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 16:53:50 -762.842666 0.654854
LBFGS: 1 16:53:52 -763.038742 0.437508
LBFGS: 2 16:53:54 -763.090096 0.392867
LBFGS: 3 16:53:56 -763.119488 0.374220
LBFGS: 4 16:53:58 -763.172830 0.346620
LBFGS: 5 16:53:59 -763.213488 0.334927
LBFGS: 6 16:54:01 -763.256842 0.327520
LBFGS: 7 16:54:03 -763.297792 0.328964
LBFGS: 8 16:54:05 -763.342419 0.332009
LBFGS: 9 16:54:07 -763.385108 0.328513
LBFGS: 10 16:54:09 -763.427187 0.308144
LBFGS: 11 16:54:11 -763.474267 0.274918
LBFGS: 12 16:54:12 -763.528185 0.234548
LBFGS: 13 16:54:14 -763.579927 0.246328
LBFGS: 14 16:54:16 -763.627605 0.245408
LBFGS: 15 16:54:18 -763.684752 0.231582
LBFGS: 16 16:54:20 -763.766360 0.283626
LBFGS: 17 16:54:22 -763.855346 0.296599
LBFGS: 18 16:54:23 -763.931149 0.188692
LBFGS: 19 16:54:25 -763.965778 0.154808
LBFGS: 20 16:54:27 -763.996599 0.213159
LBFGS: 21 16:54:29 -764.039520 0.255107
LBFGS: 22 16:54:31 -764.108589 0.255570
LBFGS: 23 16:54:33 -764.175608 0.200210
LBFGS: 24 16:54:34 -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 16:54:36 -758.975432 1.930990
LBFGS: 1 16:54:38 -759.140669 0.711957
LBFGS: 2 16:54:40 -759.209571 0.514600
LBFGS: 3 16:54:42 -759.298948 0.404890
LBFGS: 4 16:54:43 -759.316304 0.265548
LBFGS: 5 16:54:45 -759.336518 0.252446
LBFGS: 6 16:54:47 -759.351338 0.330410
LBFGS: 7 16:54:48 -759.368546 0.309163
LBFGS: 8 16:54:50 -759.378014 0.229741
LBFGS: 9 16:54:52 -759.386280 0.221552
LBFGS: 10 16:54:53 -759.395290 0.278156
LBFGS: 11 16:54:55 -759.404981 0.291370
LBFGS: 12 16:54:57 -759.411852 0.192426
LBFGS: 13 16:54:59 -759.415355 0.075502
Step Time Energy fmax
LBFGS: 0 16:55:00 -758.975436 1.930961
LBFGS: 1 16:55:02 -759.140671 0.711930
LBFGS: 2 16:55:04 -759.209572 0.514582
LBFGS: 3 16:55:05 -759.298949 0.404887
LBFGS: 4 16:55:07 -759.316305 0.265544
LBFGS: 5 16:55:09 -759.336519 0.252446
LBFGS: 6 16:55:11 -759.351338 0.330395
LBFGS: 7 16:55:12 -759.368546 0.309158
LBFGS: 8 16:55:14 -759.378015 0.229745
LBFGS: 9 16:55:16 -759.386281 0.221556
LBFGS: 10 16:55:17 -759.395291 0.278147
LBFGS: 11 16:55:19 -759.404982 0.291359
LBFGS: 12 16:55:21 -759.411852 0.192423
LBFGS: 13 16:55:23 -759.415355 0.075502
Step Time fmax
NEBOptimizer[ode]: 0 16:55:58 1.5090
NEBOptimizer[ode]: 1 16:56:10 1.1032
NEBOptimizer[ode]: 2 16:56:22 0.9983
NEBOptimizer[ode]: 3 16:56:34 0.8704
NEBOptimizer[ode]: 4 16:56:46 0.8013
NEBOptimizer[ode]: 5 16:56:58 0.7712
NEBOptimizer[ode]: 6 16:57:10 0.7441
NEBOptimizer[ode]: 7 16:57:22 0.6738
NEBOptimizer[ode]: 8 16:57:34 0.4346
NEBOptimizer[ode]: 9 16:57:58 0.4299
