Interstitial Point Defects in SnO (Formation Energy and Density of States)

1. Introduction

This tutorial calculates the formation energy of the neutral V_Sn-O_i defect pair in tin monoxide (SnO), and compares it with the value reported in the following manuscript:

Manuscript

A. Togo, F. Oba, and I. Tanaka, "First-principles calculations of native defects in tin monoxide", Physical Review B 74, 195128 (2006). DOI:10.1103/PhysRevB.74.195128. ¹

This tutorial builds upon the Oxygen Interstitial Defect in SnO tutorial, where the defective structure is created. Here, the formation energy is calculated using Quantum ESPRESSO and compared with Togo et al.'s value for the same defect.

1.1. What is being compared

Table II of the manuscript gives the neutral formation energies with the Fermi level at the valence band maximum:

	E_f (eV)
V_Sn-O_i pair, models (a), (b)	2.3
V_Sn-O_i pair, model (c)	3.9
V_Sn and O_i, independent	2.3

Model (a) is the pair built by the structure tutorial, and the one compared here. Table II does not name the chemical-potential limit it uses, so the formation energy is computed at both of them. Only the neutral (q = 0) defect is compared; its 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:

1. Complete the Oxygen Interstitial Defect in SnO tutorial, using the defect_point_interstitial_tin_oxide.ipynb notebook embedded in its section 6, to create and save SnO 2x2x2 supercell and SnO 2x2x2 V_Sn-O_i pair (Togo Fig 4a), OR
2. Have both materials saved in the uploads folder or in the account's materials collection

The chemical-potential references, α-Sn for the Sn-rich limit and SnO₂ for the O-rich one, are loaded from Standata.

3. Workflow overview

The defect formation energy calculation consists of the following steps:

1. Set up the environment and parameters: Configure material names, the DFT model, and compute resources
2. Authenticate and initialize API client: Connect to the platform
3. Load materials: Import the pristine supercell and the pair, load α-Sn and SnO₂ from Standata, print the provenance of all four and the V_Sn-O_i distance
4. Configure the model and k-grid: One DFT model and a per-material k-grid for every job below
5. Submit prerequisite jobs: Compute (or reuse) the Total Energy jobs of the pristine supercell, α-Sn and SnO₂
6. Relax the pair cell (optional): Only if RELAX is set, reusing an existing relaxed structure if one is found
7. Create and submit the Density of States job: On the pair cell, producing its total energy and its density of states
8. Retrieve and compare results: Print the chemical potentials, the formation energy at each limit, the density of states and the comparison with Togo et al.

4. Calculation parameters

	this tutorial	Togo et al.
Code	Quantum ESPRESSO	VASP
Functional	PBE	PW91
Pseudopotentials	ultrasoft (GBRV)	PAW, Sn 5s5p in valence
Cutoff	40 / 200 Ry	500 eV
k-points	density 4 Å⁻¹ (4×4×3 for the 32-atom cells)	Γ-point only
Cell	2×2×2, 32 atoms (Sn16O16 → Sn15O17)	4×4×3, 192 atoms
Lattice	a 3.814 Å, c 4.887 Å (Standata SnO)	a 3.855 Å, c 4.983 Å
Chemical potentials	Sn-rich and O-rich limits, from Standata α-Sn and SnO₂ (rutile, mp-856)	Sn-rich and O-rich limits
Relaxation	none by default, 0.05 eV/Å with RELAX = True	all atoms to 0.05 eV/Å

The settings here run in minutes; the manuscript's number needs its settings: PAW/PW91, 500 eV, a 4×4×3 cell, Γ-point. By default (RELAX = False) the calculation uses the structures as given. RELAX = True relaxes the pair cell first to 0.05 eV/Å, Togo et al.'s own threshold, at fixed cell: the atoms move, the Standata lattice is held.

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_interstitial_tin_oxide_SIMULATION.ipynb

5.2. Configure parameters

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

# Names saved by defect_point_interstitial_tin_oxide.ipynb; 2x2x2 (32 atoms) runs in minutes, Togo's cell is 4x4x3 (192).
PRISTINE_NAME = "SnO 2x2x2 supercell"
DEFECTIVE_NAME = "SnO 2x2x2 V_Sn-O_i pair (Togo Fig 4a)"
SN_REFERENCE_NAME = "Sn, Tin, FCC (Fd-3m) 3D (Bulk), mp-117"
SNO2_REFERENCE_NAME = "SnO2, Tin Dioxide, TET (P4_2/mnm) 3D (Bulk), mp-856"

# NOTE: set to True for results close to the manuscript (relaxes the pair once, ~2 h).
RELAX = False

CLUSTER_NAME = None
QUEUE_NAME = QueueName.OR
PPN = 16  # OR allows 16 cores per job
TIME_LIMIT = "12:00:00"  # covers the optional relaxation

# DFT model
FUNCTIONAL = "pbe"
PSEUDOPOTENTIAL_TYPE = "us"
ECUTWFC = 40   # Ry
ECUTRHO = 200  # Ry
KPOINT_DENSITY = 4
RELAXATION_SETTINGS = {"forc_conv_thr": 1.9e-3, "nstep": 100}  # 0.05 eV/Å, Togo's convergence target

5.3. Run the notebook

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

The notebook will:

1. Authenticate with the platform and initialize the API client
2. Load the pristine supercell and the pair from the uploads folder or the account's materials collection, load α-Sn and SnO₂ from Standata, and print the V_Sn-O_i distance
3. Submit the prerequisite Total Energy jobs, reusing any that already match
4. Relax the pair cell first, if RELAX is set and no relaxed structure exists yet
5. Create, submit and monitor the Density of States job on the pair cell
6. Print the chemical potentials, the formation energy at each limit and the density of states

5.4. Monitor progress

The notebook includes automatic job monitoring with status updates, polling every 60 seconds (POLL_INTERVAL). Jobs that already exist for the same material and workflow name are reused instead of resubmitted, and the notebook prints ♻️ for each one. Measured on cluster-001, 40 cores: the pristine supercell about 3.5 minutes of active time (about 11 minutes with the queue), α-Sn 13 seconds, SnO₂ about 1 minute, the Density of States job about 5 minutes (about 7 with the queue), the relaxation 48 minutes; on OR at 16 cores expect roughly 2.5× longer (the relaxation ≈ 2 h).

