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 00:29:34    -1077.368915        0.129115

BFGS:    1 00:29:36    -1077.370392        0.075187

BFGS:    2 00:29:37    -1077.372342        0.145320

BFGS:    3 00:29:41    -1077.374554        0.111799

BFGS:    4 00:29:43    -1077.376093        0.074297

BFGS:    5 00:29:43    -1077.377454        0.063782

BFGS:    6 00:29:44    -1077.378941        0.080752

BFGS:    7 00:29:47    -1077.380760        0.096917

BFGS:    8 00:29:47    -1077.382636        0.078405

BFGS:    9 00:29:48    -1077.384446        0.086878

BFGS:   10 00:29:48    -1077.386285        0.083329

BFGS:   11 00:29:48    -1077.388393        0.084004

BFGS:   12 00:29:49    -1077.390738        0.069094

BFGS:   13 00:29:49    -1077.393127        0.076055

BFGS:   14 00:29:50    -1077.395557        0.084287

BFGS:   15 00:29:50    -1077.398146        0.079953

BFGS:   16 00:29:50    -1077.400825        0.079994

BFGS:   17 00:29:51    -1077.403371        0.067384

BFGS:   18 00:29:51    -1077.405674        0.070421

BFGS:   19 00:29:52    -1077.407933        0.087902

BFGS:   20 00:29:55    -1077.410401        0.084010

BFGS:   21 00:29:56    -1077.413125        0.059896

BFGS:   22 00:29:56    -1077.415974        0.071914

BFGS:   23 00:29:57    -1077.418820        0.067830

BFGS:   24 00:29:57    -1077.421563        0.069978

BFGS:   25 00:29:57    -1077.424149        0.067319

BFGS:   26 00:29:58    -1077.426522        0.060845

BFGS:   27 00:29:59    -1077.428603        0.069302

BFGS:   28 00:29:59    -1077.430414        0.060295

BFGS:   29 00:30:00    -1077.431996        0.051480

BFGS:   30 00:30:01    -1077.433387        0.056303

BFGS:   31 00:30:01    -1077.434615        0.057580

BFGS:   32 00:30:02    -1077.435742        0.046093
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 00:30:02    -1091.661287        1.120236

