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")

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 20:16:21    -1077.368916        0.129115

BFGS:    1 20:16:22    -1077.370392        0.075187

BFGS:    2 20:16:22    -1077.372340        0.145327

BFGS:    3 20:16:23    -1077.374555        0.111784

BFGS:    4 20:16:23    -1077.376094        0.074312

BFGS:    5 20:16:23    -1077.377453        0.063785

BFGS:    6 20:16:24    -1077.378943        0.080815

BFGS:    7 20:16:24    -1077.380754        0.096881

BFGS:    8 20:16:24    -1077.382639        0.078410

BFGS:    9 20:16:25    -1077.384446        0.086879

BFGS:   10 20:16:25    -1077.386284        0.083309

BFGS:   11 20:16:25    -1077.388392        0.084061

BFGS:   12 20:16:25    -1077.390737        0.068982

BFGS:   13 20:16:26    -1077.393126        0.076039

BFGS:   14 20:16:26    -1077.395559        0.084249

BFGS:   15 20:16:27    -1077.398144        0.079998

BFGS:   16 20:16:27    -1077.400826        0.079938

BFGS:   17 20:16:27    -1077.403371        0.067380

BFGS:   18 20:16:28    -1077.405675        0.070446

BFGS:   19 20:16:28    -1077.407933        0.087901

BFGS:   20 20:16:28    -1077.410399        0.083980

BFGS:   21 20:16:29    -1077.413124        0.059855

BFGS:   22 20:16:29    -1077.415973        0.071981

BFGS:   23 20:16:29    -1077.418818        0.067789

BFGS:   24 20:16:30    -1077.421560        0.069799

BFGS:   25 20:16:30    -1077.424152        0.067317

BFGS:   26 20:16:30    -1077.426519        0.060820

BFGS:   27 20:16:31    -1077.428605        0.069317

BFGS:   28 20:16:31    -1077.430412        0.060335

BFGS:   29 20:16:31    -1077.431997        0.051484

BFGS:   30 20:16:32    -1077.433387        0.056306

BFGS:   31 20:16:32    -1077.434616        0.057623

BFGS:   32 20:16:32    -1077.435738        0.046092
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 20:16:33    -1091.661287        1.120236

