Energetics and Thermodynamics

The Energetics and Thermodynamics menu provides post-processing tools for common energetic quantities used in catalysis, defect chemistry, surface science, and reaction-path analysis.

It is available from:

VQkit
 -> Post-processing
 -> [5] Energetics and thermodynamics

The current menu contains:

[1] Atom / molecule adsorption energy
[2] Doping formation energy
[3] NEB / transition-state analysis and plot
[4] Surface energy
[5] Single-atom vacancy formation energy

Before using these tools, confirm that the underlying DFT calculations were performed with consistent computational settings.

Detected calculation and status

When this menu opens, VQkit reports the currently detected code and run status, for example:

Detected calculation : VASP
Status               : No completed calculation detected

The numerical energetics tools accept user-supplied energies, so a completed calculation is not always required in the current working directory.

However, the energies entered should come from properly converged and compatible calculations.

[1] Atom / molecule adsorption energy

Choose:

[1] Atom / molecule adsorption energy

VQkit supports three reference conventions:

[1] Atom adsorption - isolated-atom reference
[2] Atom adsorption - molecular reference
[3] Molecule adsorption - intact molecular reference

General adsorption-energy expression

For n adsorbates:

\[E_{\mathrm{ads}} = \frac{ E_{\mathrm{surface}+nX} - E_{\mathrm{surface}} - n f E_{\mathrm{ref}} }{n}\]

where:

\(E_{\mathrm{surface}+nX}\) is the total energy of the adsorbed system;
\(E_{\mathrm{surface}}\) is the clean-surface energy;
\(E_{\mathrm{ref}}\) is the chosen reference energy;
\(f\) converts the reference species into energy per adsorbate;
\(n\) is the number of adsorbates.

The VQkit sign convention is:

negative E_ads = exothermic / favorable adsorption
positive E_ads = endothermic adsorption

under the selected reference convention.

Isolated-atom reference

For an adsorbed atom referenced to an isolated atom:

\[f = 1\]

VQkit asks for:

E(surface + adsorbate) (eV)
E(clean surface) (eV)
Number of adsorbed atoms/molecules
E(isolated reference atom) (eV)

Example:

E(surface + O) = -125.40 eV
E(surface)     = -120.00 eV
E(O atom)      =   -4.80 eV

then:

\[E_{\mathrm{ads}} = -125.40 - (-120.00) - (-4.80) = -0.60\ \mathrm{eV}\]

Molecular reference for atomic adsorption

For atomic adsorption referenced to a molecule, VQkit asks for the number of target atoms in the reference molecule.

Examples:

O referenced to O2  -> factor = 1/2
H referenced to H2  -> factor = 1/2

If oxygen adsorption is referenced to O2:

\[E_{\mathrm{ref,per\ O}} = \frac{1}{2} E_{\mathrm{O_2}}\]

The factor is therefore:

\[f = \frac{1}{N_{\mathrm{target\ atoms\ in\ molecule}}}\]

Intact molecular adsorption

For adsorption of an intact molecule:

\[f = 1\]

and the reference is the isolated molecule.

Example:

\[E_{\mathrm{ads}} = E_{\mathrm{surface+CO_2}} - E_{\mathrm{surface}} - E_{\mathrm{CO_2}}\]

Adsorption-energy output

VQkit reports:

selected reference convention;
adsorbed-system energy;
clean-surface energy;
total reference contribution;
number of adsorbates;
adsorption energy per adsorbate.

It writes:

VQkit_ADSORPTION_ENERGY_summary.txt

Adsorption-energy cautions

All component energies should normally use the same:

exchange-correlation functional;
pseudopotential family;
plane-wave cutoff;
spin treatment;
energy correction convention.

For molecular references, verify the physically intended reference state.

[2] Doping formation energy

Choose:

[2] Doping formation energy

The current menu provides:

[1] Substitutional dopant
[2] Interstitial dopant

Substitutional doping

For a host atom Y replaced by dopant X:

\[E_{\mathrm{form}} = E_{\mathrm{doped}} - E_{\mathrm{pristine}} - \mu_{\mathrm{dopant}} + \mu_{\mathrm{removed}}\]

VQkit asks for:

E(doped system) (eV)
E(pristine host) (eV)
Chemical potential mu_dopant (eV/atom)
Chemical potential mu_removed-host (eV/atom)

The chemical-potential terms account for adding the dopant and returning the removed host atom to its reservoir.

Interstitial doping

For an interstitial dopant added without removing a host atom:

\[E_{\mathrm{form}} = E_{\mathrm{doped}} - E_{\mathrm{pristine}} - \mu_{\mathrm{dopant}}\]

VQkit asks for:

E(doped system) (eV)
E(pristine host) (eV)
Chemical potential mu_dopant (eV/atom)

Doping output

VQkit writes:

VQkit_DOPING_FORMATION_ENERGY_summary.txt

The summary includes:

doping mode;
energy terms;
chemical potentials;
final formation energy.

