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 14:48:56    -1077.368915        0.129114

BFGS:    1 14:48:57    -1077.370392        0.075187

BFGS:    2 14:48:57    -1077.372340        0.145326

BFGS:    3 14:48:58    -1077.374554        0.111789

BFGS:    4 14:48:58    -1077.376096        0.074286

BFGS:    5 14:48:58    -1077.377455        0.063780

BFGS:    6 14:49:00    -1077.378941        0.080821

BFGS:    7 14:49:00    -1077.380760        0.096851

BFGS:    8 14:49:01    -1077.382639        0.078402

BFGS:    9 14:49:04    -1077.384446        0.086890

BFGS:   10 14:49:04    -1077.386281        0.083295

BFGS:   11 14:49:05    -1077.388392        0.084063

BFGS:   12 14:49:05    -1077.390737        0.069052

BFGS:   13 14:49:05    -1077.393126        0.076013

BFGS:   14 14:49:06    -1077.395558        0.084328

BFGS:   15 14:49:06    -1077.398145        0.079955

BFGS:   16 14:49:06    -1077.400825        0.079975

BFGS:   17 14:49:07    -1077.403366        0.067396

BFGS:   18 14:49:07    -1077.405675        0.070441

BFGS:   19 14:49:08    -1077.407934        0.087883

BFGS:   20 14:49:08    -1077.410401        0.084001

BFGS:   21 14:49:09    -1077.413125        0.059825

BFGS:   22 14:49:09    -1077.415973        0.071945

BFGS:   23 14:49:09    -1077.418820        0.067802

BFGS:   24 14:49:10    -1077.421568        0.069925

BFGS:   25 14:49:10    -1077.424156        0.067339

BFGS:   26 14:49:11    -1077.426522        0.060834

BFGS:   27 14:49:11    -1077.428607        0.069320

BFGS:   28 14:49:11    -1077.430416        0.060293

BFGS:   29 14:49:12    -1077.431998        0.051494

BFGS:   30 14:49:13    -1077.433389        0.056302

BFGS:   31 14:49:13    -1077.434620        0.057619

BFGS:   32 14:49:14    -1077.435743        0.046081
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 14:49:14    -1091.661287        1.120236