BFGS:    1 20:16:33    -1091.679632        0.313939

BFGS:    2 20:16:34    -1091.683946        0.232091

BFGS:    3 20:16:34    -1091.695507        0.302352

BFGS:    4 20:16:35    -1091.701045        0.210411

BFGS:    5 20:16:35    -1091.707224        0.171332

BFGS:    6 20:16:35    -1091.712984        0.183112

BFGS:    7 20:16:36    -1091.720515        0.262527

BFGS:    8 20:16:36    -1091.727862        0.202827

BFGS:    9 20:16:36    -1091.735396        0.175242

BFGS:   10 20:16:37    -1091.743449        0.214435

BFGS:   11 20:16:37    -1091.752656        0.253333

BFGS:   12 20:16:37    -1091.762642        0.232732

BFGS:   13 20:16:38    -1091.773120        0.197345

BFGS:   14 20:16:38    -1091.784456        0.164079

BFGS:   15 20:16:38    -1091.796074        0.252761

BFGS:   16 20:16:38    -1091.806470        0.270291

BFGS:   17 20:16:39    -1091.815243        0.185977

BFGS:   18 20:16:39    -1091.822969        0.130716

BFGS:   19 20:16:40    -1091.830279        0.120060

BFGS:   20 20:16:40    -1091.837498        0.139675

BFGS:   21 20:16:40    -1091.844736        0.154418

BFGS:   22 20:16:41    -1091.851979        0.162093

BFGS:   23 20:16:42    -1091.858853        0.162977

BFGS:   24 20:16:42    -1091.864379        0.152133

BFGS:   25 20:16:42    -1091.868597        0.440036

BFGS:   26 20:16:43    -1091.873918        0.214796

BFGS:   27 20:16:44    -1091.879851        0.108201

BFGS:   28 20:16:44    -1091.884374        0.089330

BFGS:   29 20:16:44    -1091.888708        0.153483

BFGS:   30 20:16:45    -1091.893224        0.141846

BFGS:   31 20:16:45    -1091.899393        0.192028

BFGS:   32 20:16:45    -1091.905138        0.212779

BFGS:   33 20:16:46    -1091.907834        0.489752

BFGS:   34 20:16:46    -1091.913663        0.150187

BFGS:   35 20:16:46    -1091.919189        0.115479

BFGS:   36 20:16:47    -1091.927105        0.129370

BFGS:   37 20:16:47    -1091.933376        0.358715

BFGS:   38 20:16:48    -1091.938562        0.232642

BFGS:   39 20:16:48    -1091.945761        0.343698

BFGS:   40 20:16:49    -1091.952122        0.196794

BFGS:   41 20:16:49    -1091.957014        0.537800

BFGS:   42 20:16:50    -1091.965286        0.255643

BFGS:   43 20:16:50    -1091.977759        0.220361

BFGS:   44 20:16:50    -1091.987793        0.259041

BFGS:   45 20:16:51    -1092.002426        0.260653

BFGS:   46 20:16:52    -1092.015663        0.211143

BFGS:   47 20:16:52    -1092.006657        1.444386

BFGS:   48 20:16:52    -1092.045930        0.210712

BFGS:   49 20:16:52    -1092.060105        0.228300

BFGS:   50 20:16:54    -1092.095743        0.679632

BFGS:   51 20:16:54    -1092.113669        0.245867

BFGS:   52 20:16:54    -1092.131185        0.305068

BFGS:   53 20:16:55    -1092.157556        0.433155

BFGS:   54 20:16:56    -1092.169231        0.406712

BFGS:   55 20:16:56    -1092.185426        0.367572

BFGS:   56 20:16:56    -1092.200502        0.306002

BFGS:   57 20:16:57    -1092.213610        0.242939

BFGS:   58 20:16:57    -1092.225289        0.342495

BFGS:   59 20:16:57    -1092.239958        0.390204

BFGS:   60 20:16:58    -1092.250628        0.341805

BFGS:   61 20:16:58    -1092.260626        0.203801

BFGS:   62 20:16:58    -1092.267719        0.138737

BFGS:   63 20:16:58    -1092.274515        0.116595

BFGS:   64 20:16:59    -1092.280212        0.119756

BFGS:   65 20:16:59    -1092.285645        0.117721

BFGS:   66 20:16:59    -1092.290680        0.148785

BFGS:   67 20:17:00    -1092.295595        0.136036

BFGS:   68 20:17:00    -1092.300035        0.095050

BFGS:   69 20:17:00    -1092.304041        0.120510

BFGS:   70 20:17:01    -1092.307957        0.135850

BFGS:   71 20:17:01    -1092.312128        0.184295

BFGS:   72 20:17:02    -1092.316501        0.169306

BFGS:   73 20:17:02    -1092.320697        0.148341

BFGS:   74 20:17:02    -1092.324307        0.084068

BFGS:   75 20:17:03    -1092.327581        0.091545

BFGS:   76 20:17:04    -1092.330692        0.106782

BFGS:   77 20:17:05    -1092.333396        0.076284

BFGS:   78 20:17:07    -1092.335423        0.056659

BFGS:   79 20:17:08    -1092.336969        0.071396

BFGS:   80 20:17:08    -1092.338311        0.078051

BFGS:   81 20:17:09    -1092.339654        0.061586

BFGS:   82 20:17:09    -1092.341023        0.068521

BFGS:   83 20:17:09    -1092.342407        0.090987

BFGS:   84 20:17:10    -1092.343791        0.102900

BFGS:   85 20:17:10    -1092.345148        0.089042

BFGS:   86 20:17:11    -1092.346484        0.064636

BFGS:   87 20:17:11    -1092.347765        0.056527

BFGS:   88 20:17:11    -1092.348887        0.059508

BFGS:   89 20:17:12    -1092.349831        0.045951
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: -1077.150 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 20:17:12    -1077.149603        1.022743

BFGS:    1 20:17:12    -1077.191129        0.895884

BFGS:    2 20:17:12    -1077.241720        0.663198

BFGS:    3 20:17:13    -1077.289281        0.482255

BFGS:    4 20:17:15    -1077.307095        0.357078

BFGS:    5 20:17:15    -1077.323782        0.302323

BFGS:    6 20:17:16    -1077.337493        0.320504

BFGS:    7 20:17:16    -1077.349724        0.253713

BFGS:    8 20:17:16    -1077.356914        0.132152

BFGS:    9 20:17:17    -1077.361692        0.128875

BFGS:   10 20:17:17    -1077.366141        0.174351

BFGS:   11 20:17:17    -1077.370835        0.162162

BFGS:   12 20:17:18    -1077.375527        0.140575

BFGS:   13 20:17:18    -1077.380169        0.131848

BFGS:   14 20:17:19    -1077.384702        0.148746

BFGS:   15 20:17:19    -1077.388578        0.123460

BFGS:   16 20:17:20    -1077.391631        0.092607

BFGS:   17 20:17:21    -1077.394354        0.089650

BFGS:   18 20:17:21    -1077.397100        0.113447

BFGS:   19 20:17:21    -1077.399819        0.117319

BFGS:   20 20:17:22    -1077.402491        0.103658

BFGS:   21 20:17:23    -1077.405123        0.104922

BFGS:   22 20:17:23    -1077.407674        0.090760

BFGS:   23 20:17:23    -1077.410056        0.097776

BFGS:   24 20:17:24    -1077.412197        0.075702

BFGS:   25 20:17:26    -1077.414143        0.082202

BFGS:   26 20:17:27    -1077.415897        0.081802

BFGS:   27 20:17:27    -1077.417376        0.079630

BFGS:   28 20:17:29    -1077.418613        0.049237
Energy of re-relaxed empty MOF: -1077.419 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: -0.8276397398860436

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

E_mof_deform: 0.2861354227538868

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

E_ads: -0.5415043171321567

$E_{\mathrm{int}}$ 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¶