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 14:18:58    -1077.368917        0.129115

BFGS:    1 14:18:58    -1077.370393        0.075188

BFGS:    2 14:18:59    -1077.372342        0.145320

BFGS:    3 14:19:01    -1077.374555        0.111799

BFGS:    4 14:19:03    -1077.376094        0.074296

BFGS:    5 14:19:07    -1077.377454        0.063781

BFGS:    6 14:19:09    -1077.378942        0.080760

BFGS:    7 14:19:10    -1077.380756        0.096894

BFGS:    8 14:19:10    -1077.382638        0.078412

BFGS:    9 14:19:13    -1077.384447        0.086865

BFGS:   10 14:19:14    -1077.386286        0.083326

BFGS:   11 14:19:14    -1077.388395        0.084011

BFGS:   12 14:19:14    -1077.390738        0.069085

BFGS:   13 14:19:15    -1077.393129        0.076037

BFGS:   14 14:19:16    -1077.395559        0.084308

BFGS:   15 14:19:16    -1077.398149        0.079981

BFGS:   16 14:19:17    -1077.400825        0.079904

BFGS:   17 14:19:19    -1077.403368        0.067387

BFGS:   18 14:19:19    -1077.405674        0.070439

BFGS:   19 14:19:20    -1077.407933        0.087898

BFGS:   20 14:19:24    -1077.410401        0.083994

BFGS:   21 14:19:27    -1077.413125        0.059591

BFGS:   22 14:19:30    -1077.415977        0.071931

BFGS:   23 14:19:33    -1077.418823        0.067819

BFGS:   24 14:19:34    -1077.421564        0.069902

BFGS:   25 14:19:37    -1077.424156        0.067341

BFGS:   26 14:19:39    -1077.426518        0.060871

BFGS:   27 14:19:40    -1077.428604        0.069311

BFGS:   28 14:19:43    -1077.430414        0.060335

BFGS:   29 14:19:44    -1077.431999        0.051494

BFGS:   30 14:19:46    -1077.433387        0.056303

BFGS:   31 14:19:48    -1077.434618        0.057606

BFGS:   32 14:19:49    -1077.435738        0.046098
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 14:19:49    -1091.661287        1.120236

