Catalysis

The Catalysis application module groups VQkit workflows for electrocatalytic thermodynamics, reaction free-energy analysis, vibrational thermochemistry, and orbital descriptors.

It is available from:

VQkit
 -> Post-processing
 -> [7] Application-oriented analysis
 -> [2] Catalysis

The current Catalysis menu contains:

[1] ORR free-energy analysis (CHE)
[2] OER free-energy analysis (CHE)
[3] HER analysis
[4] CO2RR analysis
[5] NRR analysis (CHE)
[6] CO reduction (CORR) analysis
[7] Vibrational frequency analysis
[8] Orbital center (s/p/d)

The Catalysis module intentionally contains derived application-specific analyses.

General DOS, PDOS, band structure, Fermi energy, work function, AIMD, charge analysis, and standalone NEB analysis remain in the common Post-processing sections and are not duplicated here.

Computational hydrogen electrode

Several VQkit catalysis workflows use the computational hydrogen electrode (CHE) concept.

For a one-electron reduction step consuming:

\[\mathrm{H^+ + e^-}\]

the implemented potential shift is expressed in eV as:

\[\Delta G(U) = \Delta G(0) + U\]

for a reduction PCET step when U is entered in volts.

This sign convention is used consistently within the current VQkit implementation.

[1] ORR free-energy analysis (CHE)

The ORR workflow uses the four-electron pathway involving:

*OH
*O
*OOH

The default equilibrium potential is:

\[U_{\mathrm{eq}} = 1.23\ \mathrm{V}\]

corresponding to a four-electron total of:

\[4 \times 1.23 = 4.92\ \mathrm{eV}\]

Input modes

VQkit currently offers three ways to provide the thermodynamic data:

[1] Enter Gibbs free energies G directly
[2] Enter E_DFT + ZPE + signed TDeltaS for each state
[3] Enter DeltaG_OH, DeltaG_O and DeltaG_OOH directly

For component input, the current convention is:

\[G = E_{\mathrm{DFT}} + ZPE + T\Delta S_{\mathrm{signed}}\]

The entropy term is entered with its sign already included.

Adsorption free energies

VQkit evaluates:

\[\Delta G_{\mathrm{OH}} = G(*\mathrm{OH}) + \frac{1}{2}G(\mathrm{H_2}) - G(\mathrm{H_2O}) - G(*)\]
\[\Delta G_{\mathrm{O}} = G(*\mathrm{O}) + G(\mathrm{H_2}) - G(\mathrm{H_2O}) - G(*)\]
\[\Delta G_{\mathrm{OOH}} = G(*\mathrm{OOH}) + \frac{3}{2}G(\mathrm{H_2}) - 2G(\mathrm{H_2O}) - G(*)\]

CHE step spans

The positive OER-oriented spans at U = 0 V are:

\[\Delta G_1 = \Delta G_{\mathrm{OH}}\]
\[\Delta G_2 = \Delta G_{\mathrm{O}} - \Delta G_{\mathrm{OH}}\]
\[\Delta G_3 = \Delta G_{\mathrm{OOH}} - \Delta G_{\mathrm{O}}\]
\[\Delta G_4 = 4U_{\mathrm{eq}} - \Delta G_{\mathrm{OOH}}\]

For ORR, VQkit reverses these steps.

Limiting potential

The ORR limiting potential is taken from the smallest positive CHE step span:

\[U_L^{\mathrm{ORR}} = \min(\Delta G_i)\]

with the current energy/voltage convention.

The ORR overpotential is:

\[\eta_{\mathrm{ORR}} = U_{\mathrm{eq}} - U_L^{\mathrm{ORR}}\]

VQkit also identifies the potential-determining step.

ORR outputs

Typical outputs are:

VQkit_ORR_CHE_summary.txt
VQkit_ORR_CHE.dat
VQkit_ORR_CHE_free_energy.png
VQkit_ORR_CHE_free_energy.pdf

Existing files are not silently overwritten; VQkit creates a numbered alternative when necessary.

[2] OER free-energy analysis (CHE)

The OER workflow uses the same *OH, *O, and *OOH state set but in the oxidation direction.

The same adsorption free energies are used.

The OER limiting potential is:

\[U_L^{\mathrm{OER}} = \max(\Delta G_i)\]

and the overpotential is:

\[\eta_{\mathrm{OER}} = U_L^{\mathrm{OER}} - U_{\mathrm{eq}}\]

VQkit reports:

  • adsorption free energies;

  • all four OER step energies;

  • limiting potential;

  • overpotential;

  • potential-determining step.

