Pt Adatoms Island on MoS2 (Binding Energy)

1. Introduction

This tutorial calculates binding energies of Pt on monolayer MoS₂, reproducing results from the following manuscript:

Manuscript

W. A. Saidi, "Density Functional Theory Study of Nucleation and Growth of Pt Nanoparticles on MoS2(001) Surface", Crystal Growth & Design 15, 642–652 (2015). DOI:10.1021/cg5013395. ¹

This tutorial builds upon the Pt Nanoparticles on MoS2(001) Surface via Adatoms tutorial, where the structures are created. Here, the binding energy is calculated using Quantum ESPRESSO with Eq. 1 of the manuscript, E_b = (1/n) [E(MoS₂ + Pt_n) − E(MoS₂) − n E(Pt atom)], against the isolated Pt atom: for the t-(Mo)₄-S cluster (n = 4, three Pt atoms on top of Mo and the fourth above S) and for one Pt atom on top of Mo (n = 1). The figure below shows the t-(Mo)₄-S cluster from the manuscript and from the structure notebook:

2. Prerequisites

Before starting this tutorial, one of the following steps should be completed:

1. Follow the Pt Nanoparticles on MoS2(001) Surface via Adatoms tutorial, using the defect_point_adatom_island_molybdenum_disulfide_platinum.ipynb notebook embedded in its section 6, to create and save MoS2 5x5 monolayer (75 atoms), MoS2 5x5 Pt1 atop Mo (76 atoms) and MoS2 5x5 Pt4 t-(Mo)4-S (79 atoms), OR
2. Have the three materials saved in the uploads folder or in the account's materials collection

3. Workflow overview

The binding energy calculation consists of the following steps:

1. Set up the environment and parameters: Configure material names, the Pt atom box, the model, and compute resources
2. Authenticate and initialize API client: Connect to the platform
3. Load materials: Import the three slabs, build the isolated Pt atom, print their compositions and cells
4. Configure the model: One Density Functional Theory (DFT) model for every job
5. Configure compute resources: Select the cluster, queue, and processor settings
6. Relax the three slabs: At fixed cell, at the Γ point, with the dipole correction
7. Compute the isolated Pt atom: One spin-polarized Total Energy job at the Γ point
8. Retrieve results: Eq. 1 for Pt₄ and Pt₁, and the mean bond lengths of the relaxed Pt₄ cluster
9. Compare with the manuscript: Print the binding energies beside Table 1's

4. Calculation parameters

	this tutorial	Saidi
Code	Quantum ESPRESSO	Vienna Ab initio Simulation Package (VASP)
Functional	Perdew-Burke-Ernzerhof (PBE), no van der Waals correction	PBE, no van der Waals correction
Pseudopotentials	ultrasoft (GBRV)	projector augmented-wave (PAW)
Cutoff	40 / 200 Ry	350 eV
Cell	5×5 monolayer, a = 3.196 Å (Standata; publication 3.18 Å); 75, 76 and 79 atoms in one 15.98 × 15.98 × 26.27 Å cell	5×5 monolayer, a = 3.18 Å, vacuum over 10 Å
k-points	Γ	Γ
Smearing	Fermi-Dirac, 0.05 eV	Fermi-Dirac, 0.05 eV
Dipole correction	along z, on the three slabs	on the slabs
Relaxation	all atoms, fixed cell, 0.005 eV/Å, at most 10 ionic steps	all atoms, 0.005 eV/Å
Spin, slabs	not spin-polarized	not spin-polarized, the supported clusters being non-magnetic
Spin, Pt atom	nspin = 2, total magnetization 2	spin-polarized, two unpaired electrons
Pt atom box	12 Å cube	not stated

5. Step-by-step instructions

5.1. Open the notebook

Navigate to the API examples repository and open the binding energy notebook:

other/materials_designer/specific_examples/defect_point_adatom_island_molybdenum_disulfide_platinum_SIMULATION.ipynb

5.2. Configure parameters

Cell 1.2 sets the material names and the box of the isolated Pt atom:

