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
≈0ΔGH*  (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 ΔGH* ≈ 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 (ΔGH* ≈ 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
PtFeCoNiCu
≥ 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
HPure Ptuniform Pt surfaceHAlloymixed surfaceHPt-skin HEAPt surface · tunable corePtFeCoNiCuH
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
Conventional catalystPt-skin HEAHHHHHH0ΔGH*single representative site0ΔGH*many local environmentssingle ΔGH*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
HH hollow siteFCC/HCP 3-fold hollow on the skinPt skintopmost layer is all Ptmixed subsurfacerandomly mixed Fe–Co–Ni–Cu–PtPtFeCoNiCuH
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
H
Hollow-site DFT
per-site ΔGH*
3
Local descriptors
subsurface counts
4
Adsorption predictor
DFT-trained surrogate
5
Active-site population
μ, σ, Popt
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
Scope of this work vs not yet
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 ΔGH*
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.
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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)
H hollow
4×4 surface cell · FCC + HCP 3-fold hollow sites (96 in total)
Side view — 6 layers
vacuum H Pt skin HEA subsurface
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
Pt Fe Cu Co Ni Pt H
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

ΔGH* across all 96 sites — tight and near-thermoneutral
Distribution of ΔG_H*
Figure 1. ΔGH* distribution over 96 FCC + HCP hollow sites (3 SQS slabs); Pt(111) reference −0.09 eV.
+0.013 eV
mean ΔGH* — essentially thermoneutral
0.055 eV
standard deviation — a narrow spread
92 %
of sites within |ΔGH*| ≤ 0.10 eV
Key messageThe Pt-skin HEA naturally creates a near-optimal population of H-binding sites.
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08

A trap hides in the simplest analysis

The subsurface counts are not independent — they add to a fixed total
site 6 subsurface neighbours — 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.
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09

The apparent ranking is misleading

Raw Pearson correlation of each subsurface count with ΔGH* (n = 96)
Apparent ranking (raw r vs ΔGH*)
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, ΔGH* rising through zero
ΔG_H* vs subsurface Pt count
Figure 3. ΔGH* 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 ΔGH* from positive toward and past the optimum.
Sign convention: higher ΔGH* = 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) ΔGH* vs surface-Pt d-band center (r = −0.86). (b) d-projected DOS for high vs low subsurface Pt.
−0.86  r
ΔGH* vs surface-Pt d-band center
subsurface Pt ↑ → d-band center ↓ → Pt–H weakens → ΔGH* → 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
ΔGH* rises toward 0
4
Sabatier population
sites land on the optimum
Key messageComposition, electronics, and energetics tell one consistent story.
13 / 18
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 ΔGH*; 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.
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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 ΔGH*
for uncalculated sites
5
Active-site population
μ, σ, Popt
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 ΔGH* population — centre and spread — not one site
ΔG_H* (eV) ΔG = 0 starting alloy tuned to optimum
Tune the subsurface Pt / Cu / Ni / Co / Fe balance to slide the whole population toward ΔGH* = 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
CentreΔGH* = +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)
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