Springer Nature. (f–j) Synthesis mechanism, nanostructure evolution, and nanoconfinement effects in ultrafine AuPdPtRhIr HEAs: (f–h) MD simulations of size‐dependent solid‐state diffusion; (i) N₂ sorption/desorption isotherms and pore‐size distributions of AuPdPtRhIr@PVA and HEA@C nanohybrids; (j) finite‐element analysis of N₂ distribution with and without porous carbon shells. Reproduced with permission [136]. Copyright 2023, Wiley‐VCH.

Beyond such descriptor‐ and energetics‐guided activity optimization, computation in Stage II is also increasingly used to address synthesis feasibility, phase formation, and structural stability. In this context, DFT and MD play complementary roles. DFT is more suitable for evaluating local energetics, adsorption behavior, and activity trends, whereas MD is especially useful for tracking atomic motion, interdiffusion, and structural evolution under processing or operating conditions.

For example, an MD simulation study (LAMMPS, 2–6 nm nanoparticles) on AuPdPtRhIr high‐entropy alloys synthesized via polymer‐confined pyrolysis highlights the importance of synthesis feasibility and single‐phase formation in high‐entropy electrocatalyst design (Figure 7f–j) [136]. The simulations show that PVA confinement promotes the formation of small metal nanoparticles during the hydrothermal stage, which can more readily undergo thermodynamically driven solid‐phase diffusion during pyrolysis and evolve into a homogeneous single‐phase HEA. In contrast, larger particles are less able to achieve complete interdiffusion and tend to remain as multiphase alloys, indicating that particle size is a key determinant of single‐phase formation. The PVA‐derived carbon shell also suppresses nanoparticle aggregation during pyrolysis, further improving structural uniformity and phase stability. Experimentally, the resulting HEA@C nanohybrid delivered a NO₃ ⁻ yield rate of 23.8 µg h⁻¹ mg⁻¹ _cat and a FE of 13.8% for the nitrogen oxidation reaction (NOR), confirming the practical viability of this synthesis‐oriented design strategy.

Overall, these studies show that the distinctive contribution of Stage II is not simply improved activity prediction, but theory‐guided prioritization before synthesis. In this regime, computation narrows the vast high‐entropy design space by identifying catalytically favorable and experimentally accessible compositions, local motifs, surface terminations, defect states, and processing conditions. This shift is especially important for high‐entropy systems, where local configurational diversity, multimetallic synergy, and phase‐formation constraints make trial‐and‐error optimization inefficient. At the same time, Stage II extends computation beyond activity descriptors to synthesis feasibility, phase stability, and structural evolution, with DFT and MD providing complementary guidance for both performance and structure control. However, because most Stage II workflows still rely on limited motif sampling and simplified surface or operando representations, they mainly enable informed prioritization rather than fully predictive discovery, thereby setting the stage for Stage III data‐driven and uncertainty‐aware design.

3.2. Data‐Driven and ML‐Assisted Design

With the rapid advancement of data science and computational power, ML has quickly emerged as an indispensable tool in the field of high‐entropy electrocatalysts. ML, by leveraging high‐throughput computation, data mining, and predictive modeling, significantly enhances the efficiency of catalyst screening and design, opening new avenues for efficient exploration and optimization of complex compositional systems.

For example, in the optimization of HEA catalysts for the ORR, Bayesian optimization (BO) was combined with DFT to efficiently explore the quinary Ag–Ir–Pd–Pt–Ru and Ir–Pd–Pt–Rh–Ru composition spaces. DFT‐calculated *OH/*O adsorption energies on fcc(111) slabs (GPAW, RPBE; 2 × 2, four‐layer) were used to train a kinetic model, and a Gaussian‐process BO located locally optimal compositions in only about fifty samples. Subsequent binary composition spreads confirmed that the BO‐predicted optima lie close to the experimental activity maxima. In the Ag–Pd system, the optimum is found around Ag₁₅Pd₈₅ in theory versus Ag₁₄Pd₈₆ in experiment, a difference of only ∼1 at.%, illustrating that BO‐guided DFT can efficiently target high‐activity regions in five‐component spaces (Figure 8a,b) [137]. Machine learning algorithms based on the Nudged Elastic Band (NEB) method have also been used to pinpoint “activity ridges” within the five‐element HEA compositional landscape, substantially narrowing the search space for optimal catalysts (Figure 8c,d) [138]. In practice, ML‐NEB found connected maxima—including a global optimum near Ag₁₇Pd₈₃—with ∼10–50 samples per ternary and about 10² in quinary spaces, cutting the sampling from ∼4717 with classic NEB to 112, or 52 with directed evolution, using a Gaussian‐process surrogate trained on DFT‐derived *OH/*O adsorption on fcc(111).

FIGURE 8.

(a, b) Bayesian optimization and experimental benchmarking for HEA catalyst discovery: (a) optimization workflow for HEA compositions, terminated after 150 samples with the acquisition function evaluated on 1000 random candidates; (b) comparison of simulated and experimental activities for Ag–Pd, Pd‐Ru, and Ir‐Pt alloys at 800 mV vs. RHE (normalized currents, Pd–Ru outliers removed). Reproduced under the terms of the CC BY‐NC‐ND 4.0 license [137]. Copyright 2021, Wiley‐VCH. (c, d) Pathway exploration and directed evolution in composition space: (c) element‐substitution pathways via ternary subspaces starting from Ir₄₅Pd₅₅, tracing an activity ridge in the Ag–Ir–Pd–Pt–Ru HEA space; (d) directed‐evolution trajectories and activity landscapes in the Ir–Pd–Pt space. Reproduced under the terms of the CC BY 4.0 license [138]. Copyright 2022, Wiley‐VCH.

To operationalize segregation control in AgAuCuPdPt HEAs for CO reduction (COR), a layered workflow was established [139]. This workflow combined machine‐learned CO/H adsorption models, EAM‐based Monte Carlo/Molecular Mechanics (MC/MM) simulations to generate segregated (111) surfaces, Bayesian optimization to locate high‐activity regions, and DFT free‐energy validation (Quantum Espresso, RPBE‐PAW). This pipeline identified a top segregated alloy, 22.3%Au‐20.81%Cu‐27.11%Pd‐29.77%Pt, with Cu‐like *CO but weaker *H binding; free‐energy diagrams predict COR dominated by the *HCO pathway near −1 V vs. RHE and a smaller thermodynamic limiting potential than Cu(111), implying suppressed HER and enhanced selectivity.

