Vacancy Point Defects in Hexagonal Boron Nitride (Formation Energy)¶

1. Introduction¶

This tutorial calculates the formation energy of a neutral boron vacancy in h-BN, reproducing results from the following manuscript:

Manuscript

Fabian Bertoldo, Sajid Ali, Simone Manti & Kristian S. Thygesen, "Quantum point defects in 2D materials - the QPOD database", npj Computational Materials, 2022. DOI:10.1038/s41524-022-00730-w. ¹

This tutorial builds upon the Vacancy Point Defect in h-BN tutorial, where the defective structure is created. Here, the formation energy is calculated using Quantum ESPRESSO and compared with QPOD's value for the same defect.

The figure below shows the boron vacancy in h-BN from the manuscript (Figure 6):

Vacancy in h-BN

1.1. What is being reproduced¶

QPOD's entry 1BN-1.2d.v_B.0.1 gives the neutral vacancy formation energy at standard-state chemical potentials:

	E_f (eV)
QPOD, standard states	10.18
QPOD, B-poor	8.89

Only the neutral (q = 0) defect is compared; QPOD's charged states need a finite-size correction this workflow does not apply.

2. Prerequisites¶

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

Complete the Vacancy Point Defect in h-BN tutorial, using the defect_point_vacancy_boron_nitride.ipynb notebook embedded in its section 6, to create and save h-BN supercell and B-vacancy h-BN, OR
Have both materials saved in the uploads folder or in the account's materials collection

3. Workflow overview¶

The defect formation energy calculation consists of the following steps:

Set up the environment and parameters: Configure material names, the DFT model, and compute resources
Authenticate and initialize API client: Connect to the platform
Load materials: Import the pristine and defective structures, and resolve the elemental reference materials
Submit prerequisite jobs: Compute (or reuse) the pristine, boron and nitrogen Total Energy jobs
Relax the defective cell (optional): Only if RELAX is set, reusing an existing relaxed structure if one is found
Create and submit the defect job: Assemble and run the formation energy workflow
Monitor job status: Wait for completion
Retrieve and compare results: Print the formation energy and the comparison with QPOD

4. Calculation parameters¶

	this tutorial	QPOD
Code	Quantum ESPRESSO	GPAW
Functional	PBE	PBE
Pseudopotentials	ultrasoft (GBRV)	PAW (GPAW setups)
Cutoff	40 / 200 Ry	800 eV
k-points	density 6 Å⁻¹ (3×5×1 for the defect cell)	6 Å⁻¹ (relaxation), 12 Å⁻¹ (ground state)
Spin	fixed total magnetization, 1 μB (doublet)	1.018 μB (doublet)
Cell	48 → 47 atoms, 8.69 Å defect spacing, 20 Å vacuum	84 → 83 atoms, 15.06 Å defect spacing, 15 Å vacuum

By default (RELAX = False), the calculation uses the structure as given. Setting RELAX = True relaxes the defective cell first, to 0.01 eV/Å — QPOD's own threshold, and the one QPOD applies to every structure; only the defective cell is relaxed here. If the account already holds a relaxed version of this structure, the notebook reuses it whatever settings produced it, and prints its name and id; a settings change therefore does not trigger a fresh relaxation. To compute one with different settings, run the notebook under a different account, or relax the structure separately and point DEFECTIVE_NAME at that structure with RELAX = False.

5. Step-by-step instructions¶

5.1. Open the notebook¶

Navigate to the API examples repository and open the defect formation energy notebook:

other/materials_designer/specific_examples/defect_point_vacancy_boron_nitride_SIMULATION.ipynb

5.2. Configure parameters¶

The parameters cells set the material names, the DFT model, and the compute resources:

# Material names — saved by defect_point_vacancy_boron_nitride.ipynb
PRISTINE_NAME = "h-BN supercell"
DEFECTIVE_NAME = "B-vacancy h-BN"

# False: use the structure as given, fast. True: use the relaxed structure, running the
# relaxation once if it does not exist yet.
RELAX = False

CLUSTER_NAME = None  # or a specific cluster name
QUEUE_NAME = QueueName.OF
PPN = 40
TIME_LIMIT = "12:00:00"

# DFT model
FUNCTIONAL = "pbe"
PSEUDOPOTENTIAL_TYPE = "us"
ECUTWFC = 40   # Ry
ECUTRHO = 200  # Ry
KPOINT_DENSITY = 6

5.3. Run the notebook¶

Execute all cells by selecting Run > Run All from the menu.

