Adsorption Energies#
Pre-trained ODAC models are versatile across various MOF-related tasks. To begin, we’ll start with a fundamental application: calculating the adsorption energy for a single CO2 molecule. This serves as an excellent and simple demonstration of what you can achieve with these datasets and models.
For predicting the adsorption energy of a single CO2 molecule within a MOF structure, the adsorption energy (\(E_{\mathrm{ads}}\)) is defined as:
Each term on the right-hand side represents the energy of the relaxed state of the indicated chemical system. For a comprehensive understanding of our methodology for computing these adsorption energies, please refer to our paper.
Loading Pre-trained Models#
Need to install fairchem-core or get UMA access or getting permissions/401 errors?
Install the necessary packages using pip, uv etc
Get access to any necessary huggingface gated models
Get and login to your Huggingface account
Request access to https://huggingface.co/facebook/UMA
Create a Huggingface token at https://huggingface.co/settings/tokens/ with the permission “Permissions: Read access to contents of all public gated repos you can access”
Add the token as an environment variable using
huggingface-cli loginor by setting the HF_TOKEN environment variable.
A pre-trained model can be loaded using FAIRChemCalculator. In this example, we’ll employ UMA to determine the CO2 adsorption energies.
from fairchem.core import FAIRChemCalculator, pretrained_mlip
predictor = pretrained_mlip.get_predict_unit("uma-s-1p1")
calc = FAIRChemCalculator(predictor, task_name="odac")
WARNING:root:device was not explicitly set, using device='cuda'.
Adsorption in rigid MOFs: CO2 Adsorption Energy in Mg-MOF-74#
Let’s apply our knowledge to Mg-MOF-74, a widely studied MOF known for its excellent CO2 adsorption properties. Its structure comprises magnesium atomic complexes connected by a carboxylated and oxidized benzene ring, serving as an organic linker. Previous studies consistently report the CO2 adsorption energy for Mg-MOF-74 to be around -0.40 eV [1] [2] [3].
Our goal is to verify if we can achieve a similar value by performing a simple single-point calculation using UMA. In the ODAC23 dataset, all MOF structures are identified by their CSD (Cambridge Structural Database) code. For Mg-MOF-74, this code is OPAGIX. We’ve extracted a specific OPAGIX+CO2 configuration from the dataset, which exhibits the lowest adsorption energy among its counterparts.
import matplotlib.pyplot as plt
from ase.io import read
from ase.visualize.plot import plot_atoms
mof_co2 = read("structures/OPAGIX_w_CO2.cif")
mof = read("structures/OPAGIX.cif")
co2 = read("structures/co2.xyz")
fig, ax = plt.subplots(figsize=(5, 4.5), dpi=250)
plot_atoms(mof_co2, ax)
ax.set_axis_off()
The final step in calculating the adsorption energy involves connecting the FAIRChemCalculator to each relaxed structure: OPAGIX+CO2, OPAGIX, and CO2. The structures used here are already relaxed from ODAC23. For simplicity, we assume here that further relaxations can be neglected. We will show how to go beyond this assumption in the next section.
mof_co2.calc = calc
mof.calc = calc
co2.calc = calc
E_ads = (
mof_co2.get_potential_energy()
- mof.get_potential_energy()
- co2.get_potential_energy()
)
print(f"Adsorption energy of CO2 in Mg-MOF-74: {E_ads:.3f} eV")
Adsorption energy of CO2 in Mg-MOF-74: -0.459 eV
Adsorption in flexible MOFs#
The adsorption energy calculation method outlined above is typically performed with rigid MOFs for simplicity. Both experimental and modeling literature have shown, however, that MOF flexibility can be important in accurately capturing the underlying chemistry of adsorption [1] [2] [3]. In particular, uptake can be improved by treating MOFs as flexible. Two types of MOF flexibility can be considered: intrinsic flexibility and deformation induced by guest molecules. In the Open DAC Project, we consider the latter MOF deformation by allowing the atomic positions of the MOF to relax during geometry optimization [4]. The addition of additional degrees of freedoms can complicate the computation of the adsorption energy and necessitates an extra step in the calculation procedure.
The figure below shows water adsorption in the MOF with CSD code WOBHEB with added defects (WOBHEB_0.11_0) from a DFT simulation. A typical adsorption energy calculation would only seek to capture the effects shaded in purple, which include both chemisorption and non-bonded interactions between the host and guest molecule. When allowing the MOF to relax, however, the adsorption energy also includes the energetic effect of the MOF deformation highlighted in green.
