Nudged Elastic Band¶
In this tutorial, we will determine the activation energies of Li diffusion along the [010] and [001] directions (referred to as paths b and c respectively) in lithium iron phosphate (LiFePO_4), a cathode material for lithium ion batteries.
DFT references energies are:
Barrier heights:
path b = 0.27 eV
path c = 2.5 eV
(see table 1 in https://doi.org/10.1039/C5TA05062F)
You can toggle the following to investigate different models:
[1]:
model_params = {"arch": "mace_mp", "model": "medium-0b3"}
# model_params = {"arch": "mace_mp", "model": "medium-mpa-0"}
# model_params = {"arch": "mace_mp", "model": "medium-omat-0"}
# model_params = {"arch": "chgnet"}
# model_params = {"arch": "sevennet"}
Set up environment (optional)¶
These steps are required for Google Colab, but may work on other systems too:
[2]:
# import locale
# locale.getpreferredencoding = lambda: "UTF-8"
# ! pip uninstall torch torchaudio torchvision transformers numpy -y
# ! uv pip install janus-core[all] data-tutorials torch==2.5.1 --system
# get_ipython().kernel.do_shutdown(restart=True)
[3]:
from weas_widget import WeasWidget
from ase.io import read
from data_tutorials.data import get_data
from janus_core.calculations.geom_opt import GeomOpt
from janus_core.calculations.neb import NEB
Use data_tutorials to get the data required for this tutorial:
[4]:
get_data(
# url="https://raw.githubusercontent.com/stfc/janus-core/main/tests/data/",
url="https://raw.githubusercontent.com/stfc/janus-tutorials/main/neb/data/",
filename="LiFePO4_supercell.cif",
folder="data",
)
try to download LiFePO4_supercell.cif from https://raw.githubusercontent.com/stfc/janus-tutorials/main/neb/data/ and save it in data/LiFePO4_supercell.cif
saved in data/LiFePO4_supercell.cif
Preparing end structures¶
The initial structure can be downloaded from the Materials Project (mp-19017):
[5]:
LFPO = read("data/LiFePO4_supercell.cif")
v=WeasWidget()
v.from_ase(LFPO)
v.avr.model_style = 1
v.avr.show_hydrogen_bonds = True
v
[5]:
First, we will relax the supercell:
[6]:
GeomOpt(struct=LFPO, **model_params).run()
v1=WeasWidget()
v1.from_ase(LFPO)
v1.avr.model_style = 1
v1.avr.show_hydrogen_bonds = True
v1
/home/runner/work/janus-core/janus-core/.venv/lib/python3.12/site-packages/e3nn/o3/_wigner.py:10: UserWarning: Environment variable TORCH_FORCE_NO_WEIGHTS_ONLY_LOAD detected, since the`weights_only` argument was not explicitly passed to `torch.load`, forcing weights_only=False.
_Jd, _W3j_flat, _W3j_indices = torch.load(os.path.join(os.path.dirname(__file__), 'constants.pt'))
cuequivariance or cuequivariance_torch is not available. Cuequivariance acceleration will be disabled.
Downloading MACE model from 'https://github.com/ACEsuit/mace-mp/releases/download/mace_mp_0b3/mace-mp-0b3-medium.model'
Cached MACE model to /home/runner/.cache/mace/macemp0b3mediummodel
Using Materials Project MACE for MACECalculator with /home/runner/.cache/mace/macemp0b3mediummodel
Using float64 for MACECalculator, which is slower but more accurate. Recommended for geometry optimization.