NEBOptimizer[ode]: 10 16:58:10 0.4226
NEBOptimizer[ode]: 11 16:58:22 0.3946
NEBOptimizer[ode]: 12 16:58:34 0.2843
NEBOptimizer[ode]: 13 16:58:58 0.2726
NEBOptimizer[ode]: 14 16:59:10 0.2652
NEBOptimizer[ode]: 15 16:59:22 0.2612
NEBOptimizer[ode]: 16 16:59:35 0.2552
NEBOptimizer[ode]: 17 16:59:47 0.2323
NEBOptimizer[ode]: 18 17:00:11 0.2219
NEBOptimizer[ode]: 19 17:00:23 0.2141
NEBOptimizer[ode]: 20 17:00:35 0.2087
NEBOptimizer[ode]: 21 17:00:47 0.2055
NEBOptimizer[ode]: 22 17:00:59 0.2005
NEBOptimizer[ode]: 23 17:01:11 0.1809
NEBOptimizer[ode]: 24 17:01:35 0.1729
NEBOptimizer[ode]: 25 17:01:47 0.1664
NEBOptimizer[ode]: 26 17:01:59 0.1624
NEBOptimizer[ode]: 27 17:02:11 0.1598
NEBOptimizer[ode]: 28 17:02:23 0.1559
NEBOptimizer[ode]: 29 17:02:35 0.1409
NEBOptimizer[ode]: 30 17:02:46 0.2612
NEBOptimizer[ode]: 31 17:03:10 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 17:03:16 -759.415355 0.075502
Step Time Energy fmax
LBFGS: 0 17:03:18 -758.975431 1.930990
LBFGS: 1 17:03:19 -759.140669 0.711958
LBFGS: 2 17:03:21 -759.209571 0.514601
LBFGS: 3 17:03:23 -759.298948 0.404890
LBFGS: 4 17:03:25 -759.316304 0.265548
LBFGS: 5 17:03:26 -759.336518 0.252446
LBFGS: 6 17:03:28 -759.351338 0.330410
LBFGS: 7 17:03:30 -759.368546 0.309163
LBFGS: 8 17:03:31 -759.378014 0.229741
LBFGS: 9 17:03:33 -759.386280 0.221553
LBFGS: 10 17:03:35 -759.395290 0.278156
LBFGS: 11 17:03:36 -759.404981 0.291370
LBFGS: 12 17:03:38 -759.411852 0.192426
LBFGS: 13 17:03:40 -759.415355 0.075502
Step Time fmax
NEBOptimizer[ode]: 0 17:04:15 2.3204
NEBOptimizer[ode]: 1 17:04:27 1.6499
NEBOptimizer[ode]: 2 17:04:38 0.9977
NEBOptimizer[ode]: 3 17:04:50 0.6537
NEBOptimizer[ode]: 4 17:05:14 0.4186
NEBOptimizer[ode]: 5 17:05:25 0.3969
NEBOptimizer[ode]: 6 17:05:37 0.3176
NEBOptimizer[ode]: 7 17:06:01 0.2998
NEBOptimizer[ode]: 8 17:06:25 0.2690
NEBOptimizer[ode]: 9 17:06:37 0.2608
NEBOptimizer[ode]: 10 17:06:49 0.2293
NEBOptimizer[ode]: 11 17:07:12 0.2186
NEBOptimizer[ode]: 12 17:07:24 0.2622
NEBOptimizer[ode]: 13 17:07:36 0.2009
NEBOptimizer[ode]: 14 17:07:48 0.1946
NEBOptimizer[ode]: 15 17:08:00 0.1883
NEBOptimizer[ode]: 16 17:08:12 0.1653
NEBOptimizer[ode]: 17 17:08:36 0.1600
NEBOptimizer[ode]: 18 17:08:48 0.1538
NEBOptimizer[ode]: 19 17:09:00 0.1475
NEBOptimizer[ode]: 20 17:09:13 0.1379
NEBOptimizer[ode]: 21 17:09:25 0.1346
NEBOptimizer[ode]: 22 17:09:37 0.1288
NEBOptimizer[ode]: 23 17:09:49 0.1263
NEBOptimizer[ode]: 24 17:10:01 0.1169
NEBOptimizer[ode]: 25 17:10:13 0.1806
NEBOptimizer[ode]: 26 17:10:37 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]:
