Adsorption Energies in MOFs

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:

E_{\mathrm{ads}} = E_{\mathrm{MOF+CO2}} - E_{\mathrm{MOF}} - E_{\mathrm{CO2}} \tag{1}

(1)

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

! pip install fairchem-core fairchem-data-oc fairchem-applications-cattsunami

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 login or by setting the HF_TOKEN environment variable.

# Login using the huggingface-cli utility
! huggingface-cli login

# alternatively,
import os
os.environ['HF_TOKEN'] = 'MY_TOKEN'

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-1p2")
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")

WARNING:root:Model is being compiled this might take a while for the first time

W0820 00:02:59.776000 10290 site-packages/torch/_logging/_internal.py:1345] [0/0] Profiler record function <class 'torch.autograd.profiler.record_function'> will be ignored

WARNING:root:The UMA fast path (merge_mole + compile) is only available for fixed composition, task, charge, and spin. This is optimized for MD applications. Falling back to a less optimized version for subsequent evaluations. Reason: 'Compositions differ from merged model'.
Use inference_settings='batch' for heterogeneous batched evaluations.

Adsorption energy of CO2 in Mg-MOF-74: -0.473 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 00:03:45    -1077.368916        0.129115

BFGS:    1 00:03:46    -1077.370391        0.075187

BFGS:    2 00:03:47    -1077.372342        0.145328

BFGS:    3 00:03:49    -1077.374553        0.111788

BFGS:    4 00:03:51    -1077.376093        0.074246

BFGS:    5 00:03:51    -1077.377454        0.063782

BFGS:    6 00:03:52    -1077.378942        0.080769

BFGS:    7 00:03:54    -1077.380756        0.096930

BFGS:    8 00:03:55    -1077.382639        0.078391

BFGS:    9 00:03:55    -1077.384447        0.086892

BFGS:   10 00:03:56    -1077.386286        0.083330

BFGS:   11 00:03:56    -1077.388393        0.084060

BFGS:   12 00:03:57    -1077.390739        0.069010

BFGS:   13 00:03:58    -1077.393129        0.076032

BFGS:   14 00:03:59    -1077.395558        0.084338

BFGS:   15 00:04:02    -1077.398142        0.079947

BFGS:   16 00:04:04    -1077.400824        0.080010

BFGS:   17 00:04:06    -1077.403369        0.067389

BFGS:   18 00:04:07    -1077.405676        0.070446

BFGS:   19 00:04:08    -1077.407932        0.087905

BFGS:   20 00:04:10    -1077.410399        0.083971

BFGS:   21 00:04:14    -1077.413127        0.059663

BFGS:   22 00:04:16    -1077.415977        0.071893

BFGS:   23 00:04:17    -1077.418823        0.067859

BFGS:   24 00:04:17    -1077.421563        0.070024

BFGS:   25 00:04:18    -1077.424153        0.067313

BFGS:   26 00:04:18    -1077.426519        0.060840

BFGS:   27 00:04:19    -1077.428605        0.069341

BFGS:   28 00:04:20    -1077.430415        0.060325

BFGS:   29 00:04:20    -1077.431998        0.051493

BFGS:   30 00:04:21    -1077.433390        0.056322

BFGS:   31 00:04:21    -1077.434619        0.057610

BFGS:   32 00:04:21    -1077.435741        0.046064
Energy of empty MOF: -1077.436 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 00:04:22    -1091.661287        1.120236