Typical outputs are:

VQkit_OER_CHE_summary.txt
VQkit_OER_CHE.dat
VQkit_OER_CHE_free_energy.png
VQkit_OER_CHE_free_energy.pdf

ORR/OER free-energy diagrams

VQkit plots thermodynamic states as short horizontal energy levels joined by dashed connectors.

The diagrams compare:

U = 0 V
U = U_eq

using the same state definitions.

A negative CHE step span is allowed numerically, but VQkit warns that this can indicate an unconventional or inconsistent state/reference set.

[3] HER analysis

The HER workflow uses the hydrogen adsorption free energy:

\[\Delta G_{\mathrm{H^*}}\]

as the main descriptor.

The ideal thermoneutral value is:

\[\Delta G_{\mathrm{H^*}} = 0\ \mathrm{eV}\]

DFT adsorption energy

VQkit evaluates:

\[\Delta E_{\mathrm{H^*}} = E(\mathrm{H^*}) - E(*) - \frac{1}{2}E(\mathrm{H_2})\]

The user can either:

  • enter E(H*), E(*) and E(H2);

  • enter DeltaE_H* directly.

Thermochemical correction

The current implementation supports:

\[\Delta G_{\mathrm{H^*}} = \Delta E_{\mathrm{H^*}} + \Delta ZPE + \Delta S_{\mathrm{signed}}\]

The built-in room-temperature approximation is approximately:

\[\Delta G_{\mathrm{H^*}} \approx \Delta E_{\mathrm{H^*}} + 0.240\ \mathrm{eV}\]

The source defaults used by the implementation are approximately:

ZPE(H*)  = 0.170 eV
ZPE(H2)  = 0.27283 eV
signed entropy correction H* = 0
signed entropy correction H2 = -0.403815 eV

Interpretation

VQkit reports:

  • DeltaE_H* when available;

  • thermochemical correction;

  • DeltaG_H*;

  • absolute distance from thermoneutrality;

  • whether H* is stabilized or destabilized relative to the CHE endpoints.

HER outputs

Typical outputs are:

VQkit_HER_summary.txt
VQkit_HER.dat
VQkit_HER_free_energy.png
VQkit_HER_free_energy.pdf

The free-energy profile uses:

H+ + e-
H*
1/2 H2

at U = 0 V and pH = 0.

[4] CO2RR analysis

The CO2 reduction workflow currently supports two pathways:

  • CO formation;

  • formate / HCOOH formation.

The corrected Gibbs free energy convention is:

\[G = E_{\mathrm{DFT}} + ZPE - TS + \Delta G_{\mathrm{solv}}\]

Here TS is entered as a positive magnitude, while the solvation correction may be positive or negative.

This convention is intentionally different from the signed-TDeltaS input used in the ORR/OER component mode, so users should follow the prompts for the selected workflow carefully.

CO pathway

The implemented CO pathway is:

CO2 + * + (H+ + e-) -> *COOH
*COOH + (H+ + e-)   -> *CO + H2O
*CO                  -> * + CO

The first two steps are one-electron PCET steps.

The desorption step is chemical and does not determine the CHE limiting potential.

At U = 0:

\[\Delta G_1 = G(*\mathrm{COOH}) - G(*) - G(\mathrm{CO_2}) - \frac{1}{2}G(\mathrm{H_2})\]
\[\Delta G_2 = G(*\mathrm{CO}) + G(\mathrm{H_2O}) - G(*\mathrm{COOH}) - \frac{1}{2}G(\mathrm{H_2})\]

If gas-phase CO is supplied, VQkit also evaluates:

\[\Delta G_{\mathrm{des}} = G(*) + G(\mathrm{CO}) - G(*\mathrm{CO})\]

Formate pathway

The implemented formate route is:

CO2 -> *OCHO
*OCHO -> HCOOH

with two one-electron PCET steps.

Potential and pH corrections

For RHE reference:

\[\Delta G(U) = \Delta G(0) + U\]

For SHE reference, VQkit additionally includes:

\[k_B T \ln(10)\,\mathrm{pH}\]

for each one-electron reduction PCET step.

The user can select:

RHE
SHE

and provide:

  • applied potential;

  • pH;

  • temperature.

Limiting potential

For the PCET steps:

\[U_L = -\max(\Delta G_i)\]

The largest uphill PCET step is reported as the potential-determining step.

When the overall product free energy is available, VQkit can also report:

  • overall reaction free energy;

  • equilibrium potential;

  • thermodynamic overpotential.

Typical outputs include pathway-specific files such as:

VQkit_CO2RR_CO_summary.txt
VQkit_CO2RR_CO.dat

and corresponding formate outputs.