Chemical-potential caution

The chemical potentials must match the chosen thermodynamic environment.

For example, metal-rich, oxygen-rich, oxygen-poor, or other growth conditions can lead to different formation energies.

VQkit evaluates the supplied expression but does not choose the physical chemical-potential bounds automatically.

[3] NEB / transition-state analysis and plot

Choose:

[3] NEB / transition-state analysis and plot

This is a post-processing workflow.

It analyzes already completed NEB image calculations.

Intermediate-image generation belongs to:

Pre-processing
-> NEB Intermediate Images

Expected directory layout

The NEB root should contain numeric image directories such as:

00/
01/
02/
03/
04/
05/
06/

At least three numeric image directories are required.

Each image directory must contain a completed energy source.

VASP image energies

VQkit first checks:

OUTCAR

for:

free energy TOTEN = ...

If unavailable, it checks:

OSZICAR

and uses the latest:

E0 = ...

or, as a fallback:

F = ...

Quantum ESPRESSO image energies

For QE image folders, VQkit searches files such as:

*.out
*.pwo
pw.out*

and extracts:

! total energy = ... Ry

The value is converted using:

\[1\ \mathrm{Ry} = 13.605693122994\ \mathrm{eV}\]

Mixed-code image sets

A single NEB image set must not mix VASP and QE image outputs.

If both are detected across the same profile, VQkit stops with an error.

Relative energy

The first image is used as the zero-energy reference.

For image i:

\[\Delta E_i = E_i - E_{\mathrm{initial}}\]

The initial image therefore has:

\[\Delta E_0 = 0\]

Transition-state candidate

VQkit identifies the highest-energy image:

\[E_{\mathrm{max}} = \max_i E_i\]

as the transition-state candidate.

For a standard NEB calculation this is only an approximation to the transition-state region.

For a converged CI-NEB calculation, the climbing image is the intended saddle-point estimate.

Forward activation barrier

\[E_{\mathrm{a,fwd}} = E_{\mathrm{TS}} - E_{\mathrm{initial}}\]

Reverse activation barrier

\[E_{\mathrm{a,rev}} = E_{\mathrm{TS}} - E_{\mathrm{final}}\]

Reaction energy

\[\Delta E_{\mathrm{rxn}} = E_{\mathrm{final}} - E_{\mathrm{initial}}\]

Therefore:

negative reaction energy = exothermic final state
positive reaction energy = endothermic final state

NEB outputs

VQkit writes:

VQkit_NEB_PROFILE.dat
VQkit_NEB_ANALYSIS_summary.txt
VQkit_NEB_PROFILE.png
VQkit_NEB_PROFILE.pdf

The data file contains:

image_index
image_label
total_energy_eV
relative_energy_eV

The summary reports:

highest-energy image;
forward barrier;
reverse barrier;
reaction energy.

The PNG/PDF plot displays relative energy against NEB image/reaction coordinate.

NEB scientific caution

The highest-energy standard-NEB image is not automatically the exact transition state.

Before reporting a barrier, verify:

image convergence;
force convergence;
pathway quality;
CI-NEB convergence where used.

[4] Surface energy

Choose:

[4] Surface energy

VQkit evaluates:

\[\gamma = \frac{ E_{\mathrm{slab}} - N E_{\mathrm{bulk}} }{ n_{\mathrm{surf}} A }\]

where:

\(E_{\mathrm{slab}}\) is the slab total energy;
\(E_{\mathrm{bulk}}\) is bulk energy per chosen reference unit;
\(N\) is the number of those bulk reference units in the slab;
\(A\) is the area of one surface;
\(n_{\mathrm{surf}}\) is the number of equivalent/evaluated surfaces.

Surface treatment

VQkit provides:

[1] Symmetric slab: two equivalent surfaces
    n_surf = 2

[2] One evaluated surface / fixed-bottom treatment
    n_surf = 1

[3] Custom number of equivalent/evaluated surfaces

Choosing the correct value of n_surf is essential.

Surface area

VQkit can either:

read the area automatically from a structure file;
accept a manually entered area in Angstrom².

For a structure with lattice vectors a and b:

\[A = |\mathbf{a}\times\mathbf{b}|\]

The current workflow therefore assumes that a and b span the surface plane.

Automatically detected structures can include:

CONTCAR
POSCAR
scf.in
relax.in
vc-relax.in

Energy inputs

VQkit asks for:

Slab total energy E_slab (eV)
Bulk reference energy per unit E_bulk (eV)
Number N of those bulk reference units in the slab

The bulk reference unit must be defined consistently.