BFGS:    1 14:49:15    -1091.679631        0.313939

BFGS:    2 14:49:16    -1091.683945        0.232091

BFGS:    3 14:49:16    -1091.695507        0.302372

BFGS:    4 14:49:16    -1091.701044        0.210321

BFGS:    5 14:49:18    -1091.707226        0.171311

BFGS:    6 14:49:18    -1091.712983        0.183136

BFGS:    7 14:49:20    -1091.720515        0.262570

BFGS:    8 14:49:20    -1091.727865        0.202838

BFGS:    9 14:49:21    -1091.735396        0.175191

BFGS:   10 14:49:22    -1091.743447        0.214466

BFGS:   11 14:49:23    -1091.752655        0.253300

BFGS:   12 14:49:23    -1091.762637        0.232873

BFGS:   13 14:49:24    -1091.773118        0.197326

BFGS:   14 14:49:24    -1091.784458        0.164083

BFGS:   15 14:49:25    -1091.796073        0.252840

BFGS:   16 14:49:26    -1091.806471        0.270276

BFGS:   17 14:49:26    -1091.815238        0.186126

BFGS:   18 14:49:27    -1091.822965        0.130935

BFGS:   19 14:49:27    -1091.830272        0.120407

BFGS:   20 14:49:27    -1091.837491        0.140917

BFGS:   21 14:49:28    -1091.844729        0.154729

BFGS:   22 14:49:28    -1091.851965        0.162441

BFGS:   23 14:49:29    -1091.858807        0.165891

BFGS:   24 14:49:30    -1091.864202        0.170328

BFGS:   25 14:49:31    -1091.868721        0.411585

BFGS:   26 14:49:31    -1091.873930        0.221378

BFGS:   27 14:49:32    -1091.880144        0.092263

BFGS:   28 14:49:32    -1091.884364        0.091139

BFGS:   29 14:49:32    -1091.889064        0.135339

BFGS:   30 14:49:33    -1091.893586        0.143430

BFGS:   31 14:49:33    -1091.899476        0.231294

BFGS:   32 14:49:33    -1091.904615        0.312374

BFGS:   33 14:49:34    -1091.908880        0.329443

BFGS:   34 14:49:35    -1091.914106        0.200617

BFGS:   35 14:49:36    -1091.920894        0.173357

BFGS:   36 14:49:36    -1091.927119        0.178003

BFGS:   37 14:49:37    -1091.934498        0.313601

BFGS:   38 14:49:37    -1091.939736        0.149114

BFGS:   39 14:49:40    -1091.943184        0.666278

BFGS:   40 14:49:40    -1091.951219        0.202156

BFGS:   41 14:49:41    -1091.958015        0.134687

BFGS:   42 14:49:41    -1091.968704        0.231915

BFGS:   43 14:49:42    -1091.977391        0.308383

BFGS:   44 14:49:42    -1091.989159        0.196087

BFGS:   45 14:49:43    -1091.995971        0.884631

BFGS:   46 14:49:44    -1092.009727        0.527852

BFGS:   47 14:49:45    -1092.025016        0.196672

BFGS:   48 14:49:45    -1092.048945        0.583762

BFGS:   49 14:49:46    -1092.066870        0.473106

BFGS:   50 14:49:46    -1092.082180        1.045588

BFGS:   51 14:49:46    -1092.106965        0.400884

BFGS:   52 14:49:47    -1092.125492        0.345249

BFGS:   53 14:49:47    -1092.147880        0.349071

BFGS:   54 14:49:48    -1092.159613        0.423525

BFGS:   55 14:49:51    -1092.173599        0.387529

BFGS:   56 14:49:51    -1092.197354        0.316005

BFGS:   57 14:49:52    -1092.207718        0.284365

BFGS:   58 14:49:52    -1092.226776        0.288696

BFGS:   59 14:49:53    -1092.236144        0.357350

BFGS:   60 14:49:53    -1092.248636        0.306531

BFGS:   61 14:49:54    -1092.258910        0.274180

BFGS:   62 14:49:54    -1092.267432        0.161252

BFGS:   63 14:49:55    -1092.273004        0.132088

BFGS:   64 14:49:55    -1092.278970        0.121835

BFGS:   65 14:49:55    -1092.284636        0.124332

BFGS:   66 14:49:56    -1092.289819        0.139735

BFGS:   67 14:49:56    -1092.294424        0.169707

BFGS:   68 14:49:56    -1092.298884        0.130593

BFGS:   69 14:49:57    -1092.303164        0.134850

BFGS:   70 14:49:57    -1092.307246        0.133646

BFGS:   71 14:49:57    -1092.311313        0.144179

BFGS:   72 14:49:58    -1092.315626        0.170086

BFGS:   73 14:49:58    -1092.319998        0.162307

BFGS:   74 14:49:58    -1092.323908        0.133380

BFGS:   75 14:49:59    -1092.327224        0.094680

BFGS:   76 14:50:00    -1092.330245        0.129299

BFGS:   77 14:50:00    -1092.332990        0.108176

BFGS:   78 14:50:00    -1092.335153        0.074998

BFGS:   79 14:50:02    -1092.336739        0.067135

BFGS:   80 14:50:03    -1092.338065        0.059953

BFGS:   81 14:50:04    -1092.339383        0.066429

BFGS:   82 14:50:04    -1092.340754        0.074828

BFGS:   83 14:50:04    -1092.342141        0.081612

BFGS:   84 14:50:05    -1092.343542        0.086574

BFGS:   85 14:50:06    -1092.344934        0.092773

BFGS:   86 14:50:06    -1092.346289        0.085472

BFGS:   87 14:50:07    -1092.347557        0.055385

BFGS:   88 14:50:07    -1092.348698        0.043692
Energy of MOF + H2O: -1092.349 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 14:50:08    -1077.149992        1.015996

BFGS:    1 14:50:08    -1077.191180        0.891448

BFGS:    2 14:50:08    -1077.242261        0.659166

BFGS:    3 14:50:09    -1077.289501        0.488322

BFGS:    4 14:50:09    -1077.307292        0.357585

BFGS:    5 14:50:11    -1077.323951        0.300661

BFGS:    6 14:50:11    -1077.337914        0.323515

BFGS:    7 14:50:12    -1077.350368        0.260238

BFGS:    8 14:50:13    -1077.357629        0.135732

BFGS:    9 14:50:14    -1077.362431        0.127846

BFGS:   10 14:50:14    -1077.366942        0.177610

BFGS:   11 14:50:15    -1077.371687        0.171239

BFGS:   12 14:50:16    -1077.376450        0.137789

BFGS:   13 14:50:16    -1077.381090        0.125114

BFGS:   14 14:50:17    -1077.385634        0.149879

BFGS:   15 14:50:17    -1077.389560        0.127104

BFGS:   16 14:50:18    -1077.392628        0.091486

BFGS:   17 14:50:20    -1077.395290        0.089489

BFGS:   18 14:50:21    -1077.397968        0.113624

BFGS:   19 14:50:23    -1077.400667        0.114600

BFGS:   20 14:50:23    -1077.403348        0.105309

BFGS:   21 14:50:24    -1077.405987        0.100961

BFGS:   22 14:50:24    -1077.408531        0.085584

BFGS:   23 14:50:24    -1077.410879        0.095105

BFGS:   24 14:50:25    -1077.412990        0.075064

BFGS:   25 14:50:25    -1077.414890        0.078715

BFGS:   26 14:50:26    -1077.416601        0.078687

BFGS:   27 14:50:26    -1077.418058        0.079494

BFGS:   28 14:50:27    -1077.419281        0.049146
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: -0.539 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: -0.8252324528776267

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

E_mof_deform: 0.28575044860713206

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

E_ads: -0.5394820042704946

$E_{\mathrm{int}}$ 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¶