5.5. Analyze results

The last cell prints the regime and, per limit, E_f beside Togo et al.'s value:

Regime: relaxed defect
E_f (Togo et al., 2006):      2.300 eV
E_f (this notebook, Sn-rich): 3.081 eV
E_f (this notebook, O-rich):  2.649 eV

6. Expected results

The chemical potentials come out of the three prerequisite jobs: Sn-rich μ_Sn = −2166.540, μ_O = −439.994 eV/atom; O-rich μ_Sn = −2166.756, μ_O = −439.779 eV/atom — 0.216 eV apart in μ_Sn, against the manuscript's 0.23 eV.

6.1. Comparison with published results

configuration	limit	E_f (eV)	difference from Togo et al. 2.3 eV (eV)	difference (%)
unrelaxed SCF	Sn-rich	7.381	+5.081	+220.9
unrelaxed SCF	O-rich	6.949	+4.649	+202.1
relaxed defect	Sn-rich	3.081	+0.781	+34.0
relaxed defect	O-rich	2.649	+0.349	+15.2

The relaxed defect at the O-rich limit, 2.649 eV, is the closest to Togo et al.'s 2.3 eV and sits 15.2 % above it; the remaining 0.349 eV is the cell size (32 atoms against 192) and the pseudopotentials (GBRV ultrasoft PBE against PAW PW91). The relaxation converged in 17 BFGS steps to a maximum force of 0.036 eV/Å, lowering the energy by 4.30 eV, the oxygen interstitial moving 0.74 Å to the apex of a tin pyramid (Sn-O 1.93 Å).

The pair cell's density of states is plotted, and its band gaps printed, in section 9.2 of the notebook: 0.000 eV in both configurations, the cell being metallic in PBE. Togo et al. report no defect transition level of O_i inside the calculated band gap; this comparison is qualitative.

7. Customization options

7.1. Relax the pair cell

Set RELAX = True in the parameters cell to use the relaxed pair cell — closer to the paper. When this notebook runs the relaxation, it saves the result in the account's materials collection under SnO 2x2x2 V_Sn-O_i pair (Togo Fig 4a) relaxed; a relaxed structure found from an earlier job keeps its platform name. Later runs reuse that relaxed structure, found by content hash, or a relaxation job still running under the same name:

RELAX = True

To use a structure already relaxed elsewhere, set DEFECTIVE_NAME to its name with RELAX = False; the regime line then 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. QueueName.OR gives one node, charged by core-seconds with no flat fee; OR allows 16 cores per job:

CLUSTER_NAME = None
QUEUE_NAME = QueueName.OR
PPN = 16
TIME_LIMIT = "12:00:00"

7.3. Change the supercell or the defect

The supercell size and the interstitial site are set in the structure notebook; this notebook loads whatever it saves, by name. Togo et al.'s own 4×4×3, 192-atom cell is reached by changing the supercell there.

8. Troubleshooting

8.1. Material not found

If a material is not found in the uploads folder, run the Oxygen Interstitial Defect in SnO tutorial first, and check that its uploads folder holds both files, saved under the exact names SnO 2x2x2 supercell and SnO 2x2x2 V_Sn-O_i pair (Togo Fig 4a). If SnO2, Tin Dioxide, TET (P4_2/mnm) 3D (Bulk), mp-856 is not found, update mat3ra-standata to a release that includes the entry.

8.2. Jobs end in error and the results cell raises IndexError

The default CLUSTER_NAME = None takes the account's first listed cluster. If the prerequisite jobs end in error and the results cell raises IndexError: list index out of range, open one of them in the platform UI: if pw_scf.out ends in MPI_Init errors, that cluster cannot start it. Set CLUSTER_NAME to another cluster — cluster-001 ran every job here — and re-run; finished jobs are reused.

8.3. No formation energy on the first RELAX = True run

With RELAX = True, the first run adds a relaxation job before the Density of States job, and waits for both. If the session ends before they finish, re-run the notebook later: it finds the relaxed structure and any finished jobs; the relaxation is not repeated, and a Density of States job that does not yet exist is created then.

8.4. Formation energy far from the published value

Check the V_Sn-O_i distance printed in section 3.2 of the notebook against Fig. 4(a) of the manuscript first: the oxygen interstitial sits directly below the tin vacancy, in the interlayer gap.

9. Interactive JupyterLite notebook

The following JupyterLite notebook demonstrates the workflow for calculating the formation energy and the density of states of the V_Sn-O_i pair in SnO. Select Run > Run All Cells.

⛶ Full Screen

10. References

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1. A. Togo, F. Oba, and I. Tanaka. First-principles calculations of native defects in tin monoxide. Physical Review B, 74(19):195128, 2006. URL: https://doi.org/10.1103/PhysRevB.74.195128. ↩