TICC 2026 · Invited Talk

Subsurface Control of Active-Site Distributions in Pt-Skin HEA Electrocatalysts

How buried atoms tune — and help predict — hydrogen adsorption across 96 distinct sites

96DFT H sites

3SQS Pt-skin slabs

≈0ΔG_H* (eV)

5elements (HEA)

H*

Pt skin

HEA subsurface

Pt Fe Co Ni Cu

Chen-Cheng Liao (廖振成)
Department of Chemistry, Fu Jen Catholic University, New Taipei City, Taiwan
DFT & machine learning · 165804@mail.fju.edu.tw

Platinum is the HER benchmark — but it is expensive

HER activity peaks when hydrogen binds at ΔG_H* ≈ 0 — right where Pt sits. But Pt is costly and scarce, so the search for cheaper, tunable catalysts continues.

HER volcano: activity vs hydrogen adsorption free energy

Key messageThe goal: reach Pt-like H binding (ΔG_H* ≈ 0) with far less Pt.

What is a high-entropy alloy (HEA)?

Five or more elements mixed in near-equal amounts — disorder by design, not by defect

≥ 5 principal elements, each near-equiatomic — there is no single host metal, every element is a "solvent".

High mixing entropy stabilises a single disordered solid-solution phase instead of separating into compounds.

Why we care a vast, tunable composition space — and every surface site sees a different local mix of neighbours.

Key messageAn HEA is a near-equiatomic, disordered multi-element solid solution — a huge, tunable design space.

Pt-skin HEA: keep Pt’s surface, tune the buried core

A pure-Pt outer layer over a mixed Fe–Co–Ni–Cu–Pt core — Pt-like chemistry on top, far less Pt and new tunability underneath

The Pt skin preserves Pt-like surface chemistry, while the buried high-entropy environment is used to tune H adsorption.

Key messageKeep a Pt-like surface, let buried atoms tune it, and use less Pt.

HEA catalysis is not a single-site problem

Even under a pure-Pt skin, each hollow sits above a different subsurface — so adsorption becomes a distribution

HEA catalysis is better described by an active-site population than by one representative adsorption energy.

Key messageOn a Pt-skin HEA, activity is a distribution of sites — an active-site population problem.

Pt-skin: a controlled platform for the buried effect

The adsorbate always meets a Pt-rich surface; the variation comes from the composition underneath

The Pt skin fixes the surface chemistry, while the buried Fe–Co–Ni–Cu–Pt environment tunes the local H adsorption energy.

Key messageThe Pt skin isolates one clean question: how does the buried environment tune surface Pt?

The central question of this work

Can local composition and coordinates predict hollow-site H adsorption — turning DFT into calibration data?

1

Pt-skin slab

SQS surface model

→

2

Hollow-site DFT

per-site ΔG_H*

→

3

Local descriptors

subsurface counts

→

4

Adsorption predictor

DFT-trained surrogate

→

5

Active-site population

μ, σ, P_opt

DFT calculations serve as calibration data for a descriptor-based local adsorption-energy predictor — not a full site census, kinetics, or MLP.

Key messageIf descriptors predict adsorption, DFT becomes calibration data, not an endpoint census.

Scope: what this work is — and is not

A controlled hollow-site calibration study and predictor framework — not a full search, kinetics, or MLP

Key messageA descriptor-based local adsorption-energy predictor — the seed for active-site population estimation.

06

Methods overview

Fe–Co–Ni–Cu–Pt Pt-skin (111): from random structure to descriptors

1

SQS bulk

random alloy in a finite cell

2

Pt-skin slab

4×4×6 · 96 atoms · pure-Pt top

3

96 hollow sites

all FCC + HCP, 3 slabs

4

DFT ΔG_H*

VASP, per site

5

Descriptors

local environment · d-band · surrogate prediction

DFT settings

VASP · GGA-PBE
520 eV · spin-polarized
Γ-centered 3×3×1

Free energy

ΔGH* = ΔEads + 0.24 eV

computational hydrogen electrode

SQS gives finite periodic slabs whose local statistics approximate a random alloy.

Key messageA controlled 96-site hollow-site dataset across three Pt-skin HEA surfaces.

06 / 18

What is a special quasirandom structure (SQS)?

A small periodic cell built to imitate an infinite random alloy

An SQS reproduces the local atomic statistics of a random alloy — in a cell small enough for DFT.

1

The problem

A real random alloy is effectively infinite — it cannot enter a DFT calculation directly.

→

2

The constraint

DFT needs a finite, periodic cell — whatever it contains repeats forever.

→

3

The trick

Choose the arrangement whose neighbour statistics match a random alloy.

Key messageAn SQS is statistically random — not merely random-looking.

Choosing an SQS: match the neighbours

Same composition, different arrangement — pick the one closest to random

clustered

mismatch: high

partly ordered

medium

random-like

low ✓ SQS

Count each atom's neighbours: the fractions should match the bulk composition.