Using head default out of ['default']
/home/runner/work/janus-core/janus-core/.venv/lib/python3.12/site-packages/mace/calculators/mace.py:143: UserWarning: Environment variable TORCH_FORCE_NO_WEIGHTS_ONLY_LOAD detected, since the`weights_only` argument was not explicitly passed to `torch.load`, forcing weights_only=False.
torch.load(f=model_path, map_location=device)
Step Time Energy fmax
LBFGS: 0 17:44:51 -762.842666 0.654854
LBFGS: 1 17:44:53 -763.038742 0.437508
LBFGS: 2 17:44:55 -763.090096 0.392867
LBFGS: 3 17:44:57 -763.119488 0.374220
LBFGS: 4 17:44:59 -763.172830 0.346620
LBFGS: 5 17:45:01 -763.213488 0.334927
LBFGS: 6 17:45:03 -763.256842 0.327520
LBFGS: 7 17:45:05 -763.297792 0.328964
LBFGS: 8 17:45:07 -763.342419 0.332009
LBFGS: 9 17:45:09 -763.385108 0.328513
LBFGS: 10 17:45:11 -763.427187 0.308144
LBFGS: 11 17:45:13 -763.474267 0.274918
LBFGS: 12 17:45:14 -763.528185 0.234548
LBFGS: 13 17:45:16 -763.579927 0.246328
LBFGS: 14 17:45:18 -763.627605 0.245408
LBFGS: 15 17:45:20 -763.684752 0.231582
LBFGS: 16 17:45:22 -763.766360 0.283626
LBFGS: 17 17:45:24 -763.855346 0.296599
LBFGS: 18 17:45:26 -763.931149 0.188692
LBFGS: 19 17:45:28 -763.965778 0.154808
LBFGS: 20 17:45:29 -763.996599 0.213159
LBFGS: 21 17:45:31 -764.039520 0.255107
LBFGS: 22 17:45:33 -764.108589 0.255570
LBFGS: 23 17:45:35 -764.175608 0.200210
LBFGS: 24 17:45:37 -764.208816 0.096659
[6]:
Next, we will create the start and end structures:
[7]:
# NEB path along b and c directions have the same starting image.
# For start bc remove site 5
LFPO_start_bc = LFPO.copy()
del LFPO_start_bc[5]
# For end b remove site 11
LFPO_end_b = LFPO.copy()
del LFPO_end_b[11]
# For end c remove site 4
LFPO_end_c = LFPO.copy()
del LFPO_end_c[4]
Path b¶
We can now calculate the barrier height along path b.
This also includes running geometry optimization on the end points of this path.
[8]:
n_images = 7
interpolator="pymatgen" # ASE interpolation performs poorly in this case
neb_b = NEB(
init_struct=LFPO_start_bc,
final_struct=LFPO_end_b,
n_images=n_images,
interpolator=interpolator,
minimize=True,
fmax=0.1,
**model_params,
)
Using Materials Project MACE for MACECalculator with /home/runner/.cache/mace/macemp0b3mediummodel
Using float64 for MACECalculator, which is slower but more accurate. Recommended for geometry optimization.
Using head default out of ['default']
/home/runner/work/janus-core/janus-core/.venv/lib/python3.12/site-packages/mace/calculators/mace.py:143: UserWarning: Environment variable TORCH_FORCE_NO_WEIGHTS_ONLY_LOAD detected, since the`weights_only` argument was not explicitly passed to `torch.load`, forcing weights_only=False.