To account for this deformation, it is vital to use the most energetically favorable MOF geometry for the empty MOF term in Eqn. 1. Including MOF atomic coordinates as degrees of freedom can result in three possible outcomes:
The MOF does not deform, so the energies of the relaxed empty MOF and the MOF in the adsorbed state are the same
The MOF deforms to a less energetically favorable geometry than its ground state
The MOF locates a new energetically favorable geoemtry relative to the empty MOF relaxation
The first outcome requires no additional computation because the MOF rigidity assumption is valid. The second outcome represents physical and reversible deformation where the MOF returns to its empty ground state upon removal of the guest molecule. The third outcome is often the result of the guest molecule breaking local symmetry. We also found cases in ODAC in which both outcomes 2 and 3 occur within the same MOF.
To ensure the most energetically favorable empty MOF geometry is found, an addition empty MOF relaxation should be performed after MOF + adsorbate relaxation. The guest molecule should be removed, and the MOF should be relaxed starting from its geometry in the adsorbed state. If all deformation is reversible, the MOF will return to its original empty geometry. Otherwise, the lowest energy (most favorable) MOF geometry should be taken as the reference energy, \(E_{\mathrm{MOF}}\), in Eqn. 1.
H2O Adsorption Energy in Flexible WOBHEB with UMA#
The first part of this tutorial demonstrates how to perform a single point adsorption energy calculation using UMA. To treat MOFs as flexible, we perform all calculations on geometries determined by geometry optimization. The following example corresponds to the figure shown above (H2O adsorption in WOBHEB_0.11_0).
In this tutorial, \(E_{x}(r_{y})\) corresponds to the energy of \(x\) determined from geometry optimization of \(y\).
First, we obtain the energy of the empty MOF from relaxation of only the MOF: \(E_{\mathrm{MOF}}(r_{\mathrm{MOF}})\)
import ase.io
from ase.optimize import BFGS
mof = ase.io.read("structures/WOBHEB_0.11.cif")
mof.calc = calc
relax = BFGS(mof)
relax.run(fmax=0.05)
E_mof_empty = mof.get_potential_energy()
print(f"Energy of empty MOF: {E_mof_empty:.3f} eV")
Step Time Energy fmax
BFGS: 0 21:30:28 -1077.274065 0.206406
BFGS: 1 21:30:28 -1077.276780 0.152729
BFGS: 2 21:30:28 -1077.281942 0.169926
BFGS: 3 21:30:29 -1077.284767 0.155780
BFGS: 4 21:30:29 -1077.288837 0.108783
BFGS: 5 21:30:29 -1077.291024 0.086440
BFGS: 6 21:30:29 -1077.293360 0.093430
BFGS: 7 21:30:30 -1077.295415 0.100107
BFGS: 8 21:30:30 -1077.297831 0.102532
BFGS: 9 21:30:30 -1077.300015 0.091597
BFGS: 10 21:30:30 -1077.302011 0.079035
BFGS: 11 21:30:31 -1077.304135 0.105570
BFGS: 12 21:30:31 -1077.306723 0.087946
BFGS: 13 21:30:31 -1077.309518 0.086344
BFGS: 14 21:30:31 -1077.312257 0.086879
BFGS: 15 21:30:32 -1077.314705 0.106270
BFGS: 16 21:30:32 -1077.316991 0.106218
BFGS: 17 21:30:32 -1077.319476 0.085499
BFGS: 18 21:30:32 -1077.322264 0.109641
BFGS: 19 21:30:32 -1077.325136 0.148715
BFGS: 20 21:30:33 -1077.327763 0.125900
BFGS: 21 21:30:33 -1077.329927 0.069113
BFGS: 22 21:30:33 -1077.331950 0.087285
BFGS: 23 21:30:33 -1077.334270 0.125227
BFGS: 24 21:30:34 -1077.336834 0.166688
BFGS: 25 21:30:34 -1077.339540 0.145587
BFGS: 26 21:30:34 -1077.342151 0.087653
BFGS: 27 21:30:34 -1077.344539 0.076211
BFGS: 28 21:30:35 -1077.346896 0.148965
BFGS: 29 21:30:35 -1077.349785 0.170254
BFGS: 30 21:30:35 -1077.352530 0.109292
BFGS: 31 21:30:35 -1077.354750 0.070334
BFGS: 32 21:30:36 -1077.356776 0.089700
BFGS: 33 21:30:36 -1077.358659 0.124292
BFGS: 34 21:30:36 -1077.360599 0.108075
BFGS: 35 21:30:36 -1077.362469 0.068608
BFGS: 36 21:30:37 -1077.364168 0.070196
BFGS: 37 21:30:37 -1077.365715 0.105437
BFGS: 38 21:30:37 -1077.367257 0.104263
BFGS: 39 21:30:37 -1077.368771 0.062811
BFGS: 40 21:30:38 -1077.370140 0.057147
BFGS: 41 21:30:38 -1077.371373 0.061211
BFGS: 42 21:30:38 -1077.372442 0.064290
BFGS: 43 21:30:38 -1077.373408 0.058055
BFGS: 44 21:30:38 -1077.374353 0.046048
Energy of empty MOF: -1077.374 eV
Next, we add the H2O guest molecule and relax the MOF + adsorbate to obtain \(E_{\mathrm{MOF+H2O}}(r_{\mathrm{MOF+H2O}})\).