The notebook will:

Authenticate with the platform and initialize the API client
Load the two materials from the uploads folder or the account's materials collection, and resolve the elemental reference materials
Submit the prerequisite Total Energy jobs, reusing any that already match
Relax the defective cell first, if RELAX is set and no relaxed structure exists yet
Create, submit and monitor the defect formation energy job
Print the result and the comparison with QPOD

5.4. Monitor progress¶

The notebook includes automatic job monitoring with status updates. The default run (RELAX = False) completes in about 15 minutes the first time, or about 6 minutes once the reference jobs are reused. With RELAX = True, relaxing the defective cell takes about 52 minutes; once that relaxed structure exists, later runs find it and skip the relaxation.

5.5. Analyze results¶

Once the job completes, the formation energy is displayed next to QPOD's value, and the last cell prints the comparison:

1	`Reproduces Bertoldo et al. (2022): no (unrelaxed SCF)`

or, with RELAX = True:

1	`Reproduces Bertoldo et al. (2022): yes (relaxed defect)`

6. Expected results¶

The defect formation energy job produces one number, printed next to QPOD's target and QPOD's B-poor value for context.

6.1. Comparison with published results¶

configuration	E_f (eV)	vs QPOD 10.18 eV	verdict
unrelaxed SCF	10.46	+0.28	`no (unrelaxed SCF)`
relaxed defect	10.12	−0.06	`yes (relaxed defect)`

7. Customization options¶

7.1. Relax the defective cell¶

Set RELAX = True in the parameters cell to use the relaxed defective cell — closer to the paper. The first run relaxes it and saves the result in the account's materials collection under B-vacancy h-BN relaxed, reused by later runs of this notebook (and loadable by name elsewhere):

RELAX = True

To use a structure already relaxed elsewhere, set DEFECTIVE_NAME = "B-vacancy h-BN relaxed" (the name the relaxation saves) with RELAX = False; the notebook finds it in the account's materials collection, though the verdict line still reads (unrelaxed SCF) — the provenance lines above the results name the structure that was actually used.

7.2. Adjust computational resources¶

Modify the compute parameters in the parameters cell. 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:

CLUSTER_NAME = None  # or a specific cluster name
QUEUE_NAME = QueueName.OF
PPN = 40
TIME_LIMIT = "12:00:00"

7.3. Change the supercell or the defect¶

The supercell size and the vacancy site are set in the structure notebook; this notebook loads whatever it saves, by name.

8. Troubleshooting¶

8.1. Material not found¶

If a material is not found in the uploads folder:

Run the Vacancy Point Defect in h-BN tutorial first
Ensure the materials are saved with the exact names (h-BN supercell, B-vacancy h-BN)
Check that the material files are in the correct uploads folder

8.2. Missing elemental reference materials¶

If boron or nitrogen has no platform material tagged elemental, the notebook stops before submitting anything — seed one for the missing element first.

8.3. Job errors or time limit¶

The 12-hour time limit is the notebook's default ceiling; the measured relaxation took about 52 minutes on 40 cores. Increase TIME_LIMIT if a job runs out of time before finishing.

9. Interactive JupyterLite notebook¶

The following JupyterLite notebook demonstrates the workflow for calculating the formation energy of a boron vacancy in h-BN. Select Run > Run All Cells.

10. References¶

Fabian Bertoldo, Sajid Ali, Simone Manti, and Kristian S. Thygesen. Quantum point defects in 2d materials - the qpod database. npj Computational Materials, 2022. URL: https://doi.org/10.1038/s41524-022-00730-w. ↩