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")

Warp DeprecationWarning: The symbol `warp.vec` will soon be removed from the public API. Use `warp.types.vector` instead.

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: -0.473 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 19:13:46    -1077.368916        0.129115

BFGS:    1 19:13:47    -1077.370393        0.075188

BFGS:    2 19:13:47    -1077.372341        0.145326

BFGS:    3 19:13:49    -1077.374554        0.111789

BFGS:    4 19:13:51    -1077.376092        0.074285

BFGS:    5 19:13:56    -1077.377454        0.063783

BFGS:    6 19:13:56    -1077.378941        0.080841

BFGS:    7 19:13:57    -1077.380755        0.096820

BFGS:    8 19:13:59    -1077.382637        0.078417

BFGS:    9 19:14:01    -1077.384445        0.086867

BFGS:   10 19:14:01    -1077.386283        0.083300

BFGS:   11 19:14:02    -1077.388394        0.084040

BFGS:   12 19:14:04    -1077.390739        0.069042

BFGS:   13 19:14:05    -1077.393129        0.076008

BFGS:   14 19:14:05    -1077.395562        0.084305

BFGS:   15 19:14:06    -1077.398146        0.079979

BFGS:   16 19:14:08    -1077.400823        0.079930

BFGS:   17 19:14:09    -1077.403369        0.067396

BFGS:   18 19:14:10    -1077.405676        0.070438

BFGS:   19 19:14:10    -1077.407930        0.087896

BFGS:   20 19:14:11    -1077.410402        0.083991

BFGS:   21 19:14:12    -1077.413125        0.059686

BFGS:   22 19:14:13    -1077.415974        0.071960

BFGS:   23 19:14:13    -1077.418818        0.067832

BFGS:   24 19:14:14    -1077.421566        0.069884

BFGS:   25 19:14:18    -1077.424153        0.067326

BFGS:   26 19:14:19    -1077.426519        0.060888

BFGS:   27 19:14:23    -1077.428603        0.069325

BFGS:   28 19:14:26    -1077.430414        0.060321

BFGS:   29 19:14:27    -1077.431997        0.051487

BFGS:   30 19:14:27    -1077.433387        0.056316

BFGS:   31 19:14:28    -1077.434618        0.057618

BFGS:   32 19:14:28    -1077.435741        0.046088
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 19:14:29    -1091.661289        1.120236

BFGS:    1 19:14:29    -1091.679631        0.313939

BFGS:    2 19:14:30    -1091.683945        0.232091

BFGS:    3 19:14:34    -1091.695508        0.302352

BFGS:    4 19:14:35    -1091.701044        0.210410

BFGS:    5 19:14:37    -1091.707222        0.171330

BFGS:    6 19:14:41    -1091.712982        0.183099

BFGS:    7 19:14:41    -1091.720514        0.262517

BFGS:    8 19:14:42    -1091.727864        0.202909

BFGS:    9 19:14:42    -1091.735397        0.175152

BFGS:   10 19:14:45    -1091.743447        0.214430

BFGS:   11 19:14:47    -1091.752660        0.253292

BFGS:   12 19:14:47    -1091.762639        0.232807

BFGS:   13 19:14:48    -1091.773123        0.197415

BFGS:   14 19:14:49    -1091.784463        0.164051

BFGS:   15 19:14:49    -1091.796076        0.252811

BFGS:   16 19:14:50    -1091.806469        0.270230

BFGS:   17 19:14:51    -1091.815240        0.186191

BFGS:   18 19:14:52    -1091.822968        0.130912

BFGS:   19 19:14:53    -1091.830279        0.120292

BFGS:   20 19:14:54    -1091.837493        0.140896

BFGS:   21 19:14:56    -1091.844732        0.154740

BFGS:   22 19:14:57    -1091.851966        0.162453

BFGS:   23 19:14:57    -1091.858797        0.167902

BFGS:   24 19:14:58    -1091.864158        0.175475

BFGS:   25 19:14:58    -1091.868755        0.402637

BFGS:   26 19:14:59    -1091.873942        0.223521

BFGS:   27 19:15:00    -1091.880204        0.092076

BFGS:   28 19:15:02    -1091.884368        0.091643

BFGS:   29 19:15:03    -1091.889173        0.129506

BFGS:   30 19:15:05    -1091.893703        0.143526

BFGS:   31 19:15:05    -1091.899484        0.245092

BFGS:   32 19:15:09    -1091.904455        0.331921

BFGS:   33 19:15:10    -1091.909063        0.287575

BFGS:   34 19:15:11    -1091.914330        0.211918

BFGS:   35 19:15:12    -1091.920860        0.210662

BFGS:   36 19:15:14    -1091.927206        0.208256

BFGS:   37 19:15:15    -1091.934411        0.294691

BFGS:   38 19:15:18    -1091.939971        0.146837

BFGS:   39 19:15:19    -1091.940348        0.871097

BFGS:   40 19:15:20    -1091.950334        0.174845

BFGS:   41 19:15:21    -1091.955604        0.130794

BFGS:   42 19:15:22    -1091.969520        0.313305

BFGS:   43 19:15:22    -1091.976531        0.282312

BFGS:   44 19:15:24    -1091.993087        0.292550

BFGS:   45 19:15:25    -1092.004469        0.339959

BFGS:   46 19:15:26    -1091.994119        1.265717

BFGS:   47 19:15:29    -1092.023066        0.168518

BFGS:   48 19:15:30    -1092.035129        0.179363

BFGS:   49 19:15:32    -1092.074964        0.478843

BFGS:   50 19:15:34    -1092.091928        0.284901

BFGS:   51 19:15:37    -1092.114741        0.265471

BFGS:   52 19:15:37    -1092.134893        0.585438

BFGS:   53 19:15:38    -1092.150307        0.377559

BFGS:   54 19:15:40    -1092.144698        1.052550

BFGS:   55 19:15:41    -1092.173687        0.413166

BFGS:   56 19:15:43    -1092.184640        0.277428

BFGS:   57 19:15:43    -1092.200645        0.318348

BFGS:   58 19:15:46    -1092.220679        0.317911

BFGS:   59 19:15:50    -1092.229624        0.313956

BFGS:   60 19:15:51    -1092.245762        0.394736

BFGS:   61 19:15:51    -1092.255669        0.395916

BFGS:   62 19:15:52    -1092.264392        0.297284

BFGS:   63 19:15:55    -1092.271083        0.173798

BFGS:   64 19:15:55    -1092.277097        0.105276

BFGS:   65 19:15:56    -1092.282124        0.141937

BFGS:   66 19:15:57    -1092.287529        0.171940

BFGS:   67 19:15:58    -1092.292704        0.155978

BFGS:   68 19:16:01    -1092.297320        0.141063

BFGS:   69 19:16:02    -1092.301502        0.137568

BFGS:   70 19:16:04    -1092.305628        0.184573

BFGS:   71 19:16:05    -1092.309997        0.152052

BFGS:   72 19:16:06    -1092.314353        0.142921

BFGS:   73 19:16:07    -1092.318376        0.172888

BFGS:   74 19:16:08    -1092.322489        0.221816

BFGS:   75 19:16:08    -1092.326247        0.174973

BFGS:   76 19:16:12    -1092.329349        0.114755

BFGS:   77 19:16:12    -1092.332056        0.108454

BFGS:   78 19:16:13    -1092.334410        0.102177

BFGS:   79 19:16:14    -1092.336251        0.112487

BFGS:   80 19:16:15    -1092.337709        0.070413

BFGS:   81 19:16:19    -1092.338942        0.076689

BFGS:   82 19:16:20    -1092.340222        0.092270

BFGS:   83 19:16:21    -1092.341685        0.089014

BFGS:   84 19:16:23    -1092.343166        0.051606

BFGS:   85 19:16:25    -1092.344539        0.055440

BFGS:   86 19:16:26    -1092.345853        0.088608

BFGS:   87 19:16:27    -1092.347149        0.122894

BFGS:   88 19:16:28    -1092.348402        0.087162

BFGS:   89 19:16:28    -1092.349466        0.050990

BFGS:   90 19:16:30    -1092.350280        0.043432
Energy of MOF + H2O: -1092.350 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: -1077.148 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 19:16:31    -1077.148356        1.023600

BFGS:    1 19:16:31    -1077.190012        0.896494

BFGS:    2 19:16:32    -1077.240780        0.662940

BFGS:    3 19:16:35    -1077.288165        0.491634

BFGS:    4 19:16:37    -1077.306163        0.353680

BFGS:    5 19:16:38    -1077.322813        0.304886

BFGS:    6 19:16:38    -1077.336505        0.319768

BFGS:    7 19:16:39    -1077.348737        0.250130

BFGS:    8 19:16:39    -1077.355972        0.130303

BFGS:    9 19:16:40    -1077.360752        0.125482

BFGS:   10 19:16:40    -1077.365183        0.174448

BFGS:   11 19:16:42    -1077.369859        0.160966

BFGS:   12 19:16:42    -1077.374591        0.143534

BFGS:   13 19:16:43    -1077.379246        0.129296

BFGS:   14 19:16:43    -1077.383794        0.146667

BFGS:   15 19:16:43    -1077.387692        0.126670

BFGS:   16 19:16:44    -1077.390777        0.093601

BFGS:   17 19:16:45    -1077.393517        0.090462

BFGS:   18 19:16:47    -1077.396303        0.115509

BFGS:   19 19:16:49    -1077.399076        0.120500

BFGS:   20 19:16:52    -1077.401782        0.106518

BFGS:   21 19:16:53    -1077.404422        0.104870

BFGS:   22 19:16:53    -1077.406987        0.088850

BFGS:   23 19:16:57    -1077.409405        0.098243

BFGS:   24 19:16:59    -1077.411591        0.074799

BFGS:   25 19:17:02    -1077.413555        0.082517

BFGS:   26 19:17:04    -1077.415332        0.081815

BFGS:   27 19:17:05    -1077.416847        0.080531

BFGS:   28 19:17:06    -1077.418105        0.049391
Energy of re-relaxed empty MOF: -1077.418 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: -0.542 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: -0.8295034486979329

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

E_mof_deform: 0.28738453275173015

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

E_ads: -0.5421189159462028

$E_{\mathrm{int}}$ 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 M2(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¶