torch.load(f=model_path, map_location=device)
[9]:
results = neb_b.run()
Step Time Energy fmax
LBFGS: 0 17:45:39 -758.975432 1.930990
LBFGS: 1 17:45:41 -759.140669 0.711957
LBFGS: 2 17:45:43 -759.209571 0.514600
LBFGS: 3 17:45:44 -759.298948 0.404890
LBFGS: 4 17:45:46 -759.316304 0.265548
LBFGS: 5 17:45:48 -759.336518 0.252446
LBFGS: 6 17:45:49 -759.351338 0.330410
LBFGS: 7 17:45:51 -759.368546 0.309163
LBFGS: 8 17:45:53 -759.378014 0.229741
LBFGS: 9 17:45:54 -759.386280 0.221552
LBFGS: 10 17:45:56 -759.395290 0.278156
LBFGS: 11 17:45:58 -759.404981 0.291370
LBFGS: 12 17:45:59 -759.411852 0.192426
LBFGS: 13 17:46:01 -759.415355 0.075502
Step Time Energy fmax
LBFGS: 0 17:46:03 -758.975436 1.930961
LBFGS: 1 17:46:05 -759.140671 0.711930
LBFGS: 2 17:46:06 -759.209572 0.514582
LBFGS: 3 17:46:08 -759.298949 0.404887
LBFGS: 4 17:46:10 -759.316305 0.265544
LBFGS: 5 17:46:11 -759.336519 0.252446
LBFGS: 6 17:46:13 -759.351338 0.330395
LBFGS: 7 17:46:15 -759.368546 0.309158
LBFGS: 8 17:46:16 -759.378015 0.229745
LBFGS: 9 17:46:18 -759.386281 0.221556
LBFGS: 10 17:46:20 -759.395291 0.278147
LBFGS: 11 17:46:22 -759.404982 0.291359
LBFGS: 12 17:46:23 -759.411852 0.192423
LBFGS: 13 17:46:25 -759.415355 0.075502
Step Time fmax
NEBOptimizer[ode]: 0 17:47:01 1.5090
NEBOptimizer[ode]: 1 17:47:12 1.1032
NEBOptimizer[ode]: 2 17:47:24 0.9983
NEBOptimizer[ode]: 3 17:47:36 0.8704
NEBOptimizer[ode]: 4 17:47:48 0.8013
NEBOptimizer[ode]: 5 17:48:00 0.7712
NEBOptimizer[ode]: 6 17:48:12 0.7441
NEBOptimizer[ode]: 7 17:48:24 0.6738
NEBOptimizer[ode]: 8 17:48:36 0.4346
NEBOptimizer[ode]: 9 17:49:00 0.4299
NEBOptimizer[ode]: 10 17:49:12 0.4226
NEBOptimizer[ode]: 11 17:49:24 0.3946
NEBOptimizer[ode]: 12 17:49:36 0.2843
NEBOptimizer[ode]: 13 17:50:00 0.2726
NEBOptimizer[ode]: 14 17:50:11 0.2652
NEBOptimizer[ode]: 15 17:50:23 0.2612
NEBOptimizer[ode]: 16 17:50:35 0.2552
NEBOptimizer[ode]: 17 17:50:47 0.2323
NEBOptimizer[ode]: 18 17:51:11 0.2219
NEBOptimizer[ode]: 19 17:51:23 0.2141
NEBOptimizer[ode]: 20 17:51:35 0.2087
NEBOptimizer[ode]: 21 17:51:47 0.2055
NEBOptimizer[ode]: 22 17:51:58 0.2005
NEBOptimizer[ode]: 23 17:52:10 0.1809
NEBOptimizer[ode]: 24 17:52:34 0.1729
NEBOptimizer[ode]: 25 17:52:46 0.1664
NEBOptimizer[ode]: 26 17:52:58 0.1624
NEBOptimizer[ode]: 27 17:53:10 0.1598
NEBOptimizer[ode]: 28 17:53:22 0.1559
NEBOptimizer[ode]: 29 17:53:34 0.1409
NEBOptimizer[ode]: 30 17:53:46 0.2612
NEBOptimizer[ode]: 31 17:54:10 0.0826
The results include the barrier (without any interpolation between highest images) and maximum force at the point in the simulation
[10]:
print(results)
{'barrier': 0.28471736968049277, 'delta_E': -1.6499620869581122e-07, 'max_force': 0.09009922955812238}
We can also plot the band:
[11]:
fig = neb_b.nebtools.plot_band()
v1=WeasWidget()
v1.from_ase(neb_b.nebtools.images)
v1.avr.model_style = 1
v1.avr.show_hydrogen_bonds = True
v1
[11]:
Path c¶
We can calculate the barrier height along path c similarly
[12]:
n_images = 7
interpolator="pymatgen"
neb_c = NEB(
init_struct=LFPO_start_bc,
final_struct=LFPO_end_c,
n_images=n_images,
interpolator=interpolator,
minimize=True,
fmax=0.1,
**model_params,
)
Using Materials Project MACE for MACECalculator with /home/runner/.cache/mace/macemp0b3mediummodel
Using float64 for MACECalculator, which is slower but more accurate. Recommended for geometry optimization.