BFGS:    1 00:30:03    -1091.679632        0.313939

BFGS:    2 00:30:03    -1091.683945        0.232090

BFGS:    3 00:30:03    -1091.695511        0.302373

BFGS:    4 00:30:04    -1091.701045        0.210394

BFGS:    5 00:30:06    -1091.707225        0.171330

BFGS:    6 00:30:06    -1091.712983        0.183108

BFGS:    7 00:30:10    -1091.720513        0.262608

BFGS:    8 00:30:10    -1091.727863        0.203015

BFGS:    9 00:30:10    -1091.735396        0.175033

BFGS:   10 00:30:10    -1091.743445        0.214430

BFGS:   11 00:30:11    -1091.752655        0.253404

BFGS:   12 00:30:11    -1091.762643        0.232655

BFGS:   13 00:30:11    -1091.773118        0.197334

BFGS:   14 00:30:14    -1091.784461        0.164051

BFGS:   15 00:30:14    -1091.796077        0.252764

BFGS:   16 00:30:14    -1091.806473        0.270292

BFGS:   17 00:30:15    -1091.815239        0.186180

BFGS:   18 00:30:16    -1091.822965        0.130936

BFGS:   19 00:30:16    -1091.830278        0.120930

BFGS:   20 00:30:16    -1091.837492        0.141986

BFGS:   21 00:30:17    -1091.844732        0.154879

BFGS:   22 00:30:17    -1091.851959        0.162450

BFGS:   23 00:30:17    -1091.858810        0.165608

BFGS:   24 00:30:18    -1091.864217        0.167887

BFGS:   25 00:30:18    -1091.868699        0.416325

BFGS:   26 00:30:18    -1091.873930        0.220194

BFGS:   27 00:30:19    -1091.880088        0.092586

BFGS:   28 00:30:19    -1091.884371        0.090819

BFGS:   29 00:30:20    -1091.889009        0.136088

BFGS:   30 00:30:20    -1091.893531        0.142614

BFGS:   31 00:30:20    -1091.899523        0.221205

BFGS:   32 00:30:21    -1091.904682        0.305768

BFGS:   33 00:30:21    -1091.908656        0.369191

BFGS:   34 00:30:21    -1091.913877        0.189126

BFGS:   35 00:30:22    -1091.920604        0.134899

BFGS:   36 00:30:22    -1091.926895        0.148123

BFGS:   37 00:30:23    -1091.934237        0.344300

BFGS:   38 00:30:23    -1091.939362        0.156970

BFGS:   39 00:30:23    -1091.944746        0.477269

BFGS:   40 00:30:24    -1091.952376        0.199428

BFGS:   41 00:30:24    -1091.959389        0.229065

BFGS:   42 00:30:24    -1091.969843        0.226820

BFGS:   43 00:30:25    -1091.978631        0.336228

BFGS:   44 00:30:28    -1091.989803        0.278211

BFGS:   45 00:30:28    -1091.969788        1.573978

BFGS:   46 00:30:28    -1092.005685        0.161459

BFGS:   47 00:30:29    -1092.014717        0.149327

BFGS:   48 00:30:29    -1092.048098        0.566750

BFGS:   49 00:30:29    -1092.066330        0.347358

BFGS:   50 00:30:30    -1092.091163        0.303867

BFGS:   51 00:30:30    -1092.093979        0.785659

BFGS:   52 00:30:30    -1092.125244        0.726660

BFGS:   53 00:30:31    -1092.140743        0.508057

BFGS:   54 00:30:31    -1092.167975        0.300228

BFGS:   55 00:30:31    -1092.178039        0.251833

BFGS:   56 00:30:32    -1092.198272        0.258285

BFGS:   57 00:30:32    -1092.212106        0.380988

BFGS:   58 00:30:32    -1092.224342        0.460994

BFGS:   59 00:30:33    -1092.236205        0.529767

BFGS:   60 00:30:33    -1092.249335        0.398759

BFGS:   61 00:30:34    -1092.258720        0.264565

BFGS:   62 00:30:34    -1092.266348        0.144742

BFGS:   63 00:30:34    -1092.272883        0.120092

BFGS:   64 00:30:35    -1092.278829        0.122444

BFGS:   65 00:30:35    -1092.284275        0.146756

BFGS:   66 00:30:35    -1092.289277        0.140391

BFGS:   67 00:30:36    -1092.294155        0.151884

BFGS:   68 00:30:36    -1092.298757        0.120791

BFGS:   69 00:30:36    -1092.303024        0.172591

BFGS:   70 00:30:38    -1092.307086        0.190299

BFGS:   71 00:30:39    -1092.311201        0.185194

BFGS:   72 00:30:39    -1092.315606        0.182864

BFGS:   73 00:30:39    -1092.320085        0.157522

BFGS:   74 00:30:40    -1092.323952        0.110593

BFGS:   75 00:30:40    -1092.327202        0.079652

BFGS:   76 00:30:43    -1092.330253        0.107233

BFGS:   77 00:30:43    -1092.333033        0.089981

BFGS:   78 00:30:45    -1092.335172        0.072620

BFGS:   79 00:30:46    -1092.336709        0.052808

BFGS:   80 00:30:46    -1092.338003        0.071102

BFGS:   81 00:30:47    -1092.339344        0.077075

BFGS:   82 00:30:47    -1092.340724        0.089346

BFGS:   83 00:30:47    -1092.342113        0.078452

BFGS:   84 00:30:48    -1092.343506        0.088089

BFGS:   85 00:30:49    -1092.344918        0.085656

BFGS:   86 00:30:49    -1092.346300        0.069588

BFGS:   87 00:30:50    -1092.347595        0.045075
Energy of MOF + H2O: -1092.348 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: -1077.149 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 00:30:50    -1077.148582        1.020844

BFGS:    1 00:30:50    -1077.189979        0.894522

BFGS:    2 00:30:51    -1077.241995        0.657588

BFGS:    3 00:30:51    -1077.289215        0.497955

BFGS:    4 00:30:51    -1077.307363        0.363833

BFGS:    5 00:30:52    -1077.324075        0.299232

BFGS:    6 00:30:52    -1077.338044        0.320841

BFGS:    7 00:30:52    -1077.350523        0.252410

BFGS:    8 00:30:53    -1077.357845        0.143537

BFGS:    9 00:30:53    -1077.362654        0.129393

BFGS:   10 00:30:53    -1077.367167        0.176404

BFGS:   11 00:30:54    -1077.371895        0.168085

BFGS:   12 00:30:54    -1077.376763        0.145785

BFGS:   13 00:30:54    -1077.381555        0.129512

BFGS:   14 00:30:55    -1077.386179        0.144063

BFGS:   15 00:30:55    -1077.390138        0.127339

BFGS:   16 00:30:55    -1077.393238        0.097245

BFGS:   17 00:30:56    -1077.395940        0.097807

BFGS:   18 00:30:56    -1077.398620        0.112935

BFGS:   19 00:30:56    -1077.401291        0.111198

BFGS:   20 00:30:57    -1077.403936        0.105303

BFGS:   21 00:30:57    -1077.406560        0.100539

BFGS:   22 00:30:57    -1077.409104        0.085803

BFGS:   23 00:30:58    -1077.411445        0.092324

BFGS:   24 00:30:58    -1077.413511        0.075492

BFGS:   25 00:30:58    -1077.415375        0.076522

BFGS:   26 00:30:59    -1077.417079        0.081047

BFGS:   27 00:30:59    -1077.418532        0.078568

BFGS:   28 00:30:59    -1077.419736        0.050562

BFGS:   29 00:31:00    -1077.420869        0.062214

BFGS:   30 00:31:00    -1077.422070        0.070660

BFGS:   31 00:31:00    -1077.423246        0.074456

BFGS:   32 00:31:01    -1077.424294        0.048426
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: -0.8247209929397012

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

E_mof_deform: 0.28716003740669294

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

E_ads: -0.5375609555330083

$E_{\mathrm{int}}$ 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¶