# Names saved by defect_point_adatom_island_molybdenum_disulfide_platinum.ipynb.
PRISTINE_NAME = "MoS2 5x5 monolayer"
PT1_NAME = "MoS2 5x5 Pt1 atop Mo"
PT4_NAME = "MoS2 5x5 Pt4 t-(Mo)4-S"
PT_ATOM_NAME = "Pt atom"
PT_ATOM_BOX = 12.0  # Å, edge of the cubic box around the isolated Pt atom; manuscript: box size not stated

Cell 1.4 sets the DFT model; each comment names the manuscript's setting:

# manuscript: VASP PAW at 350 eV; ours GBRV ultrasoft at its own converged 40/200 Ry
FUNCTIONAL = "pbe"
PSEUDOPOTENTIAL_TYPE = "us"
ECUTWFC = 40   # Ry
ECUTRHO = 200  # Ry

GAMMA_KGRID = [1, 1, 1]  # manuscript: Γ only, for the slabs and the isolated atom
# manuscript: Fermi-Dirac, k_B T = 0.05 eV = 0.003675 Ry
SMEARING_SETTINGS = {"occupations": "smearing", "smearing": "fermi-dirac", "degauss": 0.003675}
# manuscript: dipole correction along z; eamp = 0 keeps the sawtooth a correction, no external field
DIPOLE_SETTINGS = {"control": {"tefield": True, "dipfield": True}, "system": {"edir": 3, "eamp": 0.0, "eopreg": 0.05}}
# manuscript: the isolated Pt atom spin-polarized with two unpaired electrons; the slabs spin-averaged
SPIN_SETTINGS = {"nspin": 2, "tot_magnetization": 2}
# manuscript: all atoms relaxed to 0.005 eV/Å = 1.9e-4 Ry/Bohr. nstep ends each relaxation inside TIME_LIMIT;
# section 7 prints the force norm (all atoms). To reach the threshold, raise nstep (and TIME_LIMIT, cluster permitting).
RELAXATION_SETTINGS = {"forc_conv_thr": 1.9e-4, "nstep": 10}
MODEL_TAG = f"{FUNCTIONAL}-{PSEUDOPOTENTIAL_TYPE} {ECUTWFC}-{ECUTRHO}Ry G fd{SMEARING_SETTINGS['degauss']}"

SCF_UNIT = "pw_scf"
RELAX_UNIT = "pw_relax"
# Names the relaxation jobs; the slab energies in Eq. 1 are read from these jobs.
RELAX_TAG = f"{MODEL_TAG} dip f{RELAXATION_SETTINGS['forc_conv_thr']} n{RELAXATION_SETTINGS['nstep']}"

5.3. Run the notebook

Execute all cells by selecting Run > Run All from the menu. The notebook first authenticates with the platform, then runs the steps listed in section 3.

5.4. Monitor progress

The notebook polls the three relaxations, then the Total Energy job of the Pt atom.

5.5. Analyze results

The output comes in three groups: the residual force each relaxation ended with, one line per material; the mean Pt-Mo, Pt-S and Pt-Pt distances in the relaxed Pt₄ cluster, over the pairs under BOND_CUTOFF; and the binding energy per Pt atom from Eq. 1. Each quantity is printed twice: the notebook's own values first, then the same lines headed "… from the manuscript" with Table 1's values.

Residual force after relaxation:
MoS2 5x5 monolayer: 0.0012 eV/angstrom
MoS2 5x5 Pt1 atop Mo: 0.2225 eV/angstrom
MoS2 5x5 Pt4 t-(Mo)4-S: 0.3845 eV/angstrom

Mean Pt distances in the relaxed Pt4 cluster:
Pt-Mo: 2.872 Å
Pt-S: 2.356 Å
Pt-Pt: 2.616 Å

Mean Pt distances from the manuscript:
Pt-Mo: 2.91 Å
Pt-S: 2.35 Å
Pt-Pt: 2.61 Å

Binding energy per Pt atom:
Pt4 t-(Mo)4-S: -3.545 eV
Pt1 atop Mo: -2.859 eV

Binding energy per Pt atom from the manuscript:
Pt4 t-(Mo)4-S: -3.43 eV
Pt1 atop Mo: -2.83 eV