mof_h2o = ase.io.read("structures/WOBHEB_H2O.cif")
mof_h2o.calc = calc
relax = BFGS(mof_h2o)
relax.run(fmax=0.05)
E_combo = mof_h2o.get_potential_energy()
print(f"Energy of MOF + H2O: {E_combo:.3f} eV")
Step Time Energy fmax
BFGS: 0 21:30:39 -1091.565590 1.145036
BFGS: 1 21:30:39 -1091.585063 0.314149
BFGS: 2 21:30:39 -1091.590210 0.243429
BFGS: 3 21:30:40 -1091.608170 0.237249
BFGS: 4 21:30:40 -1091.614632 0.227922
BFGS: 5 21:30:40 -1091.625215 0.186791
BFGS: 6 21:30:40 -1091.632359 0.178909
BFGS: 7 21:30:41 -1091.640632 0.175153
BFGS: 8 21:30:41 -1091.648043 0.184535
BFGS: 9 21:30:41 -1091.656148 0.160877
BFGS: 10 21:30:41 -1091.663841 0.178464
BFGS: 11 21:30:42 -1091.672296 0.188705
BFGS: 12 21:30:42 -1091.682091 0.157544
BFGS: 13 21:30:42 -1091.692984 0.177275
BFGS: 14 21:30:42 -1091.704436 0.158175
BFGS: 15 21:30:43 -1091.715512 0.191650
BFGS: 16 21:30:43 -1091.725713 0.197863
BFGS: 17 21:30:43 -1091.735328 0.163703
BFGS: 18 21:30:43 -1091.745540 0.151489
BFGS: 19 21:30:44 -1091.754025 0.170791
BFGS: 20 21:30:44 -1091.761493 0.153505
BFGS: 21 21:30:44 -1091.767893 0.152827
BFGS: 22 21:30:44 -1091.774204 0.166039
BFGS: 23 21:30:45 -1091.780884 0.135366
BFGS: 24 21:30:45 -1091.788358 0.180962
BFGS: 25 21:30:45 -1091.794278 0.204599
BFGS: 26 21:30:45 -1091.800641 0.131411
BFGS: 27 21:30:46 -1091.806525 0.189774
BFGS: 28 21:30:46 -1091.812307 0.199055
BFGS: 29 21:30:46 -1091.817180 0.151640
BFGS: 30 21:30:46 -1091.822212 0.100098
BFGS: 31 21:30:47 -1091.826302 0.125265
BFGS: 32 21:30:47 -1091.832530 0.177271
BFGS: 33 21:30:47 -1091.837114 0.246054
BFGS: 34 21:30:47 -1091.842050 0.112609
BFGS: 35 21:30:48 -1091.845776 0.331225
BFGS: 36 21:30:48 -1091.850861 0.173692
BFGS: 37 21:30:48 -1091.858474 0.159616
BFGS: 38 21:30:48 -1091.865282 0.141868
BFGS: 39 21:30:49 -1091.872008 0.139450
BFGS: 40 21:30:49 -1091.878235 0.267467
BFGS: 41 21:30:49 -1091.879759 0.600384
BFGS: 42 21:30:49 -1091.887485 0.522225
BFGS: 43 21:30:50 -1091.893892 0.249357
BFGS: 44 21:30:50 -1091.900389 0.180958
BFGS: 45 21:30:50 -1091.915807 0.235770
BFGS: 46 21:30:50 -1091.924341 0.386982
BFGS: 47 21:30:51 -1091.937909 0.264421
BFGS: 48 21:30:51 -1091.952902 0.467297
BFGS: 49 21:30:51 -1091.971876 0.642749
BFGS: 50 21:30:51 -1091.970482 1.392366
BFGS: 51 21:30:52 -1092.006084 0.442430
BFGS: 52 21:30:52 -1092.022826 0.280885
BFGS: 53 21:30:52 -1092.070255 0.299186
BFGS: 54 21:30:52 -1092.086442 0.297600