Using head default out of ['default']
/home/runner/work/janus-core/janus-core/.venv/lib/python3.12/site-packages/mace/calculators/mace.py:143: UserWarning: Environment variable TORCH_FORCE_NO_WEIGHTS_ONLY_LOAD detected, since the`weights_only` argument was not explicitly passed to `torch.load`, forcing weights_only=False.
torch.load(f=model_path, map_location=device)
[13]:
results = neb_c.run()
Step Time Energy fmax
LBFGS: 0 17:54:15 -759.415355 0.075502
Step Time Energy fmax
LBFGS: 0 17:54:17 -758.975431 1.930990
LBFGS: 1 17:54:19 -759.140669 0.711958
LBFGS: 2 17:54:21 -759.209571 0.514601
LBFGS: 3 17:54:22 -759.298948 0.404890
LBFGS: 4 17:54:24 -759.316304 0.265548
LBFGS: 5 17:54:26 -759.336518 0.252446
LBFGS: 6 17:54:27 -759.351338 0.330410
LBFGS: 7 17:54:29 -759.368546 0.309163
LBFGS: 8 17:54:31 -759.378014 0.229741
LBFGS: 9 17:54:32 -759.386280 0.221553
LBFGS: 10 17:54:34 -759.395290 0.278156
LBFGS: 11 17:54:36 -759.404981 0.291370
LBFGS: 12 17:54:38 -759.411852 0.192426
LBFGS: 13 17:54:39 -759.415355 0.075502
Step Time fmax
NEBOptimizer[ode]: 0 17:55:15 2.3204
NEBOptimizer[ode]: 1 17:55:26 1.6499
NEBOptimizer[ode]: 2 17:55:38 0.9977
NEBOptimizer[ode]: 3 17:55:50 0.6537
NEBOptimizer[ode]: 4 17:56:14 0.4186
NEBOptimizer[ode]: 5 17:56:26 0.3969
NEBOptimizer[ode]: 6 17:56:38 0.3176
NEBOptimizer[ode]: 7 17:57:01 0.2998
NEBOptimizer[ode]: 8 17:57:25 0.2690
NEBOptimizer[ode]: 9 17:57:37 0.2608
NEBOptimizer[ode]: 10 17:57:49 0.2293
NEBOptimizer[ode]: 11 17:58:12 0.2186
NEBOptimizer[ode]: 12 17:58:24 0.2622
NEBOptimizer[ode]: 13 17:58:36 0.2009
NEBOptimizer[ode]: 14 17:58:47 0.1946
NEBOptimizer[ode]: 15 17:58:59 0.1883
NEBOptimizer[ode]: 16 17:59:11 0.1653
NEBOptimizer[ode]: 17 17:59:35 0.1600
NEBOptimizer[ode]: 18 17:59:46 0.1538
NEBOptimizer[ode]: 19 17:59:58 0.1475
NEBOptimizer[ode]: 20 18:00:10 0.1379
NEBOptimizer[ode]: 21 18:00:22 0.1346
NEBOptimizer[ode]: 22 18:00:34 0.1288
NEBOptimizer[ode]: 23 18:00:46 0.1263
NEBOptimizer[ode]: 24 18:00:58 0.1169
NEBOptimizer[ode]: 25 18:01:10 0.1806
NEBOptimizer[ode]: 26 18:01:33 0.0821
[14]:
print(results)
{'barrier': 1.7875754406807047, 'delta_E': 4.249613994034007e-09, 'max_force': 0.09762768246406749}
[15]:
fig = neb_c.nebtools.plot_band()
v2=WeasWidget()
v2.from_ase(neb_c.nebtools.images)
v2.avr.model_style = 1
v2.avr.show_hydrogen_bonds = True
v2
[15]:
