HER Overpotential Calculation

Theory

The hydrogen evolution reaction has a single key intermediate:

* + H+ + e- --> *H    (Volmer step)
*H + H+ + e- --> H2   (Heyrovsky step)
   or
2 *H --> H2            (Tafel step)

Sabatier Criterion

The optimal HER catalyst has:

dG_H* = G(*H) - G(*) - 0.5 * G(H2) ~ 0 eV

• dG_H* < 0: H binds too strongly (poisoned surface)
• dG_H* > 0: H binds too weakly (low coverage, slow Volmer)
• dG_H* ~ 0: optimal (top of volcano plot)

pH Correction

At non-zero pH, the proton-transfer step is corrected by:

dG_H*(pH) = dG_H* - 0.059 * pH   (eV, at 298 K)

This shifts the free energy of the (H+ + e-) transfer by -0.059 eV per pH unit (Nernst relation). At pH 0, no correction is needed.

Overpotential

eta_HER = |dG_H*| / e

A perfect catalyst has eta_HER = 0 V. Pt(111) gives dG_H* ~ -0.09 eV.

Important: All G values must be Gibbs free energies (from geo_opt + freq + gibbs_energy chain), NOT raw DFT electronic energies. Using E_DFT instead of G omits ZPE and entropy, leading to errors of ~0.2 eV.

Discussion Checkpoints

🔴 Must discuss with user:

• Surface choice — Miller index and termination determine H binding site and dG_H*; e.g., Pt(111) fcc hollow vs MoS2 S-edge give very different results
• Functional — must be consistent between H slab, clean slab, and gas-phase H2; PBE vs SCAN can shift dG_H by 0.1-0.3 eV
• Competing reactions — on surfaces active for OER/ORR, H adsorption may compete; always check if HER or OER dominates at the operating potential

🟡 Recommend confirming:

• Coverage effects — at high H coverage, lateral interactions shift dG_H*; consider testing 1/4 ML vs 1/2 ML vs 1 ML
• Zero-point energy correction — ZPE contributes ~0.04 eV to dG_H*; always include freq + gibbs_energy chain rather than using raw DFT energies
• Adsorption site — test ontop, bridge, and hollow; report the most stable site (lowest |dG_H*|)

🟢 Safe defaults:

• Single intermediate (*H)
• dG_H* = G(H) - G() - 0.5*G(H2)
• eta_HER = |dG_H*| / e

MCP Workflow

1. Create workflow

{"tool": "catgo_workflow_engine", "arguments": {
  "action": "create", "name": "HER on Pt(111)"
}}

2. Build structures

Fetch bulk, cut slab, place H adsorbate:

{"tool": "catgo_fetch", "arguments": {
  "action": "crystal", "formula": "Pt", "source": "mp"
}}

{"tool": "catgo_structure", "arguments": {
  "action": "slab", "miller_index": [1,1,1],
  "min_slab_size": 12.0, "min_vacuum_size": 15.0
}}

{"tool": "catgo_structure", "arguments": {
  "action": "add_atom", "element": "H",
  "position": [2.77, 1.60, 14.2]
}}

3. Clean slab branch

{"tool": "catgo_workflow_engine", "arguments": {
  "action": "add_task", "workflow_id": "wf_her",
  "task_type": "geo_opt",
  "params": {"software": "vasp", "ENCUT": 520, "system_name": "clean_slab"}
}}

4. *H branch: geo_opt --> freq --> gibbs

{"tool": "catgo_workflow_engine", "arguments": {
  "action": "add_task", "workflow_id": "wf_her",
  "task_type": "geo_opt",
  "params": {"software": "vasp", "ENCUT": 520, "system_name": "*H"}
}}

{"tool": "catgo_workflow_engine", "arguments": {
  "action": "add_task", "workflow_id": "wf_her",
  "task_type": "freq", "depends_on": "task_h_opt",
  "params": {"software": "vasp", "freeze_mode": "layers", "freeze_layers": 4,
             "system_name": "*H"}
}}

{"tool": "catgo_workflow_engine", "arguments": {
  "action": "add_task", "workflow_id": "wf_her",
  "task_type": "gibbs_energy",
  "depends_on": ["task_h_opt", "task_h_freq"],
  "params": {"phase": "adsorbed", "system_name": "*H"}
}}

5. Gas-phase H2 reference

{"tool": "catgo_workflow_engine", "arguments": {
  "action": "add_task", "workflow_id": "wf_her",
  "task_type": "gibbs_energy",
  "depends_on": ["task_h2_opt", "task_h2_freq"],
  "params": {"phase": "gas", "system_name": "H2(g)"}
}}

6. Submit

{"tool": "catgo_workflow_engine", "arguments": {
  "action": "submit", "workflow_id": "wf_her"
}}

Python API

from catgo.workflow import Workflow

wf = Workflow("HER on Pt(111)")

# Clean slab
slab_inp = wf.add_task("structure_input", structure=clean_slab_json)
slab_opt = wf.add_task("geo_opt", structure=slab_inp.output.structure,
                        software="vasp", ENCUT=520)

# *H on slab
h_inp = wf.add_task("structure_input", structure=slab_h_json)
h_opt = wf.add_task("geo_opt", structure=h_inp.output.structure,
                     software="vasp", ENCUT=520)
h_frq = wf.add_task("freq", structure=h_opt.output.structure,
                     software="vasp", freeze_mode="layers", freeze_layers=4)
h_gib = wf.add_task("gibbs_energy", energy=h_opt.output.energy,
                     frequencies=h_frq.output.frequencies, phase="adsorbed")

# Gas-phase H2
h2_inp = wf.add_task("structure_input", structure=h2_json)
h2_opt = wf.add_task("geo_opt", structure=h2_inp.output.structure,
                      software="vasp")
h2_frq = wf.add_task("freq", structure=h2_opt.output.structure,
                      software="vasp")
h2_gib = wf.add_task("gibbs_energy", energy=h2_opt.output.energy,
                      frequencies=h2_frq.output.frequencies, phase="gas")

wf.submit()

DAG Structure

clean_slab --> geo_opt
*H   --> geo_opt --> freq --> gibbs_energy (adsorbed)
H2   --> geo_opt --> freq --> gibbs_energy (gas)

Three independent branches, 7 total tasks.

Interpreting Results

dG_H* (eV)	Interpretation	Action
-0.5 to -0.1	Strong binding, decent catalyst	May need surface modification
-0.1 to +0.1	Near optimal (volcano peak)	Excellent HER catalyst
+0.1 to +0.5	Weak binding, moderate activity	Consider alloying or doping
> +0.5	Too weak, poor HER catalyst	Different material needed

Adsorption Sites for H

Surface Type	Preferred H Site	Typical dG_H*
Pt(111)	fcc hollow	-0.09 eV
MoS2 edge	S-edge top	+0.08 eV
Graphene + N-doped	C adjacent to N	varies

Common Pitfalls

1. H is small -- use tight EDIFFG (-0.01 eV/A) to ensure proper relaxation.
2. Only freeze bottom slab layers in freq, not the H atom itself.
3. For alloy surfaces, test multiple adsorption sites (top, bridge, hollow) and report the most stable one (lowest dG_H*).
4. Always verify H does not migrate subsurface during geo_opt -- check the final structure with catgo_view.
5. For MoS2 and 2D materials, the "slab" is the monolayer itself with vacuum. Set freeze_layers=0 and use freeze_mode="none" in freq.