BFGS:    1 14:19:50    -1091.679632        0.313939

BFGS:    2 14:19:52    -1091.683944        0.232091

BFGS:    3 14:19:55    -1091.695506        0.302363

BFGS:    4 14:19:58    -1091.701044        0.210337

BFGS:    5 14:20:00    -1091.707224        0.171323

BFGS:    6 14:20:01    -1091.712981        0.183105

BFGS:    7 14:20:01    -1091.720514        0.262596

BFGS:    8 14:20:02    -1091.727865        0.202898

BFGS:    9 14:20:02    -1091.735396        0.175141

BFGS:   10 14:20:03    -1091.743448        0.214445

BFGS:   11 14:20:07    -1091.752660        0.253309

BFGS:   12 14:20:08    -1091.762639        0.232780

BFGS:   13 14:20:09    -1091.773121        0.197356

BFGS:   14 14:20:10    -1091.784458        0.164080

BFGS:   15 14:20:11    -1091.796075        0.252751

BFGS:   16 14:20:12    -1091.806469        0.270299

BFGS:   17 14:20:13    -1091.815242        0.186062

BFGS:   18 14:20:14    -1091.822969        0.130834

BFGS:   19 14:20:18    -1091.830275        0.120371

BFGS:   20 14:20:20    -1091.837494        0.140491

BFGS:   21 14:20:20    -1091.844736        0.154595

BFGS:   22 14:20:21    -1091.851973        0.162196

BFGS:   23 14:20:21    -1091.858841        0.163076

BFGS:   24 14:20:22    -1091.864336        0.156147

BFGS:   25 14:20:23    -1091.868622        0.434226

BFGS:   26 14:20:27    -1091.873920        0.216139

BFGS:   27 14:20:28    -1091.879918        0.103492

BFGS:   28 14:20:28    -1091.884370        0.089738

BFGS:   29 14:20:29    -1091.888782        0.149156

BFGS:   30 14:20:35    -1091.893305        0.142163

BFGS:   31 14:20:36    -1091.899423        0.199021

BFGS:   32 14:20:36    -1091.905042        0.237880

BFGS:   33 14:20:37    -1091.908028        0.462781

BFGS:   34 14:20:38    -1091.913662        0.159976

BFGS:   35 14:20:39    -1091.919533        0.098934

BFGS:   36 14:20:41    -1091.926837        0.131946

BFGS:   37 14:20:41    -1091.933437        0.365912

BFGS:   38 14:20:42    -1091.938593        0.218758

BFGS:   39 14:20:42    -1091.945577        0.347225

BFGS:   40 14:20:46    -1091.952173        0.190654

BFGS:   41 14:20:47    -1091.957377        0.498817

BFGS:   42 14:20:49    -1091.965799        0.278090

BFGS:   43 14:20:52    -1091.978220        0.274013

BFGS:   44 14:20:56    -1091.988356        0.203465

BFGS:   45 14:20:59    -1092.000088        0.626668

BFGS:   46 14:20:59    -1092.006514        0.763307

BFGS:   47 14:21:00    -1092.025725        0.284805

BFGS:   48 14:21:00    -1092.043554        0.395779

BFGS:   49 14:21:01    -1092.062259        0.882020

BFGS:   50 14:21:02    -1092.086192        0.414512

BFGS:   51 14:21:03    -1092.111293        0.291057

BFGS:   52 14:21:06    -1092.129334        0.732854

BFGS:   53 14:21:06    -1092.143992        0.430138

BFGS:   54 14:21:07    -1092.164359        0.374092

BFGS:   55 14:21:08    -1092.177481        0.325447

BFGS:   56 14:21:09    -1092.193323        0.228512

BFGS:   57 14:21:12    -1092.207749        0.251896

BFGS:   58 14:21:13    -1092.221841        0.333958

BFGS:   59 14:21:16    -1092.234015        0.399857

BFGS:   60 14:21:17    -1092.245236        0.390004

BFGS:   61 14:21:17    -1092.256708        0.282643

BFGS:   62 14:21:19    -1092.265055        0.174242

BFGS:   63 14:21:22    -1092.271638        0.126868

BFGS:   64 14:21:24    -1092.277221        0.126462

BFGS:   65 14:21:24    -1092.282878        0.127897

BFGS:   66 14:21:25    -1092.288371        0.129596

BFGS:   67 14:21:27    -1092.293223        0.166977

BFGS:   68 14:21:31    -1092.297711        0.135118

BFGS:   69 14:21:34    -1092.301968        0.139775

BFGS:   70 14:21:37    -1092.305902        0.164848

BFGS:   71 14:21:38    -1092.309897        0.189156

BFGS:   72 14:21:39    -1092.314215        0.181365

BFGS:   73 14:21:42    -1092.318594        0.156157

BFGS:   74 14:21:43    -1092.322559        0.126846

BFGS:   75 14:21:46    -1092.326041        0.088853

BFGS:   76 14:21:47    -1092.329305        0.121012

BFGS:   77 14:21:51    -1092.332259        0.112808

BFGS:   78 14:21:52    -1092.334626        0.078532

BFGS:   79 14:21:53    -1092.336384        0.079207

BFGS:   80 14:21:53    -1092.337807        0.059229

BFGS:   81 14:21:54    -1092.339134        0.063933

BFGS:   82 14:21:57    -1092.340470        0.084288

BFGS:   83 14:21:59    -1092.341827        0.105156

BFGS:   84 14:22:00    -1092.343214        0.104317

BFGS:   85 14:22:01    -1092.344594        0.091787

BFGS:   86 14:22:02    -1092.345942        0.076086

BFGS:   87 14:22:03    -1092.347222        0.069454

BFGS:   88 14:22:07    -1092.348397        0.053871

BFGS:   89 14:22:08    -1092.349443        0.038048
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: -1077.149 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 14:22:08    -1077.149305        1.022068

BFGS:    1 14:22:09    -1077.190817        0.895214

BFGS:    2 14:22:11    -1077.241659        0.662570

BFGS:    3 14:22:11    -1077.289212        0.482407

BFGS:    4 14:22:14    -1077.306983        0.357667

BFGS:    5 14:22:15    -1077.323631        0.302100

BFGS:    6 14:22:16    -1077.337488        0.321930

BFGS:    7 14:22:16    -1077.349797        0.257280

BFGS:    8 14:22:17    -1077.356978        0.134732

BFGS:    9 14:22:17    -1077.361767        0.129605

BFGS:   10 14:22:18    -1077.366272        0.176027

BFGS:   11 14:22:18    -1077.371041        0.166113

BFGS:   12 14:22:19    -1077.375743        0.134315

BFGS:   13 14:22:20    -1077.380384        0.130561

BFGS:   14 14:22:21    -1077.384949        0.151711

BFGS:   15 14:22:21    -1077.388865        0.124835

BFGS:   16 14:22:22    -1077.391923        0.091722

BFGS:   17 14:22:22    -1077.394616        0.088809

BFGS:   18 14:22:23    -1077.397345        0.114583

BFGS:   19 14:22:24    -1077.400072        0.116739

BFGS:   20 14:22:25    -1077.402749        0.103742

BFGS:   21 14:22:27    -1077.405378        0.103394

BFGS:   22 14:22:28    -1077.407919        0.088820

BFGS:   23 14:22:30    -1077.410295        0.097398

BFGS:   24 14:22:32    -1077.412432        0.075307

BFGS:   25 14:22:33    -1077.414360        0.080454

BFGS:   26 14:22:33    -1077.416092        0.081145

BFGS:   27 14:22:33    -1077.417564        0.080486

BFGS:   28 14:22:34    -1077.418801        0.048850
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: -0.540 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: -0.8269326882840939

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

E_mof_deform: 0.286432945952356

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

E_ads: -0.5404997423317379

$E_{\mathrm{int}}$ 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¶