[5] NRR analysis (CHE)

The NRR workflow treats nitrogen reduction as a six-PCET process:

\[\mathrm{N_2} + 6(\mathrm{H^+ + e^-}) \rightarrow 2\mathrm{NH_3}\]

The default associative distal state template is:

*N2
*NNH
*NNH2
*N + NH3
*NH + NH3
*NH2 + NH3
*NH3 + NH3

VQkit expects seven relative state free energies:

  • one initial *N2 state;

  • six subsequent one-electron PCET states.

The first state is normally entered as:

0.0 eV

Incremental free energies

For neighboring states:

\[\Delta G_i = G_i - G_{i-1}\]

The potential-determining step is the largest uphill step.

The limiting potential is:

\[U_L = -\max(\Delta G_i)\]

The default NRR equilibrium potential in the current implementation is:

\[U_{\mathrm{eq}} = 0.092\ \mathrm{V}\]

When an equilibrium potential is used, VQkit reports an overpotential-like quantity as:

\[\eta = U_{\mathrm{eq}} - U_L\]

NRR outputs

The workflow exports:

  • summary text;

  • profile data;

  • PNG/PDF free-energy diagram.

The plot compares:

U = 0 V
U = U_L

Custom NRR pathway

VQkit also allows a custom six-PCET NRR pathway while retaining the same CHE step analysis.

The user is responsible for ensuring that the custom sequence is chemically consistent.

[6] CO reduction (CORR) analysis

CO reduction chemistry depends strongly on:

  • target product;

  • catalyst;

  • chosen intermediates;

  • protonation sequence.

For this reason, VQkit does not hard-code one CORR mechanism.

Instead, the user supplies a custom one-electron PCET sequence.

The menu asks for:

Number of one-electron PCET steps

with a current allowed range of:

1 to 20

The user then supplies:

  • an ordered label for every state;

  • the relative Gibbs free energy of every state at U = 0 V.

The first state defaults to:

*CO

Each neighboring state is treated as one:

H+ + e-

transfer.

For each step:

\[\Delta G_i(U) = \Delta G_i(0) + U\]

and:

\[U_L = -\max(\Delta G_i(0))\]

VQkit reports:

  • every incremental step free energy;

  • potential-determining step;

  • maximum uphill free energy;

  • limiting potential.

Typical outputs are:

VQkit_CORR_summary.txt
VQkit_CORR.dat
VQkit_CORR_free_energy.png
VQkit_CORR_free_energy.pdf

Because the pathway is user-defined, chemical consistency must be verified manually.

[7] Vibrational frequency analysis

The catalysis vibrational module reads completed VASP or Quantum ESPRESSO frequency calculations.

The menu provides:

[1] Analyze frequency calculation in current directory
[2] Analyze a specific output file
[3] Explain ZPE / entropy / HER correction

The parser scans complete output files rather than only their initial lines.

This is important because vibrational frequencies often appear near the end of large VASP OUTCAR files.

Supported sources

VASP

Typical source:

OUTCAR

VQkit identifies VASP vibrational modes from recognizable frequency lines.

Quantum ESPRESSO

Typical source:

*.out
*.log

containing ph.x / frequency information.

Mode classification

VQkit separates:

  • positive real modes;

  • imaginary modes;

  • zero modes.

Imaginary modes are reported but excluded from thermochemical corrections.

Zero-point energy

For one positive mode:

\[ZPE_i = \frac{1}{2}h\nu_i\]

Total ZPE is the sum over all positive real modes.

Finite-temperature vibrational terms

At a user-selected temperature, VQkit evaluates harmonic:

  • thermal vibrational energy above ZPE;

  • vibrational entropy;

  • T*S_vib;

  • harmonic vibrational free energy.

The free-energy form is:

\[F_{\mathrm{vib}} = ZPE + U_{\mathrm{thermal}} - TS_{\mathrm{vib}}\]

Low-frequency cutoff

Very low positive frequencies can create unrealistically large harmonic entropy contributions.

VQkit therefore offers:

[1] 10 cm^-1   - Minimal filtering [default]
[2] 50 cm^-1   - Moderate filtering
[3] 100 cm^-1  - Conservative for surface/adsorbate modes
[4] Custom cutoff

Modes below the selected cutoff are excluded only from finite-temperature entropy/free-energy terms.

ZPE still includes all positive real modes.

Outputs

VQkit writes:

VQkit_vibrational_summary.txt
VQkit_vibrational_frequencies.dat

The summary reports:

  • source file;

  • code;

  • temperature;

  • cutoff;

  • total mode count;

  • real/imaginary/zero modes;

  • ZPE;

  • thermal vibrational energy;

  • vibrational entropy;

  • T*S_vib;

  • harmonic F_vib.

