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# Sphinx build info version 1 | ||
# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done. | ||
config: d81abe5bca4711c0a089df227c9a417f | ||
tags: 645f666f9bcd5a90fca523b33c5a78b7 |
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latest/_downloads/3237a57d8246eaec10a69b4e251f623d/environment.yml
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channels: | ||
- conda-forge | ||
dependencies: | ||
- python=3.11 | ||
- pip | ||
- pip: | ||
- ase | ||
- matplotlib |
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latest/_downloads/328f2a3eeccb4e902f81e5646c33e2e8/environment.yml
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channels: | ||
- conda-forge | ||
dependencies: | ||
- python=3.11 | ||
- pip | ||
- rust >=1.65 | ||
- pip: | ||
- ase | ||
- chemiscope | ||
- matplotlib | ||
- metatensor | ||
- rascaline @ git+https://github.com/Luthaf/rascaline@ca957642f512e141c7570e987aadc05c7ac71983 | ||
- skmatter | ||
- equisolve @ git+https://github.com/lab-cosmo/equisolve.git@c858bedef4b2799eb445e4c92535ee387224089a |
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latest/_downloads/372c6744f93b866ccf802a12006619bb/roy-gch.py
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""" | ||
Generalized Convex Hull construction for the polymorphs of ROY | ||
============================================================== | ||
:Authors: Michele Ceriotti `@ceriottm <https://github.com/ceriottm/>`_ | ||
This notebook analyzes the structures of 264 polymorphs of ROY, from | ||
`Beran et Al, Chemical Science | ||
(2022) <https://doi.org/10.1039/D1SC06074K>`__, comparing the | ||
conventional density-energy convex hull with a Generalized Convex Hull | ||
(GCH) analysis (see `Anelli et al., Phys. Rev. Materials | ||
(2018) <https://doi.org/10.1103/PhysRevMaterials.2.103804>`__). | ||
It uses features computed with `rascaline <https://github.com/lab-cosmo/rascaline>`__ | ||
and uses the directional convex hull function from | ||
`scikit-matter <https://github.com/lab-cosmo/scikit-matter>`__ | ||
to make the figure. | ||
""" | ||
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import chemiscope | ||
import matplotlib.tri | ||
import numpy as np | ||
from matplotlib import pyplot as plt | ||
from metatensor import mean_over_samples | ||
from rascaline import SoapPowerSpectrum | ||
from sklearn.decomposition import PCA | ||
from skmatter.datasets import load_roy_dataset | ||
from skmatter.sample_selection import DirectionalConvexHull | ||
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# %% | ||
# Loads the structures (that also contain properties in the ``info`` field) | ||
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roy_data = load_roy_dataset() | ||
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structures = roy_data["structures"] | ||
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density = np.array([s.info["density"] for s in structures]) | ||
energy = np.array([s.info["energy"] for s in structures]) | ||
structype = np.array([s.info["type"] for s in structures]) | ||
iknown = np.where(structype == "known")[0] | ||
iothers = np.where(structype != "known")[0] | ||
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# %% | ||
# Energy-density hull | ||
# ------------------- | ||
# | ||
# The Directional Convex Hull routines can be used to compute a | ||
# conventional density-energy hull | ||
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dch_builder = DirectionalConvexHull(low_dim_idx=[0]) | ||
dch_builder.fit(density.reshape(-1, 1), energy) | ||
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# %% | ||
# We can get the indices of the selection, and compute the distance from | ||
# the hull | ||
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sel = dch_builder.selected_idx_ | ||
dch_dist = dch_builder.score_samples(density.reshape(-1, 1), energy) | ||
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# %% | ||
# | ||
# Hull energies | ||
# ^^^^^^^^^^^^^ | ||
# | ||
# Structures on the hull are stable with respect to synthesis at constant | ||
# molar volume. Any other structure would lower the energy by decomposing | ||
# into a mixture of the two nearest structures along the hull. Given that | ||
# the lattice energy is an imperfect proxy for the free energy, and that | ||
# synthesis can be performed in other ways than by fixing the density, | ||
# structures that are not exactly on the hull might also be stable. One | ||
# can compute a “hull energy” as an indication of how close these | ||
# structures are to being stable. | ||
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fig, ax = plt.subplots(1, 1, figsize=(6, 4)) | ||