Minimise the mismatch — the Warren–Cowley parameter α → 0 — over the nearest shells.

Next the following two slides show how that arrangement is actually found.

Key messageThe SQS is chosen by neighbour statistics, not by eye.

Finding an SQS is an optimization

Swap two atoms, re-score the neighbour statistics, keep what gets closer to random

Atomic swapping reduces the statistical error from 0.62 to 0.31 to 0.12 — Each swap proposes a candidate structure; the **correlation mismatch (error)** falls as the arrangement approaches a random alloy.

Key messageAn SQS is found by minimising the mismatch between its neighbour statistics and a true random alloy.

Monte Carlo annealing finds the global best

Always accept improving swaps; accept worsening ones with probability exp(−ΔE/T), cooling slowly

Monte Carlo simulated annealing: Metropolis acceptance rule and temperature cooling schedule — Simulated annealing accepts occasional **uphill moves** and lowers the "temperature" gradually, so the search escapes local minima and converges to the smallest statistical error.

Key messageAnnealing reaches the SQS with the lowest correlation mismatch — not just a nearby local minimum.

Our model: a Pt-skin (111) high-entropy slab

Top view and side view of the 4×4×6 slab — 96 atoms, six layers

Top view — Pt skin (16 surface Pt)

4×4 surface cell · FCC + HCP 3-fold hollow sites (96 in total)

Side view — 6 layers

Pt skin on top · Fe–Co–Ni–Cu–Pt below (top 3 relaxed, bottom 3 fixed)

Key messageA pure-Pt skin over the HEA subsurface — the surface looks like Pt; the layers beneath do the tuning.

What we count: the 6 atoms beneath a hollow site

An x-ray view from the Pt skin into the subsurface ring

An H atom adsorbs in a 3-fold hollow site on the Pt skin.

Make the skin transparent: directly beneath sit 6 subsurface atoms — the local ring.

Descriptor ls_X = counts in that ring → here Pt 2 · Fe 1 · Co 1 · Ni 1 · Cu 1.

Key messageEach site's descriptor is the element makeup of the 6 atoms under its hollow.

07

The site population sits on the Sabatier optimum

ΔG_H* across all 96 sites — tight and near-thermoneutral

Distribution of ΔG_H* — **Figure 1.** ΔG_H* distribution over 96 FCC + HCP hollow sites (3 SQS slabs); Pt(111) reference −0.09 eV.

+0.013 eV

mean ΔG_H* — essentially thermoneutral

0.055 eV

standard deviation — a narrow spread

92 %

of sites within |ΔG_H*| ≤ 0.10 eV

Key messageThe Pt-skin HEA naturally creates a near-optimal population of H-binding sites.

07 / 18

08

A trap hides in the simplest analysis

The subsurface counts are not independent — they add to a fixed total

Add one Fe and you must remove another element. The five counts are compositionally coupled.

Caution A raw correlation for one element absorbs everyone else's effect — correlation, not cause.

The fix is partial correlation: hold the other counts fixed, then ask what each element does.

Key messageIn a constrained alloy, naïve correlation can point at the wrong element.

08 / 18

09

The apparent ranking is misleading

Raw Pearson correlation of each subsurface count with ΔG_H* (n = 96)

Apparent ranking (raw r vs ΔG_H*)

ls_Pt−0.64

ls_Fe+0.54

ls_Cu−0.22

ls_Co+0.20

ls_Ni+0.02

Bars left of centre = strengthen H binding · right = weaken. Fe is flagged.

ls_Pt is genuinely the strongest signal (r = −0.64, p < 10⁻¹²).

Trap Fe looks important (+0.54) — but this is mostly Pt's complement: "few Pt here," not "Fe acting."

Cu and Co look weak here — only a method that removes the coupling can tell.

Key messageAt face value Fe rivals Pt — a classic collinearity artifact.

09 / 18

10

The corrected hierarchy follows chemistry

Partial correlation — after controlling for the other counts

Controlling for the other counts unmasks the true ranking

strongest

Pt

χ 2.28

>

Cu

χ 1.90

>

Ni

χ 1.91

≈

Co

χ 1.88

>

weakest

Fe

χ 1.83

Fe collapses from apparent hero to weakest; Cu rises to second. The order tracks electronegativity (χ), not arithmetic.

More-electronegative subsurface neighbours pull charge from surface Pt → weaker H binding.

Key messageA stable, electronegativity-ordered descriptor hierarchy: Pt > Cu > Ni ≈ Co > Fe.

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11

Subsurface Pt is the dominant handle

More Pt beneath the skin → weaker H binding, ΔG_H* rising through zero

**Figure 3.** ΔG_H* vs subsurface Pt count; points coloured by local Fe count, black = group mean ± 1 SD. Trend r = −0.64 (≈ −43 meV per subsurface Pt).

−0.64 r

monotonic trend in subsurface Pt count

0 → 3 subsurface Pt walks a site's ΔG_H* from positive toward and past the optimum.

Sign convention: higher ΔG_H* = weaker H binding.

Key messageOne countable quantity — subsurface Pt — predicts which way H binding moves.

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12

The electronics confirm the mechanism

A site-projected d-band-center effect, measured atom by atom

ΔG_H* vs d-band center and d-PDOS — **Figure 6.** (a) ΔG_H* vs surface-Pt d-band center (r = −0.86). (b) d-projected DOS for high vs low subsurface Pt.

−0.86 r

ΔG_H* vs surface-Pt d-band center

subsurface Pt ↑ → d-band center ↓ → Pt–H weakens → ΔG_H* → 0

Key messageThe descriptor is not a fit — it is the d-band center doing the work.

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13

The mechanism in one line

A closed causal chain, each link independently measured

1

Buried atoms

subsurface Pt count

→

2

d-band center ↓

surface-Pt states shift down

→

3

H binding weakens

ΔG_H* rises toward 0

→

4

Sabatier population

sites land on the optimum

Key messageComposition, electronics, and energetics tell one consistent story.

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14

A compact local-environment predictor is already possible

Seven regression algorithms converge to the same error

Predicted vs DFT ΔG_H* parity — **Figure 4.** Predicted vs DFT ΔG_H*; seven models, leave-one-out cross-validation.

27–31 meV

LOO-CV MAE — the band all seven models share

Ridge, LASSO, Random Forest, GBRT, SVR, GPR, KRR — same accuracy. The 96 sites are a compact training set for adsorption prediction.

Key messageDFT learns the rule; descriptors predict the rest.

14 / 18

From DFT census to adsorption predictor

DFT is the calibration data, not the endpoint

1

Local composition + coordinates

each hollow site's environment

2

Local descriptors

subsurface counts · geometry · d-band

3

DFT-trained surrogate model

96 sites as the training set

4

Predicted ΔG_H*

for uncalculated sites

5

Active-site population

μ, σ, P_opt

DFT learns the rule — it does not enumerate every site.

The current model is a local-environment adsorption predictor, not yet a full MLP.

Goal rapid estimation of active-site populations across HEA composition space.

Key messageThe 96 DFT sites are not just results — they are training data for a fast adsorption predictor.

15

Design rule: shift the distribution with composition

Engineer the ΔG_H* population — centre and spread — not one site

Tune the subsurface Pt / Cu / Ni / Co / Fe balance to slide the whole population toward ΔG_H* = 0.

The d-band center is the transferable bridge from composition to reactivity.

Key messageChoose a subsurface composition that centres the site population on the optimum.

15 / 18

16

Scope, honestly — and where it goes next

Firm within these compositions; the frontier is generalization

Established / limits

Current claim: the predictor is validated within the studied Pt-skin hollow-site dataset (96 sites)
Only three compositions: cross-composition transfer not yet proven
So far, only the electronic d-band descriptor transfers across compositions

Outlook

Next: test cross-composition transfer — binary → ternary → quaternary → quinary hierarchy
Carry the subsurface framing to OER / ORR / CO₂RR
Toward descriptor-guided, autonomous catalyst discovery

Key messageWithin-composition claims are firm; cross-composition generalization is next.

16 / 18

17

Three things to take home

Subsurface control of active-site distributions in Pt-skin HEA

1

HEA catalysis is a distribution problem

96 Pt-skin sites form a near-optimal population (μ = +0.013 eV; 92% within ±0.10 eV) — study the distribution, not one site.

2

Subsurface composition controls H adsorption through the d-band

An electronegativity-ordered hierarchy (Pt > Cu > Ni ≈ Co > Fe); subsurface Pt lowers the surface-Pt d-band center.

3

Local environments can predict adsorption energies

Seven algorithms converge to 27–31 meV, suggesting the HEA adsorption landscape is descriptor-compressible.

Key messageHEA site heterogeneity is, at heart, a subsurface problem — and a solvable one.

17 / 18

Thank you · Questions welcome

Buried atoms are a design handle for surface reactivity

distribution on the optimum → electronegativity-ordered hierarchy → d-band mechanism → descriptor-limited ceiling

At a glance

SystemFe–Co–Ni–Cu–Pt Pt-skin (111)

Data96 DFT sites · 3 SQS slabs

CentreΔG_H* = +0.013 eV · 92% optimal

Driversubsurface Pt → d-band (r = −0.86)

Ceiling7 models · 27–31 meV

Chen-Cheng Liao (廖振成) · Department of Chemistry, Fu Jen Catholic University
165804@mail.fju.edu.tw · Supported by NSTC 114-2113-M-030-015-MY2
With students Peggy P. M. J. and Yu-Huan Huang (黃宇桓)