In the development of low‐platinum catalysts, crystal graph convolutional neural networks (CGCNNs) have been applied to accelerate the discovery of high‐entropy intermetallics such as Pt(FeCoNiCu)₃ by predicting formation energy and surface strain (CGCNN trained on 538 DFT datapoints; VASP PBE‐PAW; MAE ≈ 0.011 eV atom⁻¹ for formation energy and 0.003 for surface strain) (Figure 9a–h) [140]. This ML‐guided route yielded Pt(FeCoNiCu)₃/C with a specific activity of 7.92 mA cm⁻² and a mass activity of 4.09 A mg⁻¹ _Pt at 0.9 V vs. RHE for ORR, and excellent durability, showing only an 11 mV E _1/2 loss after 5000 cycles.

FIGURE 9.

(a–h) ML‐aided design, structural/electrochemical characterization, and ORR performance of low‐Pt high‐entropy intermetallic catalysts: (a) schematic of surface strain at the intermetallic/alloy core‐Pt shell interface; (b) ML‐assisted element selection workflow; (c, d) CV and LSV curves in 0.1 M HClO₄; (e) mass and specific activities at 0.90 V vs. RHE; (f) correlation between specific activity and surface strain; (g) LSV curves before and after 5000 accelerated cycles; (h) Pt leaching in PtCu₃ and Pt(FeCoNiCu)₃ after durability tests. Reproduced with permission [140]. Copyright 2024, Wiley‐VCH. (i, j) Bayesian optimization of composition and OER activity in multielement perovskite HEOs: (i) BO‐guided experimental workflow over multiple generations; (j) OER activity and Cr/Mn/Fe/Co/Ni contents of BO‐HEOs and reference HEOs. Reproduced with permission [141]. Copyright 2022, American Chemical Society.

In addition, the composition optimization of multicomponent perovskite oxides such as La(Cr,Mn,Fe,Co,Ni)O₃ has benefited from Bayesian optimization, which identifies ideal elemental ratios for maximizing OER performance and surpasses equimolar references (Figure 9i,j) [141]. Using three rounds of Bayesian optimization coupled with experiments and targeting the current density at 1.6 V vs. RHE, the study identified compositions with a peak activity of 0.26 mA cm⁻². Perovskites selected by Bayesian optimization outperformed the equimolar LaCr_0.2Mn_0.2Fe_0.2Co_0.2Ni_0.2O₃ benchmark in 92% of cases, compared with 13% for random selections.

Of particular note, the OxiGraphX GNN model enables efficient prediction of oxygen‐vacancy formation energies (OVFE) in high‐entropy perovskite oxides and rapid screening of high‐activity compositions (trained on ∼9000 DFT labels; MAE ≈ 0.023 eV) (Figure 10a) [142]. Guided by the model, Ba₄Sr₄La₂₄Co₈Ni₈Mn₈Fe₈O₉₆ with higher vacancy content (∼29%) achieved the lowest OER overpotential of ∼540 mV at 10 mA cm⁻² in 1 M KOH, outperforming Sr₈La₂₄Co₈Ni₈Mn₈Fe₈O₉₆ (∼600 mV) and La₃₂Co₈Ni₈Mn₈Fe₈O₉₆ (∼670 mV).

FIGURE 10.

(a) ML‐guided framework and neural‐network model for oxygen‐vacancy formation energy prediction in high‐entropy perovskite oxides: integrated ML‐DFT‐experiment workflow. Reproduced under the terms of the CC BY‐NC‐ND 4.0 license [142]. Copyright 2025, Wiley‐VCH. (b, c) High‐throughput synthesis, characterization, and ML‐assisted activity evaluation of microscale HEA catalyst arrays: workflow for element selection, array fabrication, SEM/EDS mapping, rapid HER activity screening with SECCM, and ensemble‐ML prediction. Reproduced with permission [143]. Copyright 2024, American Chemical Society.

To enable efficient experimental screening of complex systems, scanning electrochemical cell microscopy (SECCM) was coupled with an ensemble ML model to rapidly identify HER‐active HEA compositions (Figure 10b,c) [143]. In a Fe–Co–Ni–Pt–Pd quinary space, 238 microscale compositions were measured and used to train an ensemble of random forest, gradient boosting, XGBoost, and a small Multi‐Layer Perceptron (MLP), which then guided macro‐scale validation. The best composition, Fe_0.15Co_0.4Ni_0.05Pt_0.32Pd_0.08, delivered an overpotential of 13 mV at 10 mA cm⁻² in 0.5 M H₂SO₄ and a mass activity of 5.92 A mg⁻¹ at −0.05 V vs. RHE, outperforming equiatomic analogues and Pt/C.

In CO₂RR catalyst design, ML has been used to overcome adsorption‐scaling limits by predicting site‐specific activity in FeCoNiCuMo HEAs. A compact deep model trained on 1280 DFT labels (VASP/PBE‐PAW) achieved MAE ≈ 0.07–0.10 eV for *COOH/*CO/*CHO and identified sites with computed CH₄ limiting potentials of 0.29–0.51 V vs. RHE, outperforming Cu(111) at ∼0.74 V; the scaling break stems from flexible rotation of COOH/CHO at Mo/Cu‐neighbor top sites that decouples ΔE _CO from ΔE _COOH/ΔE _CHO [61]. Furthermore, machine‐learning‐accelerated DFT (VASP, PBE‐PAW) screening of Cu‐based HEAs enabled the prediction of ethylene‐selective compositions [144]. Among 106 045 Cu‐Zn‐Pd‐Ag‐Au candidates, Cu_0.36Zn_0.18Pd_0.1Ag_0.18Au_0.18 was identified, lowering the limiting step to 0.78 eV versus 0.87 eV on Cu(111) and suppressing HER.

For the nitrogen reduction reaction (NRR), deep neural networks (DNNs) enabled rapid screening of ∼3000 Mo–Cr–Mn–Fe–Co–Ni–Cu–Zn HEA candidates, trained on ∼1568 DFT (VASP, BEEF‐vdW/PAW) adsorption energies. Top‐ranked compositions show ∼42% of sites with exothermic N₂ adsorption and *N₂→*NNH barriers as low as 0.74 eV, lower than on Fe(111), indicating facilitated activation and strong NRR prospects (Figure 11a–e) [145]. Another recent study highlighted the significance of competitive adsorption under aqueous conditions, showing how quantum‐mechanics‐guided DNNs reveal the interplay among N, O, and H adsorption and suggest tuning surface coverages to enhance NRR (Figure 11f,g) [146]. Trained on DFT (VASP, BEEF‐vdW/PAW; MAE ≈ 0.2 eV), the model evaluated coverages from −0.6 to +0.6 V vs. RHE across 9668 quinary HEAs (2000 microstructures per composition) and found that even at the *H/*O crossover the probability of N₂ adsorption remains low, indicating the need for O/H‐repelling strategies or elevated N₂ pressure to boost NRR.

FIGURE 11.

(a–e) Workflow, descriptors, and adsorption energetics for high‐entropy alloy NRR catalysts: (a) schematic screening procedure; (b, c) activity (ALPHA) and selectivity (SELE) versus Pauling and Mulliken electronegativities; (d, e) histograms of N₂ and N adsorption energies for two representative HEAs. Reproduced under the terms of the CC BY 4.0 license [145]. Copyright 2023, Elsevier. (f, g) Surface‐coverage analysis and compositional correlations for HEA NRR catalysts: (f) modeling and prediction workflow; (g) Schematic surface‐coverage scenarios under different potentials and the corresponding computed surface‐coverage probabilities for two representative HEA compositions. Reproduced under the terms of the CC BY 4.0 license [146]. Copyright 2024, American Chemical Society.

In another example, large language model (LLM)‐guided element selection, microscale precursor printing, pulse high‐temperature synthesis, and SECCM‐based high‐throughput measurements were integrated with DFT‐assisted analysis to accelerate the discovery of Pt‐based HEA catalysts for ORR (Figure 12a–e) [147]. This workflow enabled rapid identification of advantageous quinary HEA combinations from a large candidate pool and subsequent practical validation of the top‐ranked catalysts. Among them, FeNiCuCoPt@CNFs achieved an E _1/2 of 0.892 V vs. RHE, a mass activity of 1.32 A mg⁻¹ _Pt at 0.85 V, and excellent durability with only a 10 mV E _1/2 loss after 10 000 cycles. DFT calculations (VASP, PBE‐PAW) qualitatively reproduced the experimental activity ranking and helped clarify the contribution of Fe sites together with the synergistic effects of Cu/Co in promoting ORR activity.

FIGURE 12.

(a–e) LLM‐guided high‐throughput discovery workflow for Pt‐based HEA ORR catalysts: (a) element‐library construction and quinary‐combination design; (b) preparation of microscale HEA arrays by precursor printing and pulse heating; (c) SECCM setup for intrinsic ORR activity mapping; (d) representative current density‐potential curves; (e) heatmap of relative current density for 70 Pt‐based quinary HEA compositions at 0.10 V vs. RHE. Reproduced with permission [147]. Copyright 2024, Wiley‐VCH. (f–k) Computational workflow, stability analysis, and deep‐learning strategy for Cu‐based HEA electrocatalyst discovery: (f) elemental composition space; (g) phase‐formation and stability criteria; (h) stability descriptors (Ω, δ) versus VEC; (i) metal content versus mixing enthalpy; (j, k) surface‐bulk ratios highlighting Ag/Au segregation and other element pairs. Reproduced with permission [148]. Copyright 2025, Elsevier.

At the same time, Stage III workflows increasingly incorporate MD‐based surface modeling to capture structural complexity that cannot be represented by bulk composition alone. In one such example, a workflow combining segregation‐aware atomistic simulation with graph neural network (GNN)‐driven screening was developed for Cu‐based high‐entropy alloy catalysts for CO₂ reduction (Figure 12f–k) [148]. The compositional space was first screened for stable solid‐solution HEAs, after which Monte Carlo/molecular dynamics (MC/MD) simulations (LAMMPS, EAM potentials) were used to resolve surface segregation behavior. The simulations showed that Ag and Au have the strongest surface segregation tendencies, with the overall surface‐propensity order following Ag > Au > Al > Cu > Pd > Pt, indicating that the near‐surface composition can differ markedly from the bulk. On this basis, a GNN model was trained to predict the free energies of key CO₂RR intermediates on segregation‐modified HEA surfaces, achieving mean absolute errors of 0.08–0.15 eV relative to DFT. This combined workflow enabled high‐throughput optimization of Cu‐based HEA compositions and identified promising candidates for CO, HCOOH, and C2 products.

Collectively, these studies show that the distinctive contribution of Stage III is not simply the addition of machine learning or high‐throughput tools, but the emergence of data‐driven discovery workflows for high‐entropy electrocatalysts. In this regime, computation begins to navigate combinatorial disorder, site heterogeneity, and experimental feedback more explicitly, enabling efficient exploration of large composition‐property spaces and more realistic treatment of local environments, surface coverages, and segregated or reconstructed states. This shift is especially important for high‐entropy systems, where catalytic behavior is governed by statistical site populations rather than by a single representative structure. At the same time, Stage III also exposes major bottlenecks, including data sparsity and bias, descriptor transferability across diverse local motifs, incomplete treatment of operando surface evolution, and the challenge of linking predicted site distributions to macroscopic activity and selectivity. These limitations define the boundary between accelerated screening and truly predictive design.

From what has been discussed above, computation in high‐entropy electrocatalyst research has progressed from post hoc interpretation to increasingly predictive design. In Stage II, the key advance is that theory begins to prioritize synthetically accessible compositions, local motifs, surface terminations, and treatment‐dependent states before synthesis, thereby making the vast high‐entropy design space more tractable [100]. Stage III extends this shift by integrating machine learning, high‐throughput experimentation, and, increasingly, segregation‐ or reconstruction‐aware modeling, enabling more explicit navigation of combinatorial disorder, hidden structure‐performance correlations, and uncertainty across complex composition‐site spaces. Methodologically, this transition is supported by a compact workflow in which DFT defines structure‐property maps, ML accelerates composition‐site exploration, MD captures segregation, reconstruction, and diffusion, and multiscale models connect site‐energy distributions to device‐level metrics, while synthesis‐aware filters and high‐throughput validation help close the design loop. In this sense, the central contribution of Section 3 is not merely faster screening, but the emergence of a new design logic for high‐entropy electrocatalysts, in which catalytic performance is treated as a statistical outcome of local‐environment distributions, surface‐state evolution, and experimentally accessible motif populations rather than as the property of a single ideal site. Major high‐entropy‐specific bottlenecks nevertheless remain, including transferable descriptors across diverse local environments, explicit treatment of operando reconstruction and segregation, multiscale coupling from site energetics to current and selectivity, and uncertainty‐aware linking of site distributions to macroscopic catalytic response [149]. These unresolved issues define the frontier of predictive design of high‐entropy electrocatalysts and motivate the challenges and strategies discussed in the next section.