Imaginary-mode caution

For a stable minimum, significant imaginary modes normally require investigation.

For a transition state, one physically meaningful imaginary mode may be expected depending on the method.

VQkit reports the frequencies but does not decide whether the structure is a valid minimum or transition state.

[8] Orbital center (s/p/d)

The Catalysis menu exposes an orbital-center descriptor workflow.

The currently validated and documented backend is the VASP projected DOSCAR d-band-center analysis.

The d-band center is defined as:

\[\varepsilon_d = \frac{ \int_{E_1}^{E_2} (E-E_F)n_d(E)\,dE }{ \int_{E_1}^{E_2} n_d(E)\,dE }\]

where:

  • \(n_d(E)\) is the d-projected density of states;

  • \(E_F\) is the Fermi level;

  • \(E_1\) and \(E_2\) define the integration window.

The reported center is therefore referenced to:

E_F = 0 eV

Spin-polarized calculations

For collinear spin-polarized calculations, VQkit uses:

\[n_d(E) = n_d^\uparrow(E) + n_d^\downarrow(E)\]

before calculating the first moment.

Integration windows

The validated d-band workflow supports:

  • full projected-DOS range;

  • occupied range up to E_F;

  • custom lower/upper energy limits relative to E_F.

Custom limits are interpolated onto the DOS grid when required.

Atom selection

The user can analyze:

  • all atoms;

  • selected one-based atom indices.

For multiple selected atoms, the combined d-band center is calculated from the summed moment divided by summed d-PDOS weight.

It is not an unweighted arithmetic average of individual atom centers.

Required VASP data

The validated backend requires:

DOSCAR

with atom-projected d states.

POSCAR or CONTCAR is recommended for species labels.

A projected-DOS setup such as:

LORBIT = 11

is typically appropriate.

Output

The validated d-band implementation writes:

VQkit_D_BAND_CENTER.dat

The file records:

  • source DOSCAR;

  • Fermi energy;

  • integration window;

  • d-orbital channels;

  • atom/species labels;

  • atom-resolved d-band centers;

  • integrated d-PDOS weights;

  • combined d-band center.

Current backend scope

At present, the independently validated backend documented in VQkit is:

VASP projected DOSCAR : available
QE projwfc.x          : not yet enabled for validated d-band-center analysis

Therefore comparisons should not assume that every s/p/d label exposed by the menu has identical backend maturity.

Comparison rule

For meaningful catalyst comparison, use the same:

  • pseudopotential family;

  • orbital-projection settings;

  • DOS energy grid;

  • smearing/broadening;

  • Fermi-level reference;

  • integration window.

Catalysis workflow relationships

The Catalysis menu contains application-specific descriptors, while supporting data may come from other VQkit sections.

Electronic structure

Use:

Post-processing
-> Electronic structure

for:

  • DOS;

  • PDOS;

  • band structure;

  • Fermi level;

  • work function.

Charge and bonding

Use the relevant Post-processing section for:

  • charge-density difference;

  • Bader charge;

  • ELF.

Reaction barriers

Use:

Post-processing
-> Energetics and thermodynamics
-> NEB / transition-state analysis and plot

for activation barriers.

AIMD

Use:

Post-processing
-> AIMD / trajectory analysis

for dynamic stability and trajectory descriptors.

Thermochemistry consistency

Do not mix:

  • raw DFT energies;

  • ZPE-corrected energies;

  • full Gibbs energies;

  • solvated and unsolvated states

within one reaction profile unless the reference convention explicitly requires it.

All states in one catalytic free-energy analysis should use a common and transparent thermodynamic convention.

Scientific limitations

The Catalysis module performs transparent descriptor calculations.

It does not automatically determine:

  • the true reaction mechanism;

  • solvent structure;

  • electrode double-layer effects;

  • constant-potential corrections;

  • field effects;

  • kinetic prefactors;

  • reaction rates;

  • transition-state entropies;

  • microkinetic coverage effects.

These require additional calculations and physical modeling.

Summary

The current Catalysis application provides:

ORR       -> four-electron CHE analysis
OER       -> reverse four-electron CHE analysis
HER       -> H* adsorption free-energy descriptor
CO2RR     -> CO and formate CHE pathways
NRR       -> six-PCET CHE profile
CORR      -> custom one-electron PCET profile
Vibrations-> ZPE and harmonic thermochemistry
Orbital   -> validated VASP d-band-center descriptor

The workflows are designed to preserve transparent equations and user-defined reference states rather than hiding the thermodynamic assumptions.