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5.4 Adsorption energies with consistent references

These are unexecuted teaching templates, with no computed ABACUS results. The baseline is ABACUS 3.9.0; verify your executable version and data files before use.

Original model and balanced energy workflow schematic

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5.4.1 Scientific question

Does a molecule bind to a chosen surface in the selected electronic-structure model? Establish a balanced energy cycle before assigning a sign or comparing sites. An adsorption energy is not an activation barrier, a finite-temperature free energy or a measured sticking probability.

5.4.2 Model and prerequisites

Use one intact water molecule on a symmetric silicon slab as a bookkeeping exercise, with the adsorption motif deliberately left to the learner. Water may dissociate on a reactive termination; therefore identify whether the final structure is molecular or dissociated rather than assuming its identity. Compute the bare slab and isolated water using compatible Si, O and H pseudopotentials and LCAO orbitals. Check the molecule in a converged vacuum box through isolated water. For a single adsorbate on one face, recognize the new asymmetric electrostatic problem; use a symmetric two-face adsorption model as the baseline energy cycle instead.

5.4.3 Worked input delta

# Delta for relaxation of the combined slab + two adsorbates.
calculation    relax
suffix         adsorption_pair
symmetry       0
cal_force      1
relax_nmax     150
force_thr_ev   0.01
# STRU must contain the actual Si/O/H counts and matched files.

5.4.4 Physics and units

For n equivalent molecules added to a slab, divide the balanced total-energy difference by n. Under the chosen sign convention, a negative value indicates that the combined state is lower in electronic energy than the separate relaxed references. This convention is not universal, so print the formula next to the result. A dissociated final state still uses the intact molecule as a reference if that is the reaction being modeled; its atom counts must remain balanced. The change contains both surface and adsorbate deformation as well as their interaction. Dispersion, zero-point motion, entropy and solvent change the question and require separately controlled methods.

\[ E_{\mathrm{ads}}=\frac{E_{\mathrm{slab}+nM}-E_{\mathrm{slab}}-nE_M}{n} \]

5.4.5 Workflow and outputs

  1. Define the stoichiometric cycle on paper. For two waters, confirm the combined STRU contains the original Si count plus four H and two O atoms. Keep both faces chemically equivalent in the initial model.
  2. Compare at least two initial orientations and adsorption sites. Keep the same in-plane area, slab thickness, mobile-layer mask and number of adsorbates.
  3. Relax the combined structures, inspect bond distances and decide whether the state remained molecular. A converged force threshold does not classify the chemical species for you.
  4. Re-evaluate combined, bare slab and isolated molecule references with consistent functional, orbital family, SCF tolerance and energy-unit handling. The molecule uses its validated vacuum and k-point policy; the slab branches use identical KPT.
  5. Read final energies and forces from OUT.<suffix>/running_scf.log, record the final structures and apply the equation explicitly. Never use an isolated H/O atomic energy accidentally in place of the molecular reference.
  6. Increase lateral area while keeping a similar in-plane k spacing. This changes coverage and tests periodic adsorbate interaction. Repeat a selected site pair with a richer LCAO basis or a converged PW comparison to diagnose basis sensitivity.

5.4.6 Convergence and acceptance

Localized orbitals belonging to one fragment can improve the other fragment’s variational freedom in the combined system. This basis-set superposition effect can exaggerate apparent binding. Increasing orbital completeness and comparing with a converged PW baseline are transparent tests. Do not invent a ghost-atom STRU syntax or imply that an unverified counterpoise workflow is implemented. If frozen-fragment energies are also computed, label their geometries explicitly and distinguish interaction energy from adsorption relative to relaxed references. Report coverage as molecules per simulated area, and retain structural and spin labels for every site. A small energy ordering can reverse under basis or coverage refinement.

5.4.7 Pitfalls

One-sided adsorption can introduce a dipole even when the bare slab is symmetric. Two faces should not interact through a thin slab, so repeat thickness checks for the adsorbed model. Comparing two sites at different coverage or different numbers of constrained layers is not a clean site preference. A negative electronic adsorption energy does not prove adsorption is favored at every temperature and gas pressure.

5.4.8 Exercises with guidance

  1. Write the balanced expression for two dissociated waters with all atoms retained. Guidance: the reference is still two intact waters if dissociative adsorption is the defined reaction.
  2. Design a basis-versus-coverage test for two nearly degenerate sites. Guidance: cross at least two orbital qualities with two lateral cell sizes and compare the site-energy difference, not only binding to vacuum.

5.4.9 Primary sources