BFGS: 55 21:30:53 -1092.119382 0.639797
BFGS: 56 21:30:53 -1092.123852 0.388005
BFGS: 57 21:30:53 -1092.139129 0.207870
BFGS: 58 21:30:53 -1092.151142 0.259459
BFGS: 59 21:30:54 -1092.168609 0.379455
BFGS: 60 21:30:54 -1092.178893 0.396199
BFGS: 61 21:30:54 -1092.189958 0.329143
BFGS: 62 21:30:54 -1092.200873 0.230602
BFGS: 63 21:30:55 -1092.213025 0.162941
BFGS: 64 21:30:55 -1092.222517 0.180913
BFGS: 65 21:30:55 -1092.230899 0.155001
BFGS: 66 21:30:55 -1092.237170 0.104157
BFGS: 67 21:30:55 -1092.242637 0.110665
BFGS: 68 21:30:56 -1092.248371 0.138767
BFGS: 69 21:30:56 -1092.253427 0.147775
BFGS: 70 21:30:56 -1092.258659 0.121972
BFGS: 71 21:30:56 -1092.263501 0.109480
BFGS: 72 21:30:57 -1092.267531 0.134906
BFGS: 73 21:30:57 -1092.271253 0.147310
BFGS: 74 21:30:57 -1092.274833 0.132684
BFGS: 75 21:30:58 -1092.278150 0.108192
BFGS: 76 21:30:58 -1092.281536 0.094407
BFGS: 77 21:30:58 -1092.284638 0.093898
BFGS: 78 21:30:58 -1092.287078 0.095589
BFGS: 79 21:30:59 -1092.289629 0.080145
BFGS: 80 21:30:59 -1092.291664 0.069954
BFGS: 81 21:30:59 -1092.293483 0.071901
BFGS: 82 21:30:59 -1092.295011 0.082019
BFGS: 83 21:31:00 -1092.296363 0.082774
BFGS: 84 21:31:00 -1092.297791 0.077927
BFGS: 85 21:31:00 -1092.299264 0.082854
BFGS: 86 21:31:00 -1092.301101 0.069568
BFGS: 87 21:31:01 -1092.302698 0.059666
BFGS: 88 21:31:01 -1092.304543 0.054870
BFGS: 89 21:31:01 -1092.306082 0.063356
BFGS: 90 21:31:01 -1092.307463 0.054477
BFGS: 91 21:31:02 -1092.308768 0.052977
BFGS: 92 21:31:02 -1092.309773 0.062237
BFGS: 93 21:31:02 -1092.310670 0.062466
BFGS: 94 21:31:02 -1092.311405 0.055456
BFGS: 95 21:31:03 -1092.312168 0.045535
Energy of MOF + H2O: -1092.312 eV
We can now isolate the MOF atoms from the relaxed MOF + H2O geometry and see that the MOF has adopted a geometry that is less energetically favorable than the empty MOF by ~0.2 eV. The energy of the MOF in the adsorbed state corresponds to \(E_{\mathrm{MOF}}(r_{\mathrm{MOF+H2O}})\).
mof_adsorbed_state = mof_h2o[:-3]
mof_adsorbed_state.calc = calc
E_mof_adsorbed_state = mof_adsorbed_state.get_potential_energy()
print(f"Energy of MOF in the adsorbed state: {E_mof_adsorbed_state:.3f} eV")
Energy of MOF in the adsorbed state: -1077.091 eV
H2O adsorption in this MOF appears to correspond to Case #2 as outlined above. We can now perform re-relaxation of the empty MOF starting from the \(r_{\mathrm{MOF+H2O}}\) geometry.