ax.scatter(density, energy, c=dch_dist, marker=".") | ||
ssel = sel[np.argsort(density[sel])] | ||
ax.plot(density[ssel], energy[ssel], "k--") | ||
ax.set_xlabel("density / g/cm$^3$") | ||
ax.set_ylabel("energy / kJ/mol") | ||
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print( | ||
f"Mean hull energy for 'known' stable structures {dch_dist[iknown].mean()} kJ/mol" | ||
) | ||
print(f"Mean hull energy for 'other' structures {dch_dist[iothers].mean()} kJ/mol") | ||
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# %% | ||
# Interactive visualization | ||
# ^^^^^^^^^^^^^^^^^^^^^^^^^ | ||
# | ||
# You can also visualize the hull with ``chemiscope``. | ||
# This runs only in a notebook, and | ||
# requires having the ``chemiscope`` package installed. | ||
# | ||
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cs = chemiscope.show( | ||
structures, | ||
dict( | ||
energy=energy, | ||
density=density, | ||
hull_energy=dch_dist, | ||
structure_type=structype, | ||
), | ||
settings={ | ||
"map": { | ||
"x": {"property": "density"}, | ||
"y": {"property": "energy"}, | ||
"color": {"property": "hull_energy"}, | ||
"symbol": "structure_type", | ||
"size": {"factor": 35}, | ||
}, | ||
"structure": [{"unitCell": True, "supercell": {"0": 2, "1": 2, "2": 2}}], | ||
}, | ||
) | ||
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if chemiscope.jupyter._is_running_in_notebook(): | ||
from IPython.display import display | ||
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display(cs) | ||
else: | ||
cs.save("roy_ch.json.gz") | ||
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# %% | ||
# Generalized Convex Hull | ||
# ----------------------- | ||
# | ||
# A GCH is a similar construction, in which generic structural descriptors | ||
# are used in lieu of composition, density or other thermodynamic | ||
# constraints. The idea is that configurations that are found close to the | ||
# GCH are locally stable with respect to structurally-similar | ||
# configurations. In other terms, one can hope to find a thermodynamic | ||
# constraint (i.e. synthesis conditions) that act differently on these | ||
# structures in comparison with the others, and may potentially stabilize | ||
# them. | ||
# | ||
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# %% | ||
# Compute structural descriptors | ||
# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ | ||
# | ||
# A first step is to computes suitable ML descriptors. Here we have used | ||
# ``rascaline`` to evaluate average SOAP features for the structures. | ||
# If you don't want to install these dependencies for this example you | ||
# can also use the pre-computed features, but you can use this as a stub | ||
# to apply this analysis to other chemical systems | ||
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hypers = { | ||
"cutoff": 4, | ||
"max_radial": 6, | ||
"max_angular": 4, | ||
"atomic_gaussian_width": 0.7, | ||
"cutoff_function": {"ShiftedCosine": {"width": 0.5}}, | ||
"radial_basis": {"Gto": {"accuracy": 1e-6}}, | ||
"center_atom_weight": 1.0, | ||
} | ||
calculator = SoapPowerSpectrum(**hypers) | ||
rho2i = calculator.compute(structures) | ||
rho2i = rho2i.keys_to_samples(["species_center"]).keys_to_properties( | ||
["species_neighbor_1", "species_neighbor_2"] | ||
) | ||
rho2i_structure = mean_over_samples(rho2i, sample_names=["center", "species_center"]) | ||
np.savez("roy_features.npz", feats=rho2i_structure.block(0).values) | ||
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# features = roy_data["features"] | ||
features = rho2i_structure.block(0).values | ||
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# %% | ||
# PCA projection | ||
# ^^^^^^^^^^^^^^ | ||
# | ||
# Computes PCA projection to generate low-dimensional descriptors that | ||
# reflect structural diversity. Any other dimensionality reduction scheme | ||
# could be used in a similar fashion. | ||
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pca = PCA(n_components=4) | ||
pca_features = pca.fit_transform(features) | ||