4. Challenges and Strategies in Computation‐Guided Design of High‐Entropy Electrocatalysts

In this section, the main bottlenecks that currently limit computation‐guided design of high‐entropy electrocatalysts are discussed, with particular emphasis on method‐specific constraints of DFT, MD, and ML, the theory‐experiment gap, dynamic surface reconstruction, descriptor development for multi‐element synergy, and the integration of synthesizability, stability, and workflow‐level design into predictive strategies.

4.1. Current Limitations of Computational Methods

High‐entropy electrocatalysts pose unique challenges for theoretical design due to their compositional complexity, which pushes the limits of traditional computational methods. DFT, MD, and ML each offer powerful tools to guide catalyst development, but each comes with methodological limitations that must be critically understood [150, 151]. A concise comparison of these methods is summarized in Table 1. We analyze the limitations of these methods, including DFT's exchange‐correlation functional bias, MD's force‐field transferability issues, and the “black‐box” nature of ML, in which the predictive input‐output relationships of models are difficult to interpret in physically meaningful terms, making it challenging to identify the descriptors, local atomic environments, or interaction patterns truly responsible for the predicted catalytic behavior. We also discuss when each method is appropriate and highlight recent strategies and hybrid frameworks designed to overcome these challenges in high‐entropy electrocatalyst research (Figure 13).

FIGURE 13.

Major challenges, strategic responses, and future prospects in computation‐guided design of high‐entropy electrocatalysts.

4.1.1. DFT

DFT provides atomic‐scale insights into electronic structure and adsorption energetics, making it indispensable for mechanistic studies and the screening of active sites. However, its accuracy is sensitive to the choice of exchange‐correlation functional, leading to functional selection bias. Different functionals can predict significantly different adsorption energies and reaction barriers, introducing uncertainty in catalyst screening. Despite continuous improvements (e.g., developing meta‐GGA or dispersion‐corrected functionals), no single functional is universally reliable across all chemisorption systems [152].

Another challenge is that standard DFT calculations often neglect or oversimplify the electrochemical environment. Modeling constant electrode potential conditions, explicit solvation, and the electric double layer from first principles is non‐trivial. Conventional DFT operates at fixed electron count, making it difficult to simulate an electrode under a controlled potential or pH. Recent advances introduced a constant inner potential (CIP) DFT scheme that treats the electrode potential as a thermodynamic variable, enabling more realistic constant‐potential simulations of electrochemical interfaces [68]. This kind of grand‐canonical DFT approach is helping bridge the gap between theoretical models and experimental electrochemical conditions.

High‐entropy systems also present an immense configurational space. Explicitly sampling the multitude of possible surface atomic arrangements or adsorbate coverages is prohibitively expensive [116]. Techniques like cluster expansion (CE) and Ab initio thermodynamics can extend DFT to disordered multi‐component surfaces, but they require many DFT calculations [153]. To overcome the cost, researchers are increasingly turning to hybrid DFT‐ML frameworks. In an active‐learning approach, Park et al. used a Gaussian process regression model as a surrogate for DFT, iteratively selecting the most informative alloy compositions to evaluate with DFT. Remarkably, this closed‐loop DFT‐ML strategy searched a compositional space of over 390 000 alloy surface sites with only around 600 DFT calculations, successfully pinpointing promising multimetallic HER catalysts that were later experimentally verified [154]. Such an approach dramatically reduced the cost and bias associated with exhaustive brute‐force DFT searches while maintaining DFT‐level accuracy on critical evaluations.

DFT‐derived theoretical overpotentials are valuable for mechanistic interpretation, but in high‐entropy electrocatalysts they are generally more reliable for relative trends and comparative ranking than for quantitatively accurate absolute predictions [155]. This is because the measured response of high‐entropy systems is governed not by a single ideal active site, but by a statistical ensemble of heterogeneous local motifs, whose populations may further evolve through operando segregation and reconstruction. Consequently, the DFT‐experiment gap arises not only from familiar sources such as exchange‐correlation uncertainty and simplified treatment of the electrochemical interface, but also from the difficulty of adequately sampling the relevant site‐ensemble distribution under working conditions. As illustrated by Batchelor et al. [53], high‐entropy alloy surfaces can exhibit near‐continuous adsorption‐energy distributions in which a minority of near‐optimal sites dominate the apparent ORR activity, making ensemble sampling itself a central source of model uncertainty. Therefore, uncalibrated DFT should be viewed primarily as a comparative and mechanistic tool in high‐entropy electrocatalysis, whereas quantitatively reliable absolute prediction requires improved interface modeling together with broader treatment of configurational and operando complexity. In practice, this gap can be reduced by combining improved constant‐potential/interface treatments with broader sampling of local site ensembles and uncertainty‐aware analysis [156].

4.1.2. MD

MD simulations are well‐suited to probe finite‐temperature effects, dynamic restructuring, and entropy in high‐entropy electrocatalysts. Classical MD can handle systems with thousands of atoms over nanosecond timescales, providing insights into phenomena like surface segregation, atomic diffusion, and thermal stability that static DFT cannot capture. MD excels at exploring configurational fluctuations and long‐time behaviors (e.g., catalyst nanoparticle annealing or reaction‐induced surface changes) that are intractable for DFT. However, the reliability of classical MD hinges on the quality and transferability of the force field. Empirical interatomic potentials (e.g., the embedded atom method, EAM) have fixed functional forms calibrated to specific chemistries, and they often fail to generalize to new compositions or local environments in a high‐entropy alloy. In other words, a potential tuned for one alloy may give unphysical results for a different composition—a serious issue when a catalyst contains five or more elements. This lack of transferability is a known bottleneck: developing a single potential that accurately spans a broad compositional space is highly nontrivial. Furthermore, classical MD lacks electronic degrees of freedom, meaning it cannot model bond breaking/forming or charge transfer (which are important in catalysis) unless one uses reactive force fields—though those themselves require extensive parameterization. Ab initio MD (AIMD), which evaluates forces on‐the‐fly with DFT, includes electronic effects but is limited to very small systems and picosecond timescales due to its enormous computational cost. Key rare events (e.g., catalyst surface reconstruction or high diffusion barriers) often occur at timescales or length scales beyond MD's reach, leaving straightforward MD sampling incomplete.