6. Expected results

6.1. Comparison with published results

	E_b (eV per Pt atom)	Pt-Mo (Å)	Pt-S (Å)	Pt-Pt (Å)
Pt₄, t-(Mo)₄-S (Fig. 4b), Saidi Table 1	−3.43	2.91	2.35	2.61
Pt₄, t-(Mo)₄-S, this tutorial	−3.545	2.872	2.356	2.616
Pt₁, on top of Mo (Fig. 1a), Saidi Table 1	−2.83	2.76	2.29	—
Pt₁, on top of Mo, this tutorial	−2.859	not computed	not computed	—

The printed mean Pt-Pt distance, 2.616 Å, is the mean of the three apex-base pairs; the three base-base pairs are at 3.00 Å, at Table 1's 3 Å cutoff (BOND_CUTOFF), and are not counted; Table 1 gives 2.61 Å.

The relaxation jobs return these structures, named <name> relaxed <RELAX_TAG> by section 7.2 of the notebook:

7. Customization options

7.1. Adjust the isolated-atom box and the relaxation threshold

PT_ATOM_BOX in cell 1.2 is the edge of the cubic box around the isolated Pt atom. A new box is a new material, so the Total Energy job of the Pt atom runs again. RELAXATION_SETTINGS in cell 1.4 holds the manuscript's force threshold, 0.005 eV/Å, which stays the stopping criterion, and nstep, the number of ionic steps after which each relaxation ends inside TIME_LIMIT. In order to reach the threshold, raise nstep together with TIME_LIMIT, as far as the cluster allows. Both values are part of the relaxation jobs' names, so a change relaxes the three slabs again.

7.2. Adjust computational resources

QUEUE_NAME, PPN and TIME_LIMIT in cell 1.3 set the queue, the cores and the time limit of every job. The default, CLUSTER_NAME = None, uses the account's first listed cluster; setting a specific name picks that cluster instead, and a name that is not available makes the notebook stop and list the ones that are.

7.3. Use the manuscript's settings

Apart from the code, the pseudopotentials, the cutoff and the lattice constant, section 4 follows the manuscript wherever it states a setting; the Pt atom box, the fixed cell and the nstep bound are this tutorial's. In order to match the manuscript's 3.18 Å instead of Standata's 3.196 Å, apply create_strain to the substrate in the structure notebook before the slab is built, as in Graphene on h-BN. The manuscript's PAW potentials are VASP's and cannot be matched. Quantum ESPRESSO's are selected with PSEUDOPOTENTIAL_TYPE = "paw"; neither they nor a cutoff for them is tested here, and the manuscript's 350 eV does not transfer. The structure notebook's 3x3 materials are used by changing the three names in section 1.2.

8. Troubleshooting

8.1. Material not found

If a material of section 2 is not found in the uploads folder or the account's materials collection, run the structure tutorial first; the names must match exactly.

8.2. No cluster available

If section 5.1 of the notebook prints an empty list of clusters, there is nothing to submit to, and section 5.2 stops.

8.3. Residual force above the threshold

A relaxation that stops on nstep ends with forces above the manuscript's 0.005 eV/Å, and Eq. 1 then uses the energy of its last ionic step. In order to relax further, raise nstep as in section 7.1.

8.4. Binding energy far from the published value

Check the provenance printed in section 3.1 of the notebook first: the three slabs read Mo25S50, Mo25Pt1S50 and Mo25Pt4S50, each in a 15.98 x 15.98 x 26.27 Å cell, and the Pt atom Pt1 in a 12.00 x 12.00 x 12.00 Å cell. Then open the Total Energy job of the Pt atom, select the Files tab, and check that pw_scf.in sets nspin = 2 and tot_magnetization = 2.

9. Interactive JupyterLite notebook

The following JupyterLite notebook calculates the binding energies of Pt on MoS₂. Select Run > Run All Cells.

⛶ Full Screen

10. References

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1. W. A. Saidi. Density functional theory study of nucleation and growth of pt nanoparticles on mos2(001) surface. Crystal Growth & Design, 15(2):642–652, 2015. URL: https://doi.org/10.1021/cg5013395. ↩