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fig, ax = plt.subplots(1, 1, figsize=(6, 4)) | ||
scatter = ax.scatter(pca_features[:, 0], pca_features[:, 1], c=energy) | ||
ax.set_xlabel("PCA[1]") | ||
ax.set_ylabel("PCA[2]") | ||
cbar = fig.colorbar(scatter, ax=ax) | ||
cbar.set_label("energy / kJ/mol") | ||
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# %% | ||
# Builds the Generalized Convex Hull | ||
# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ | ||
# | ||
# Builds a convex hull on the first two PCA features | ||
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dch_builder = DirectionalConvexHull(low_dim_idx=[0, 1]) | ||
dch_builder.fit(pca_features, energy) | ||
sel = dch_builder.selected_idx_ | ||
dch_dist = dch_builder.score_samples(pca_features, energy) | ||
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# %% | ||
# Generates a 3D Plot | ||
# | ||
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triang = matplotlib.tri.Triangulation(pca_features[sel, 0], pca_features[sel, 1]) | ||
fig = plt.figure(figsize=(7, 5), tight_layout=True) | ||
ax = fig.add_subplot(projection="3d") | ||
ax.plot_trisurf(triang, energy[sel], color="gray") | ||
ax.scatter(pca_features[:, 0], pca_features[:, 1], energy, c=dch_dist) | ||
ax.set_xlabel("PCA[1]") | ||
ax.set_ylabel("PCA[2]") | ||
ax.set_zlabel("energy / kJ/mol\n \n", labelpad=11) | ||
ax.view_init(25, 110) | ||
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# %% | ||
# The GCH construction improves the separation between the hull energies | ||
# of “known” and hypothetical polymorphs (compare with the density-energy | ||
# values above) | ||
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print( | ||
f"Mean hull energy for 'known' stable structures {dch_dist[iknown].mean()} kJ/mol" | ||
) | ||
print(f"Mean hull energy for 'other' structures {dch_dist[iothers].mean()} kJ/mol") | ||
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# %% | ||
# Visualize in ``chemiscope``. This runs only in a notebook, and | ||
# requires having the ``chemiscope`` package installed. | ||
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for i, f in enumerate(structures): | ||
for j in range(len(pca_features[i])): | ||
f.info["pca_" + str(j + 1)] = pca_features[i, j] | ||
structure_properties = chemiscope.extract_properties(structures) | ||
structure_properties.update({"per_atom_energy": energy, "hull_energy": dch_dist}) | ||
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# shows chemiscope if not run in terminal | ||
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cs = chemiscope.show( | ||
frames=structures, | ||
properties=structure_properties, | ||
meta={ | ||
"name": "GCH for ROY polymorphs", | ||
"description": """ | ||
Demonstration of the Generalized Convex Hull construction for | ||
polymorphs of the ROY molecule. Molecules that are closest to | ||
the hull built on PCA-based structural descriptors and having the | ||
internal energy predicted by electronic-structure calculations as | ||
the z axis are the most thermodynamically stable. Indeed most of the | ||
known polymorphs of ROY are on (or very close) to this hull. | ||
""", | ||
"authors": ["Michele Ceriotti <[email protected]>"], | ||
"references": [ | ||
'A. Anelli, E. A. Engel, C. J. Pickard, and M. Ceriotti, \ | ||
"Generalized convex hull construction for materials discovery," \ | ||
Physical Review Materials 2(10), 103804 (2018).', | ||
'G. J. O. Beran, I. J. Sugden, C. Greenwell, D. H. Bowskill, \ | ||
C. C. Pantelides, and C. S. Adjiman, "How many more polymorphs of \ | ||
ROY remain undiscovered," Chem. Sci. 13(5), 1288–1297 (2022).', | ||
], | ||
}, | ||
settings={ | ||
"map": { | ||
"x": {"property": "pca_1"}, | ||
"y": {"property": "pca_2"}, | ||
"z": {"property": "energy"}, | ||
"symbol": "type", | ||
"color": {"property": "hull_energy"}, | ||
"size": { | ||
"factor": 35, | ||
"mode": "linear", | ||
"property": "", | ||
"reverse": True, | ||
}, | ||
}, | ||
"structure": [ | ||
{ | ||
"bonds": True, | ||
"unitCell": True, | ||
"keepOrientation": True, | ||
} | ||
], | ||
}, | ||
) | ||
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if chemiscope.jupyter._is_running_in_notebook(): | ||
from IPython.display import display | ||
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display(cs) | ||
else: | ||
cs.save("roy_gch.json.gz") |
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