One major advance to address these challenges is the rise of machine‐learned interatomic potentials. These ML potentials (such as high‐dimensional neural networks or Gaussian approximation potentials) can achieve near‐DFT accuracy by training on large DFT datasets, while retaining orders‐of‐magnitude lower cost during MD simulations. Importantly, they offer far more flexible functional forms than classical EAM potentials, enabling better generalization across diverse local configurations. For instance, Song et al. reported a unified neural‐network potential that spans 16 elemental metals and their binary alloys, and demonstrated its transferability to more complex alloys with accuracy surpassing conventional potentials. Such general‐purpose ML potentials effectively “learn” the interactions in multi‐component systems, addressing the transferability issue and empowering MD to simulate high‐entropy materials with both scale and fidelity [157]. In addition, enhanced‐sampling techniques (accelerated MD, Monte Carlo, etc.) are increasingly combined with these accurate ML potentials to capture infrequent events and equilibrate disordered systems more efficiently [158]. In summary, while MD is appropriate for exploring thermodynamic stability and dynamic phenomena, one must ensure the force field is robust—or leverage ML‐trained potentials—to reliably represent the intricate energetic landscape of high‐entropy electrocatalysts.

4.1.3. ML

Data‐driven ML models are emerging as a third pillar of catalyst design, capable of mining patterns in large materials datasets and rapidly screening vast compositional spaces. For high‐entropy electrocatalysts—where tens of elements and compositional variations create a combinatorial explosion of candidates—ML can serve as a high‐throughput screening tool once trained. ML is most useful when abundant data (either experimental measurements or simulation outputs) are available, and when one needs to quickly predict properties (e.g., activity metrics or formation energies) for thousands of candidate compositions or structures. In recent studies, ML has been used to predict adsorption energies or alloy stability orders of magnitude faster than DFT, enabling an initial down‐selection of candidates prior to confirmation by experiments or more rigorous calculations [124, 154].

However, ML approaches face notable challenges [159, 160, 161, 162]. One issue is their dependence on high‐quality training data: if the data are sparse or biased (as is often the case for new high‐entropy materials), the model's predictions will be unreliable. For example, Semnani et al. note that experimental catalyst datasets are typically small and skewed toward low‐performing samples due to the difficulty of producing large numbers of high‐performance examples [163]. This sparsity makes it hard for an ML model to learn generalizable trends. Moreover, unlike physics‐based methods, ML models struggle with extrapolation. They excel at interpolating within the domain of their training data, but can fail under a domain shift (e.g., a novel catalyst composition or operating condition not represented in the training set). In addition, literature data for high‐entropy electrocatalysts are collected under heterogeneous conditions (electrolyte, pH, iR‐correction, loading, cell configuration, and durability protocol), so nominally similar metrics such as η or Tafel slope are often not directly comparable. This heterogeneity further complicates the construction of clean, machine‐readable benchmark datasets for robust ML training.

A further limitation is that many ML models in electrocatalysis are trained on DFT‐derived labels, meaning that they inherit rather than eliminate functional‐related errors, ideal‐slab assumptions, and simplified interface or potential treatments [164, 165]. This issue is especially acute in high‐entropy systems, where even a single nominal composition can contain many distinct local motifs that are difficult to sample comprehensively. In addition, experimental datasets are often highly heterogeneous, reflecting differences in electrolyte identity and concentration, testing protocols, electrode/substrate configuration, and normalization procedures, which further hinder cross‐study comparability and model transferability. As a result, current ML models are better viewed as task‐specific surrogates for internally consistent datasets rather than as universally transferable predictors. Practical mitigation requires stricter metadata curation, more consistent reporting and normalization, reaction‐specific dataset partitioning, uncertainty quantification, and out‐of‐distribution checking.

In the context of high‐entropy electrocatalysts, the black‐box limitation of many ML models, especially deep neural networks, is particularly problematic because predicted activity or stability may arise from complex correlations among composition, local coordination, and electronic descriptors, while the model itself does not directly reveal whether these correlations reflect causal physicochemical mechanisms or merely dataset‐specific patterns. As a result, such models may provide accurate predictions without transparent reasoning, which limits mechanistic interpretation and can reduce researchers’ confidence in using the model for catalyst discovery. This concern has spurred efforts in explainable AI (XAI) and uncertainty quantification tailored for catalyst ML. To improve interpretability, scientists are integrating techniques that reveal which features or atomic constituents drive a model's predictions. A recent example is the framework by Semnani et al., which incorporates XAI methods into catalyst performance prediction. Their approach identified the key catalyst components contributing to high activity, thereby opening the black box and providing chemical insights [163]. Together with rigorous cross‐validation on limited datasets and physics‐informed feature engineering, such approaches are gradually helping to mitigate the black‐box problem.

Additionally, strategies like Gaussian process regression (which provides intrinsic uncertainty estimates) and ensemble modeling are used to quantify the confidence in ML predictions. This is crucial in high‐entropy alloy discovery: for instance, active‐learning schemes employ uncertainty estimates to decide which new compositions require DFT evaluation, ensuring the ML model only extrapolates when it can do so reliably. Indeed, Xu et al. demonstrated a multi‐objective Bayesian optimization approach that guided the search for optimal HEA electrocatalysts by balancing performance with material cost and entropic stability [124]. Such probabilistic ML frameworks explicitly account for uncertainties and multiple design criteria, yielding candidates that are not only highly active but also thermodynamically stable as high‐entropy alloys.

4.1.4. Hybrid Frameworks

Recognizing that no single computational method suffices for all aspects of high‐entropy electrocatalyst design, recent research emphasizes hybrid strategies that leverage the complementary strengths of DFT, MD, and ML. In these multi‐scale or multi‐fidelity frameworks, each technique informs or enhances the others. For example, DFT can provide reliable data to train ML models or to parametrize MD force fields, while ML can act as a surrogate to rapidly scan candidate materials before confirming with DFT. MD simulations (especially with ML potentials) can generate thermodynamic insights (e.g., surface ordering or phase segregation) that feed back into DFT calculations of the most relevant structures. The active‐learning HER catalyst study by Park et al. [154]. is a prime illustration of DFT‐ML synergy, using an ML model to navigate a vast compositional space far more efficiently than brute‐force DFT alone. Likewise, the HEA screening study by Xu et al. [124]. Combined DFT‐computed objectives with Bayesian optimization to find a balance between catalytic activity and stability. On the MD side, coupling Ab initio calculations with molecular dynamics in a grand‐canonical framework has enabled simulations under realistic electrochemical conditions (e.g., constant‐potential MD) that were previously inaccessible. Moreover, by deploying ML‐trained potentials within large‐scale MD or Monte Carlo simulations, researchers have observed nanoscale phase evolution in HEAs that agrees with experimental characterizations. These examples underscore a key point: each method is most powerful when used in the regime it handles best, and their integration can overcome individual limitations. By addressing DFT's accuracy and scaling issues, MD's force‐field transferability problems, and ML's data and interpretability challenges, such hybrid frameworks are accelerating the rational design of high‐entropy electrocatalysts.

4.1.5. Theory‐Experiment Gap

In practice, a systematic gap remains between theoretical targets and experimental realizations [166, 167, 168, 169]. Most computations optimize adsorption thermodynamics on idealized, compositionally uniform slabs at well‐defined potentials, whereas experiments probe rough, dynamically reconstructing surfaces with ill‐defined site distributions, electrolyte impurities, and transport limitations. As a result, predicted site‐level energetics do not map one‐to‐one onto device‐level metrics such as η, Tafel slopes, or Faradaic efficiencies. Additional sources of mismatch include synthesis feasibility of targeted stoichiometries and phases, bias‐induced leaching and phase segregation, binder/support and ionomer interactions, and normalization uncertainties such as electrochemical surface area (ECSA), and roughness, iR‐compensation. Making the theory‐experiment link reliable therefore requires uncertainty‐aware predictions, constant‐potential boundary conditions, explicit defect/coverage sampling, and systematic operando verification of the assumed active motifs. This pattern is consistent with the case studies in Section 3, where DFT often reproduces the correct activity ranking but overestimates or underestimates experimental overpotentials by tens to hundreds of millivolts.

4.2. Atomic‐Scale Simulations of Surface Reconstruction in High‐Entropy Materials

High‐entropy materials often undergo dynamic surface reconstruction under reaction conditions, including atomic rearrangements, segregation of certain elements, and phase transformations [170]. Capturing these processes requires advanced simulation techniques beyond static DFT calculations. AIMD has been employed to probe initial finite‐temperature surface dynamics in multi‐component systems, albeit typically over short timescales due to its high computational cost. To reach longer times and larger length scales, researchers are turning to machine‐learning interatomic potentials. Such potentials (e.g., neural network or Gaussian approximation potentials) are trained on DFT data and can faithfully reproduce complex potential energy landscapes, enabling extended MD simulations of high‐entropy systems [114]. Modern ML potentials also demonstrate high accuracy for properties like surface energies across multi‐element alloys, outperforming classical force fields. With GPU‐accelerated implementations, they now allow MD simulations with millions of atoms, opening the door to the realistic time and length scales needed to observe surface reconstruction events [157].

To further explore reconstruction phenomena, researchers are integrating enhanced‐sampling techniques into these simulations. Hybrid Monte Carlo/MD algorithms, for instance, can swap atom identities during MD, effectively sampling many different atomic configurations to find equilibrium surface compositions. This approach acts as an accelerated sampling of segregation and ordering processes that would otherwise require prohibitively long MD trajectories. Other advanced sampling methods like metadynamics and accelerated MD have been applied to drive critical events (e.g., subsurface diffusion or oxide layer formation) by biasing key collective variables. Meanwhile, combining these techniques with cluster‐expansion Monte Carlo models for alloy surfaces allows estimation of thermodynamically preferred surface states over a range of compositions and temperatures. By using AIMD for validation of key events and ML‐driven or Monte Carlo simulations for scale‐up, current studies can capture the atomic‐scale dynamics of high‐entropy electrocatalyst surfaces—from rapid reconstructions to slow elemental segregation. This computational toolkit is vital for understanding how operational conditions might induce in situ surface phase changes that affect catalytic performance [170].

4.3. Quantitative Descriptors for Multi‐Element Synergy

A major challenge in high‐entropy electrocatalysts is the lack of simple quantitative descriptors to capture the synergistic effects of multiple elements on catalytic activity. Traditional single‐metal descriptors (e.g., the d‐band center) often break down on compositionally complex surfaces. Because each active site in a high‐entropy material has a distinct local environment, properties like intermediate binding energies form broad distributions rather than fixed values.

Recent efforts have begun to tackle this issue by formulating new physics‐informed descriptors that incorporate local chemical environment effects. For example, Cao et al. introduced a descriptor Ω that combines the intrinsic d‐band filling of an active site with a term for the average electronegativity of its neighboring atoms. This simple linear descriptor (d‐band filling plus weighted neighbor electronegativity) was shown to predict adsorption energies on noble‐metal HEA surfaces in close agreement with exhaustive DFT calculations. Importantly, it addresses the “element identity loss” problem in HEAs by explicitly accounting for how a heterogeneous coordination environment shifts the d‐band and reactivity of a given active atom. Such environment‐sensitive descriptors move beyond single‐element properties, offering a quantitative handle on multi‐element synergy [100].

Complementary to analytical descriptors, data‐driven frameworks are also being developed to capture multi‐element effects. Graph‐based machine learning models have been applied to high‐entropy electrocatalyst surfaces, representing each element as a node and each interaction between elements as an edge in the graph. In a recent study, a graph attention neural network was trained on hundreds of thousands of DFT‐derived configurations to predict ORR activity across a vast HEA composition space. The model was not only predictive but also interpretable: the attention weights highlighted which elemental combinations in an active site contributed most to variations in binding energy. Likewise, other interpretable ML approaches in catalysis are extracting meaningful features (e.g., adsorbate‐metal bond lengths, ensemble effects) that correlate with activity. These data‐driven methods effectively serve as high‐dimensional descriptors, capturing subtle multi‐metal synergies that are difficult to reduce to a single formula.

Together, the emergence of physically grounded descriptors and ML‐derived feature frameworks is beginning to fill this quantitative gap, enabling rational high‐entropy electrocatalyst design in the multi‐component space. For instance, using such tools, researchers have mapped out activity “heatmaps” over composition ranges and identified specific alloy compositions as promising optimal catalysts—thereby concretely leveraging multi‐element synergy for high‐entropy electrocatalyst discovery.