For example, if E_bulk is energy per formula unit, N must be the number of formula units represented in the slab.

Surface-energy units

VQkit reports:

eV/Angstrom^2
J/m^2

using:

\[1\ \mathrm{eV/\AA^2} = 16.021766208\ \mathrm{J/m^2}\]

It also reports:

\[2\gamma\]

as a cleavage-equivalent quantity.

Surface-energy output

VQkit writes:

VQkit_SURFACE_ENERGY_summary.txt

The summary contains:

surface treatment;
surface area;
number of surfaces;
slab energy;
bulk reference;
excess energy;
gamma in eV/Angstrom²;
gamma in J/m²;
2 gamma.

Symmetric versus asymmetric slabs

Use:

n_surf = 2

only when the slab excess energy corresponds to two equivalent surfaces.

Use:

n_surf = 1

for a one-surface or fixed-bottom treatment when only one surface contribution is being evaluated.

For chemically inequivalent top and bottom surfaces, a simple division by two may not provide an individual surface energy.

[5] Single-atom vacancy formation energy

Choose:

[5] Single-atom vacancy formation energy

VQkit evaluates:

\[E_{\mathrm{vac}} = E_{\mathrm{defective}} - E_{\mathrm{pristine}} + \mu_{\mathrm{removed}}\]

where:

\(E_{\mathrm{defective}}\) is the energy of the system containing one vacancy;
\(E_{\mathrm{pristine}}\) is the pristine-system energy;
\(\mu_{\mathrm{removed}}\) is the chemical potential of the removed atom.

VQkit asks for:

E(system with one vacancy) (eV)
E(pristine system) (eV)
Chemical potential mu_removed (eV/atom)

Vacancy output

VQkit writes:

VQkit_SINGLE_VACANCY_ENERGY_summary.txt

The summary contains all three energy terms and the final vacancy formation energy.

Vacancy-energy caution

The vacancy formation energy depends strongly on the chosen chemical potential.

For multicomponent materials, physically allowed chemical potentials can be restricted by phase stability.

VQkit evaluates the entered expression but does not automatically construct a phase-stability diagram or chemical-potential range.

Common requirements for energetic comparisons

For adsorption, doping, surface, and vacancy energies, the calculations being combined should normally use consistent settings.

These include:

exchange-correlation functional;
pseudopotential family;
plane-wave cutoff;
k-point sampling;
spin treatment;
Hubbard U;
smearing convention;
relativistic treatment;
total-energy correction scheme.

Reference cells and k meshes may differ when scientifically necessary, but they must be individually converged and thermodynamically consistent.

Energy versus free energy

The current VQkit formulas operate on user-supplied DFT total energies.

They do not automatically include:

zero-point energy;
vibrational entropy;
configurational entropy;
gas-phase entropy;
solvent free energy;
electrochemical potential corrections;
temperature/pressure corrections.

Therefore a quantity labeled formation energy or adsorption energy is an electronic-energy result unless the user has already incorporated the appropriate corrections into the entered values.

Recommended workflow

For adsorption energy:

Compute the clean surface.
Compute the adsorbed system.
Compute the chosen atomic or molecular reference.
Use identical or consistently converged computational settings.
Enter the energies in VQkit.
Save the generated summary.

For doping formation energy:

Compute pristine host.
Compute doped host.
Define physically justified chemical potentials.
Select substitutional or interstitial mode.
Enter energies and chemical potentials.
Record the VQkit summary.

For NEB:

Generate images in Pre-processing.
Run and converge the NEB calculation.
Place completed outputs inside numeric image directories.
Run the post-processing NEB analyzer.
Inspect the profile and barriers.
Verify CI-NEB convergence when claiming a transition state.

For surface energy:

Compute the slab.
Compute a consistent bulk reference.
Determine the number of bulk reference units in the slab.
Determine surface area.
Choose the correct number of evaluated surfaces.
Evaluate gamma in VQkit.

For vacancy energy:

Compute pristine structure.
Compute the one-vacancy structure.
Define the removed-atom chemical potential.
Enter the three energy terms.
Save the summary.

Generated files summary

Adsorption

VQkit_ADSORPTION_ENERGY_summary.txt

Doping

VQkit_DOPING_FORMATION_ENERGY_summary.txt

NEB

VQkit_NEB_PROFILE.dat
VQkit_NEB_ANALYSIS_summary.txt
VQkit_NEB_PROFILE.png
VQkit_NEB_PROFILE.pdf

Surface energy

VQkit_SURFACE_ENERGY_summary.txt

Vacancy

VQkit_SINGLE_VACANCY_ENERGY_summary.txt

The Energetics and Thermodynamics module provides transparent formula-based analysis while leaving the choice of reference states and thermodynamic conditions to the researcher.