BFGS:    1 00:04:22    -1091.679631        0.313939

BFGS:    2 00:04:23    -1091.683945        0.232091

BFGS:    3 00:04:23    -1091.695507        0.302352

BFGS:    4 00:04:23    -1091.701043        0.210409

BFGS:    5 00:04:23    -1091.707223        0.171332

BFGS:    6 00:04:25    -1091.712984        0.183112

BFGS:    7 00:04:25    -1091.720515        0.262519

BFGS:    8 00:04:25    -1091.727863        0.202883

BFGS:    9 00:04:26    -1091.735395        0.175177

BFGS:   10 00:04:27    -1091.743446        0.214433

BFGS:   11 00:04:27    -1091.752662        0.253377

BFGS:   12 00:04:27    -1091.762640        0.232720

BFGS:   13 00:04:28    -1091.773123        0.197350

BFGS:   14 00:04:28    -1091.784460        0.164042

BFGS:   15 00:04:28    -1091.796075        0.252704

BFGS:   16 00:04:29    -1091.806471        0.270286

BFGS:   17 00:04:29    -1091.815243        0.186040

BFGS:   18 00:04:29    -1091.822971        0.130875

BFGS:   19 00:04:30    -1091.830282        0.119917

BFGS:   20 00:04:30    -1091.837502        0.139434

BFGS:   21 00:04:31    -1091.844739        0.154425

BFGS:   22 00:04:31    -1091.851981        0.162015

BFGS:   23 00:04:32    -1091.858858        0.162966

BFGS:   24 00:04:33    -1091.864376        0.153369

BFGS:   25 00:04:33    -1091.868605        0.438495

BFGS:   26 00:04:33    -1091.873920        0.215349

BFGS:   27 00:04:34    -1091.879874        0.106734

BFGS:   28 00:04:34    -1091.884368        0.089531

BFGS:   29 00:04:35    -1091.888732        0.153087

BFGS:   30 00:04:35    -1091.893242        0.141894

BFGS:   31 00:04:37    -1091.899397        0.193578

BFGS:   32 00:04:37    -1091.905126        0.218516

BFGS:   33 00:04:38    -1091.907894        0.482193

BFGS:   34 00:04:38    -1091.913676        0.152396

BFGS:   35 00:04:38    -1091.919298        0.111572

BFGS:   36 00:04:39    -1091.927040        0.130021

BFGS:   37 00:04:40    -1091.933394        0.359937

BFGS:   38 00:04:41    -1091.938579        0.228338

BFGS:   39 00:04:41    -1091.945699        0.346874

BFGS:   40 00:04:42    -1091.952103        0.196927

BFGS:   41 00:04:42    -1091.957162        0.518020

BFGS:   42 00:04:43    -1091.965439        0.268629

BFGS:   43 00:04:44    -1091.978068        0.252883

BFGS:   44 00:04:44    -1091.988008        0.227154

BFGS:   45 00:04:45    -1092.002246        0.423861

BFGS:   46 00:04:45    -1092.006645        0.838167

BFGS:   47 00:04:45    -1092.021696        0.662632

BFGS:   48 00:04:45    -1092.039744        0.350554

BFGS:   49 00:04:46    -1092.057138        0.248289

BFGS:   50 00:04:46    -1092.092312        0.486711

BFGS:   51 00:04:46    -1092.109359        0.283720

BFGS:   52 00:04:47    -1092.129635        0.333481

BFGS:   53 00:04:47    -1092.149414        0.870044

BFGS:   54 00:04:47    -1092.162541        0.391591

BFGS:   55 00:04:47    -1092.176792        0.274305

BFGS:   56 00:04:48    -1092.194778        0.212725

BFGS:   57 00:04:48    -1092.209865        0.267658

BFGS:   58 00:04:49    -1092.222048        0.366605

BFGS:   59 00:04:49    -1092.233828        0.458573

BFGS:   60 00:04:50    -1092.246121        0.425474

BFGS:   61 00:04:51    -1092.256131        0.301706

BFGS:   62 00:04:51    -1092.265067        0.131821

BFGS:   63 00:04:52    -1092.271473        0.116882

BFGS:   64 00:04:53    -1092.277562        0.117352

BFGS:   65 00:04:55    -1092.283314        0.117426

BFGS:   66 00:04:55    -1092.288657        0.137114

BFGS:   67 00:04:56    -1092.293465        0.158545

BFGS:   68 00:04:56    -1092.298016        0.123431

BFGS:   69 00:04:58    -1092.302298        0.138715

BFGS:   70 00:04:58    -1092.306297        0.150358

BFGS:   71 00:04:58    -1092.310193        0.178738

BFGS:   72 00:04:59    -1092.314416        0.195365

BFGS:   73 00:04:59    -1092.318869        0.163001

BFGS:   74 00:04:59    -1092.322875        0.090580

BFGS:   75 00:05:00    -1092.326255        0.075819

BFGS:   76 00:05:00    -1092.329425        0.110616

BFGS:   77 00:05:00    -1092.332404        0.099666

BFGS:   78 00:05:00    -1092.334776        0.050924

BFGS:   79 00:05:01    -1092.336473        0.052347

BFGS:   80 00:05:01    -1092.337817        0.085807

BFGS:   81 00:05:02    -1092.339132        0.068699

BFGS:   82 00:05:02    -1092.340498        0.070546

BFGS:   83 00:05:02    -1092.341872        0.078621

BFGS:   84 00:05:03    -1092.343222        0.106496

BFGS:   85 00:05:03    -1092.344587        0.095798

BFGS:   86 00:05:04    -1092.345961        0.070413

BFGS:   87 00:05:04    -1092.347266        0.041141
Energy of MOF + H2O: -1092.347 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: -1077.147 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 00:05:04    -1077.146978        1.021033