4.4. Synthesizability, Stability, and Multi‐Objective Design Constraints

For high‐entropy electrocatalysts, synthesizability and phase/electrochemical stability should be treated as explicit constraints prior to, or at least in parallel with, activity prediction. At the synthesis stage, the CALPHAD (CALculation of PHAse Diagrams) approach and related phase‐diagram analyses, especially for alloy‐based high‐entropy systems or composition spaces with sufficiently reliable thermodynamic descriptions, are already useful for eliminating compositions that are unlikely to form accessible single‐phase windows or that are prone to competing intermetallic formation. For example, large‐scale CALPHAD screening of more than 130 000 multi‐principal‐element alloy systems showed that single‐phase solid solutions become less likely, rather than more likely, as the number of components increases, and only a small subset of compositions survived stringent credibility and property filters for further consideration, illustrating how phase‐diagram‐based screening can proactively rule out synthetically unpromising candidates before costly experiments [171].

Complementary to phase‐diagram‐based screening, descriptor‐based frameworks have provided efficient routes for evaluating the relative synthesizability or phase formability of high‐entropy candidates. An early representative example is the entropy‐forming ability (EFA) descriptor, which uses the width of configurational energy distributions to assess the ease of forming homogeneous high‐entropy carbide phases [172]. More recently, the mixed enthalpy‐entropy descriptor (MEED) [173] combines the relative formation enthalpy with respect to the most stable competing phase and the spread of substitutional defect formation energies, thereby capturing both the enthalpic penalty and disorder‐forming tendency of candidate HEMs. Similarly, the disordered enthalpy‐entropy descriptor (DEED) [174] balances the entropy gain of disorder against the enthalpy cost relative to the convex hull and introduces a process‐aware concept of functional synthesizability. Recent descriptor‐based and ML‐assisted studies have further extended this concept, for example by using mixing enthalpy and bond‐length distribution to map single‐phase rocksalt high‐entropy oxide stability, or by combining high‐throughput experiments, ML models, and physically interpretable descriptors to predict single‐phase formability and phase‐property trade‐offs in high‐entropy carbides [175, 176]. These descriptors and workflows can complement CALPHAD and related phase‐diagram methods by rapidly pre‐screening synthetically accessible compositions before more expensive activity and electrochemical stability calculations.

At the electrochemical stage, Pourbaix‐type stability mapping and related potential‐dependent decomposition or dissolution descriptors can likewise be used as pre‐screening criteria rather than post hoc interpretation tools. In a recent Pareto‐front framework for OER high‐entropy alloys, the decomposition energy derived from Pourbaix analysis at 1.23 V vs. RHE and pH 7 was explicitly adopted as the stability descriptor and was evaluated before or alongside activity, allowing the workflow to exclude compositions that were either too oxophilic and prone to oxidation‐driven collapse or too inert to reconstruct into sufficiently active surfaces [177]. Although such approaches are generally more informative for thermodynamic instability windows than for full kinetic degradation pathways, they already provide a more realistic stability filter than activity‐only screening, and highlight the need for more explicit potential‐dependent stability assessment, including emerging constant‐potential treatments of dissolution or decomposition tendencies. Beyond thermodynamic screening, stability‐aware structural analysis can also connect synthesis conditions to accessible defect states and subsequent durability, while long‐timescale atomistic simulations enabled by machine‐learned interatomic potentials are emerging as a promising route for probing segregation, diffusion, coarsening, and surface/compositional evolution beyond the time and length scales accessible to conventional DFT. For instance, recent work on PtZnFeCoNiCr high‐entropy intermetallics showed that the ordered phase required elevated annealing temperatures that normally risk particle growth and aggregation, whereas sluggish diffusion and pore confinement enabled controllable formation of Pt antisite defects through temperature tuning, thereby linking processing constraints directly to defect formation and catalytic performance [178]. Under operating conditions, compositionally complex surfaces may also undergo rapid bias‐induced redistribution: atom‐probe tomography of a Cantor‐alloy OER catalyst revealed that a thin passivating oxide layer formed within seconds and that Cr/Mn/Fe tended toward dissolution while Co/Ni became enriched in the passivated surface layer, underscoring the importance of explicitly considering operando surface evolution when translating theoretical predictions to realistic catalyst design [179]. Taken together, these examples suggest that phase‐diagram analyses, descriptor‐based synthesizability screening, electrochemical stability mapping, and stability‐aware structural modeling should become integral components of future high‐entropy electrocatalyst discovery, helping prioritize compositions that are not only potentially active, but also experimentally accessible and operationally viable.

Building on such stability‐aware pre‐screening, future discovery of high‐entropy electrocatalysts should move toward multi‐objective optimization that explicitly balances activity, stability, cost, and scalability, rather than focusing on reaction activity alone. Although such workflows have so far been demonstrated mainly in broader multimetal catalyst spaces, their methodological implications are highly relevant to high‐entropy systems, where the compositional space is even larger and exhaustive durability testing is even less practical, making it especially important to account for the most common degradation and failure pathways at the design stage. These include preferential leaching or dissolution of less‐noble elements under bias, surface segregation/reconstruction or phase separation that shifts the catalyst away from its intended single‐phase composition, particle sintering/coarsening that reduces the accessible active surface area, and passivating oxide/hydroxide formation that alters or blocks active sites [180, 181, 182, 183]. To address these challenges, integrated workflows that combine synthesis feasibility, activity evaluation, and stability prediction, as well as sequential active‐learning strategies that account for unequal‐cost objectives, point to a more efficient route for navigating activity‐stability trade‐offs under realistic experimental constraints [184, 185]. From this perspective, high‐entropy electrocatalyst design should increasingly treat resistance to leaching, segregation, coarsening, and passivation, together with durability, noble‐metal usage, and experimental throughput, as co‐equal considerations alongside catalytic activity. More broadly, the next generation of high‐entropy electrocatalyst discovery will rely not only on identifying highly active compositions, but also on developing workflow‐level strategies that can reconcile performance, durability, and practical deployability.