relax = BFGS(mof_adsorbed_state)
relax.run(fmax=0.05)
E_mof_rerelax = mof_adsorbed_state.get_potential_energy()
print(f"Energy of re-relaxed empty MOF: {E_mof_rerelax:.3f} eV")
Step Time Energy fmax
BFGS: 0 21:31:03 -1077.090691 0.986969
BFGS: 1 21:31:03 -1077.122893 0.873715
BFGS: 2 21:31:03 -1077.172072 0.819483
BFGS: 3 21:31:04 -1077.210892 0.524544
BFGS: 4 21:31:04 -1077.230394 0.438003
BFGS: 5 21:31:04 -1077.246866 0.281794
BFGS: 6 21:31:04 -1077.257624 0.260275
BFGS: 7 21:31:05 -1077.266911 0.248043
BFGS: 8 21:31:05 -1077.276479 0.223250
BFGS: 9 21:31:05 -1077.283430 0.156201
BFGS: 10 21:31:05 -1077.288376 0.140762
BFGS: 11 21:31:06 -1077.292367 0.136074
BFGS: 12 21:31:06 -1077.295826 0.154850
BFGS: 13 21:31:06 -1077.300804 0.165283
BFGS: 14 21:31:06 -1077.305052 0.147138
BFGS: 15 21:31:07 -1077.309324 0.132472
BFGS: 16 21:31:07 -1077.313259 0.159472
BFGS: 17 21:31:07 -1077.317539 0.162140
BFGS: 18 21:31:07 -1077.322166 0.149846
BFGS: 19 21:31:08 -1077.325868 0.124290
BFGS: 20 21:31:08 -1077.328466 0.117708
BFGS: 21 21:31:08 -1077.330834 0.112576
BFGS: 22 21:31:08 -1077.333397 0.120809
BFGS: 23 21:31:08 -1077.336318 0.113469
BFGS: 24 21:31:09 -1077.339180 0.097609
BFGS: 25 21:31:09 -1077.341477 0.088476
BFGS: 26 21:31:09 -1077.343543 0.081588
BFGS: 27 21:31:09 -1077.345199 0.071557
BFGS: 28 21:31:10 -1077.347012 0.083841
BFGS: 29 21:31:10 -1077.348584 0.100688
BFGS: 30 21:31:10 -1077.350335 0.078066
BFGS: 31 21:31:10 -1077.351653 0.052311
BFGS: 32 21:31:11 -1077.352968 0.061359
BFGS: 33 21:31:11 -1077.354314 0.079768
BFGS: 34 21:31:11 -1077.355733 0.085340
BFGS: 35 21:31:11 -1077.357373 0.074116
BFGS: 36 21:31:12 -1077.358910 0.068620
BFGS: 37 21:31:12 -1077.360228 0.071790
BFGS: 38 21:31:12 -1077.361458 0.074948
BFGS: 39 21:31:12 -1077.362863 0.088109
BFGS: 40 21:31:13 -1077.364020 0.070085
BFGS: 41 21:31:13 -1077.365146 0.052598
BFGS: 42 21:31:13 -1077.366248 0.063836
BFGS: 43 21:31:13 -1077.367380 0.069145
BFGS: 44 21:31:14 -1077.368744 0.079322
BFGS: 45 21:31:15 -1077.370047 0.048332
Energy of re-relaxed empty MOF: -1077.370 eV
The MOF returns to its original empty reference energy upon re-relaxation, confirming that this deformation is physically relevant and is induced by the adsorbate molecule. In Case #3, this re-relaxed energy will be more negative (more favorable) than the original empty MOF relaxation. Thus, we take the reference empty MOF energy (\(E_{\mathrm{MOF}}\) in Eqn. 1) to be the minimum of the original empty MOF energy and the re-relaxed MOf energy:
E_mof = min(E_mof_empty, E_mof_rerelax)
# get adsorbate reference energy
h2o = mof_h2o[-3:]
h2o.calc = calc
E_h2o = h2o.get_potential_energy()
# compute adsorption energy
E_ads = E_combo - E_mof - E_h2o
print(f"Adsorption energy of H2O in WOBHEB_0.11_0: {E_ads:.3f} eV")
Adsorption energy of H2O in WOBHEB_0.11_0: -0.689 eV
This adsorption energy closely matches that from DFT (–0.699 eV) [1]. The strong adsorption energy is a consequence of both H2O chemisorption and MOF deformation. We can decompose the adsorption energy into contributions from these two factors. Assuming rigid H2O molecules, we define \(E_{\mathrm{int}}\) and \(E_{\mathrm{MOF,deform}}\), respectively, as
\(E_{\mathrm{int}}\) describes host host–guest interactions for the MOF in the adsorbed state only. \(E_{\mathrm{MOF,deform}}\) quantifies the magnitude of deformation between the MOF in the adsorbed state and the most energetically favorable empty MOF geometry determined from the workflow presented here. It can be shown that
For H2O adsorption in WOBHEB_0.11, we have
E_int = E_combo - E_mof_adsorbed_state - E_h2o
print(f"E_int: {E_int}")
E_int: -0.9727649092670116
E_mof_deform = E_mof_adsorbed_state - E_mof_empty
print(f"E_mof_deform: {E_mof_deform}")
E_mof_deform: 0.2836618423461914
E_ads = E_int + E_mof_deform
print(f"E_ads: {E_ads}")
E_ads: -0.6891030669208202
\(E_{\mathrm{int}}\) is equivalent to \(E_{\mathrm{ads}}\) when the MOF is assumed to be rigid. In this case, failure to consider adsorbate-induced deformation would result in an overestimation of the adsorption energy magnitude.