BFGS:    1 00:05:06    -1077.188800        0.894810

BFGS:    2 00:05:07    -1077.240546        0.660935

BFGS:    3 00:05:08    -1077.288099        0.501487

BFGS:    4 00:05:08    -1077.306405        0.361481

BFGS:    5 00:05:08    -1077.323414        0.303570

BFGS:    6 00:05:08    -1077.337430        0.323740

BFGS:    7 00:05:09    -1077.350027        0.256704

BFGS:    8 00:05:10    -1077.357532        0.145863

BFGS:    9 00:05:10    -1077.362473        0.128691

BFGS:   10 00:05:10    -1077.367017        0.175297

BFGS:   11 00:05:11    -1077.371845        0.162323

BFGS:   12 00:05:11    -1077.376713        0.147254

BFGS:   13 00:05:12    -1077.381561        0.132026

BFGS:   14 00:05:12    -1077.386235        0.142650

BFGS:   15 00:05:12    -1077.390172        0.121294

BFGS:   16 00:05:14    -1077.393266        0.091308

BFGS:   17 00:05:14    -1077.395997        0.094728

BFGS:   18 00:05:15    -1077.398674        0.110119

BFGS:   19 00:05:15    -1077.401306        0.105755

BFGS:   20 00:05:16    -1077.403946        0.106415

BFGS:   21 00:05:17    -1077.406604        0.106877

BFGS:   22 00:05:17    -1077.409187        0.082751

BFGS:   23 00:05:17    -1077.411511        0.090659

BFGS:   24 00:05:19    -1077.413550        0.074326

BFGS:   25 00:05:19    -1077.415426        0.080510

BFGS:   26 00:05:20    -1077.417158        0.080477

BFGS:   27 00:05:20    -1077.418612        0.076045

BFGS:   28 00:05:21    -1077.419811        0.050857

BFGS:   29 00:05:22    -1077.420944        0.065518

BFGS:   30 00:05:22    -1077.422156        0.074632

BFGS:   31 00:05:22    -1077.423334        0.071978

BFGS:   32 00:05:23    -1077.424370        0.046092
Energy of re-relaxed empty MOF: -1077.424 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: -0.538 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}} = E_{\mathrm{MOF+H2O}}(r_{\mathrm{MOF+H2O}}) - E_{\mathrm{MOF}}(r_{\mathrm{MOF+H2O}}) - E_{\mathrm{H2O}}(r_{\mathrm{MOF+H2O}}) \tag{2}

(2)

E_{\mathrm{MOF,deform}} = E_{\mathrm{MOF}}(r_{\mathrm{MOF+H2O}}) - E_{\mathrm{MOF}}(r_{\mathrm{MOF}}) \tag{3}

(3)

$E_{\mathrm{int}}$ 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

E_{\mathrm{ads}} = E_{\mathrm{int}} + E_{\mathrm{MOF,deform}} \tag{4}

(4)

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: -0.8269143107117696

E_mof_deform = E_mof_adsorbed_state - E_mof_empty
print(f"E_mof_deform: {E_mof_deform}")

E_mof_deform: 0.28876350059613287

E_ads = E_int + E_mof_deform
print(f"E_ads: {E_ads}")

E_ads: -0.5381508101156367

$E_{\mathrm{int}}$ 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.

Acknowledgements & Authors¶

Logan Brabson and Sihoon Choi (Georgia Tech) and the OpenDAC project.

References¶

Sriram, A., Choi, S., Yu, X., Brabson, L. M., Das, A., Ulissi, Z., Uyttendaele, M., Medford, A. J., & Sholl, D. S. (2024). The Open DAC 2023 Dataset and Challenges for Sorbent Discovery in Direct Air Capture. ACS Central Science, 10(5), 923–941. 10.1021/acscentsci.3c01629
Queen, W. L., Hudson, M. R., Bloch, E. D., Mason, J. A., Gonzalez, M. I., Lee, J. S., Gygi, D., Howe, J. D., Lee, K., Darwish, T. A., James, M., Peterson, V. K., Teat, S. J., Smit, B., Neaton, J. B., Long, J. R., & Brown, C. M. (2014). Comprehensive study of carbon dioxide adsorption in the metal–organic frameworks M 2 (dobdc) (M = Mg, Mn, Fe, Co, Ni, Cu, Zn). Chem. Sci., 5(12), 4569–4581. 10.1039/c4sc02064b
Yu, D., Yazaydin, A. O., Lane, J. R., Dietzel, P. D. C., & Snurr, R. Q. (2013). A combined experimental and quantum chemical study of CO2 adsorption in the metal–organic framework CPO-27 with different metals. Chemical Science, 4(9), 3544. 10.1039/c3sc51319j
Alonso, G., Bahamon, D., Keshavarz, F., Giménez, X., Gamallo, P., & Sayós, R. (2018). Density Functional Theory-Based Adsorption Isotherms for Pure and Flue Gas Mixtures on Mg-MOF-74. Application in CO2 Capture Swing Adsorption Processes. The Journal of Physical Chemistry C, 122(7), 3945–3957. 10.1021/acs.jpcc.8b00938
Witman, M., Ling, S., Jawahery, S., Boyd, P. G., Haranczyk, M., Slater, B., & Smit, B. (2017). The Influence of Intrinsic Framework Flexibility on Adsorption in Nanoporous Materials. Journal of the American Chemical Society, 139(15), 5547–5557. 10.1021/jacs.7b01688

Loading Pre-trained Models¶

Adsorption in rigid MOFs: CO2 Adsorption Energy in Mg-MOF-74¶

Adsorption in flexible MOFs¶

H2O Adsorption Energy in Flexible WOBHEB with UMA¶

Acknowledgements & Authors¶

Adsorption in rigid MOFs: CO₂ Adsorption Energy in Mg-MOF-74¶

H₂O Adsorption Energy in Flexible WOBHEB with UMA¶