4.5. Recommended Integrated Workflow

A coherent, closed‐loop workflow for high‐entropy electrocatalyst design couples multiscale computation with targeted synthesis, standardized testing, and operando feedback (Figure 14). It begins by mapping broad composition‐structure spaces via DFT, optionally at constant potential, augmented by cluster expansion and Monte Carlo (CE/MC), to sample disordered bulk and surface configurations and to compute formation and binding energetics. At this stage, synthesizability and phase stability are screened in parallel with activity, rather than being treated only after candidate nomination. These DFT labels train interpretable ML surrogates such as graph neural networks or Bayesian models with physics‐informed descriptors and calibrated uncertainty, which rapidly predict surface and adsorbate energies and nominate promising composition‐site motifs. The ML models then steer molecular dynamics, preferably with ML interatomic potentials calibrated to DFT/AIMD, to capture temperature‐ and potential‐dependent surface reconstruction, segregation, and site dynamics; active learning iteratively selects high‐value DFT or MD points to refine the models on the fly. Ensembles of site energetics and barriers feed microkinetic models to predict activity and selectivity under realistic electrochemical conditions. Guided by these predictions, controlled synthesis yields candidates with atomic‐level mixing and precise stoichiometry, for example, sol–gel or autocombustion and aerosol pyrolysis for oxides, rapid thermal‐shock alloying, and magnetron co‐sputtering or pulsed electrodeposition for thin films and (oxy)hydroxides; in situ self‐reconstruction through electrochemical oxidation or leaching can generate active surface phases. Candidates undergo standardized benchmarking across OER, HER, ORR, and CO₂RR; report η and Tafel slopes for OER/HER, half‐wave potential and electron‐transfer number for ORR, and CO₂RR Faradaic efficiencies by GC, NMR, and IC, with rigorous iR compensation and properly calibrated references, followed by durability protocols including chronoamperometry or chronopotentiometry and accelerated cycling at device‐relevant currents. Such standardized testing and reporting are a prerequisite for compiling reliable benchmark datasets and for training ML models that can generalise across different high‐entropy electrocatalyst families. Device‐level validation in gas‐diffusion or flow cells or in membrane‐electrode assemblies, including electrolyzer tests and stack integration where relevant, assesses practicality. Throughout, in situ and operando characterization using XAS/EXAFS, Raman, XPS, liquid‐cell TEM, and isotope‐labeling MS tracks oxidation state, coordination, segregation, and intermediates under bias. These observations feed back to update CE/MC thermodynamics, retrain ML surrogates and potentials, refine DFT boundary conditions and microkinetics, and tighten design constraints, thereby converging through repeated computational‐experimental cycles on high‐entropy electrocatalysts that jointly optimize activity, selectivity, and long‐term stability.

FIGURE 14.

Closed‐loop multiscale computation‐experiment workflow for the design, benchmarking, and operando refinement of high‐entropy electrocatalysts.

5. Summary and Perspectives

High‐entropy electrocatalytic materials, with their compositional complexity, local configurational diversity, and broad distributions of active sites, have emerged as distinctive platforms for achieving catalytic activity, selectivity, and durability beyond what is typically accessible in simpler systems. In this context, the integration of theoretical calculations with high‐throughput experimentation and machine learning has done more than improve screening efficiency: it has fundamentally changed how these materials are understood and designed. Computation has revealed that catalytic behavior in high‐entropy systems is governed not by a single representative site, but by multielement synergy, local‐environment‐dependent energetics, and dynamically evolving surface states. By linking these microscopic features to experimentally accessible performance trends, computational approaches have accelerated the shift from empirical exploration toward increasingly predictive, mechanism‐informed, and design‐oriented development of high‐entropy electrocatalysts.

From the cases surveyed in this review, several practical design rules can be distilled for the predictive development of high‐entropy electrocatalysts. (i) Use DFT not only to rank compositions, but to resolve local structure‐property relations, identify motif‐sensitive energetics, and define physically meaningful descriptors; whenever possible, these calculations should incorporate constant‐potential conditions together with explicit treatment of disorder, coverage, and solvation. (ii) When configurational complexity, surface evolution, or relevant time scales exceed what static DFT can capture, deploy MD, ideally with machine‐learned interatomic potentials, to screen thermodynamically realistic surface states, segregation tendencies, and reconstruction pathways before evaluating catalytic performance. (iii) Use ML as an interpretable and uncertainty‐aware surrogate to navigate vast composition‐site spaces, prioritize promising and experimentally accessible candidates, and capture trends across diverse local environments, rather than as a purely black‐box predictor. (iv) Most importantly, embed these elements into closed‐loop DFT‐MD‐ML workflows linked to reproducible experimental benchmarks, so that theory moves beyond post hoc explanation toward the predictive design of synthesizable and phase‐stable high‐entropy electrocatalysts with target activity, selectivity, and stability.

Despite significant progress, several fundamental challenges still limit the truly predictive design of high‐entropy electrocatalysts. A central issue is that catalytic behavior in these systems is rarely governed by a single representative site, but instead by distributions of local motifs whose populations evolve with composition, coverage, segregation, and reconstruction under operating conditions. This creates a persistent gap between idealized theoretical models and experimentally relevant surfaces, and makes it difficult to establish transferable descriptors across diverse local environments or to connect site‐level energetics directly to macroscopic activity, selectivity, and stability. Moving forward, further progress will require more explicit treatment of disorder, electrode potential, solvation, and operando surface evolution, together with multiscale frameworks that couple atomistic energetics to kinetics, transport, and experimentally observable response. At the same time, uncertainty‐aware machine learning, standardized workflows, and reproducible open datasets will be essential for improving generalizability and for building robust feedback between theory, experiments, and data. In this sense, the next frontier is not simply faster screening, but a more realistic and quantitatively predictive design paradigm for high‐entropy electrocatalysts.

Author Contributions

Fangshi Fan: data curation, investigation, formal analysis, visualization, writing – original draft, methodology. Tuxiang Guan: writing – review and editing. Weiwei Cai: writing – review and editing, writing – original draft, investigation. Zhen Huang: writing – review and editing, data curation, writing – original draft, investigation. Lingjie Zhang: resources, writing – review and editing, funding acquisition, supervision, project administration, conceptualization, methodology. Xinhui Xia: writing – review and editing, supervision, project administration. Yongjun Wu: writing – review and editing. Ningzhong Bao: writing – review and editing, supervision, project administration, resources, funding acquisition. Yiqi Qiu: writing – review and editing. Zhiqiang Zhou: writing – review and editing.

Conflicts of Interest

The authors declare no conflicts of interest.

Data Availability Statement

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.