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 22:07:46    -1077.368917        0.129115

BFGS:    1 22:07:47    -1077.370392        0.075187

BFGS:    2 22:07:47    -1077.372341        0.145327

BFGS:    3 22:07:48    -1077.374554        0.111785

BFGS:    4 22:07:49    -1077.376095        0.074310

BFGS:    5 22:07:49    -1077.377454        0.063783

BFGS:    6 22:07:50    -1077.378943        0.080748

BFGS:    7 22:07:50    -1077.380761        0.096882

BFGS:    8 22:07:51    -1077.382636        0.078401

BFGS:    9 22:07:51    -1077.384447        0.086892

BFGS:   10 22:07:51    -1077.386284        0.083315

BFGS:   11 22:07:52    -1077.388390        0.084134

BFGS:   12 22:07:52    -1077.390737        0.068921

BFGS:   13 22:07:52    -1077.393128        0.076021

BFGS:   14 22:07:52    -1077.395558        0.084277

BFGS:   15 22:07:53    -1077.398147        0.079999

BFGS:   16 22:07:55    -1077.400826        0.080013

BFGS:   17 22:07:56    -1077.403371        0.067384

BFGS:   18 22:07:56    -1077.405674        0.070434

BFGS:   19 22:07:56    -1077.407935        0.087912

BFGS:   20 22:08:00    -1077.410399        0.083988

BFGS:   21 22:08:00    -1077.413126        0.060153

BFGS:   22 22:08:02    -1077.415977        0.071967

BFGS:   23 22:08:03    -1077.418822        0.067814

BFGS:   24 22:08:03    -1077.421562        0.069960

BFGS:   25 22:08:04    -1077.424154        0.067344

BFGS:   26 22:08:04    -1077.426521        0.060847

BFGS:   27 22:08:04    -1077.428604        0.069333

BFGS:   28 22:08:05    -1077.430414        0.060343

BFGS:   29 22:08:05    -1077.431995        0.051488

BFGS:   30 22:08:06    -1077.433388        0.056295

BFGS:   31 22:08:06    -1077.434615        0.057612

BFGS:   32 22:08:06    -1077.435741        0.046065
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 22:08:07    -1091.661288        1.120236

BFGS:    1 22:08:07    -1091.679631        0.313939

BFGS:    2 22:08:08    -1091.683945        0.232091

BFGS:    3 22:08:08    -1091.695507        0.302352

BFGS:    4 22:08:08    -1091.701044        0.210409

BFGS:    5 22:08:09    -1091.707224        0.171332

BFGS:    6 22:08:09    -1091.712982        0.183113

BFGS:    7 22:08:09    -1091.720514        0.262507

BFGS:    8 22:08:10    -1091.727864        0.202908

BFGS:    9 22:08:10    -1091.735394        0.175170

BFGS:   10 22:08:11    -1091.743446        0.214443

BFGS:   11 22:08:11    -1091.752656        0.253314

BFGS:   12 22:08:11    -1091.762639        0.232741

BFGS:   13 22:08:12    -1091.773122        0.197343

BFGS:   14 22:08:12    -1091.784458        0.164057

BFGS:   15 22:08:12    -1091.796074        0.252735

BFGS:   16 22:08:13    -1091.806472        0.270237

BFGS:   17 22:08:13    -1091.815240        0.186080

BFGS:   18 22:08:13    -1091.822968        0.130896

BFGS:   19 22:08:14    -1091.830282        0.120030

BFGS:   20 22:08:14    -1091.837498        0.139870

BFGS:   21 22:08:14    -1091.844737        0.154561

BFGS:   22 22:08:15    -1091.851980        0.162209

BFGS:   23 22:08:15    -1091.858837        0.163031

BFGS:   24 22:08:16    -1091.864306        0.160501

BFGS:   25 22:08:16    -1091.868653        0.427658

BFGS:   26 22:08:17    -1091.873916        0.218012

BFGS:   27 22:08:18    -1091.879999        0.097440

BFGS:   28 22:08:18    -1091.884359        0.090277

BFGS:   29 22:08:19    -1091.888865        0.146694

BFGS:   30 22:08:19    -1091.893377        0.142659

BFGS:   31 22:08:19    -1091.899434        0.208001

BFGS:   32 22:08:20    -1091.904942        0.261291

BFGS:   33 22:08:20    -1091.908363        0.418489

BFGS:   34 22:08:20    -1091.913779        0.172695

BFGS:   35 22:08:22    -1091.920170        0.102729

BFGS:   36 22:08:22    -1091.926863        0.138122

BFGS:   37 22:08:22    -1091.933853        0.362937

BFGS:   38 22:08:23    -1091.938980        0.181785

BFGS:   39 22:08:24    -1091.945249        0.389251

BFGS:   40 22:08:24    -1091.952499        0.181203

BFGS:   41 22:08:25    -1091.958562        0.358617

BFGS:   42 22:08:25    -1091.968435        0.313826

BFGS:   43 22:08:25    -1091.977735        0.313727

BFGS:   44 22:08:27    -1091.990748        0.251057

BFGS:   45 22:08:28    -1092.003263        0.318336

BFGS:   46 22:08:28    -1092.002997        1.213856

BFGS:   47 22:08:28    -1092.010571        0.970673

BFGS:   48 22:08:29    -1092.036491        0.261379

BFGS:   49 22:08:29    -1092.049181        0.203108

BFGS:   50 22:08:30    -1092.083917        0.495363

BFGS:   51 22:08:30    -1092.104309        0.359868

BFGS:   52 22:08:30    -1092.126360        0.402218

BFGS:   53 22:08:31    -1092.141658        0.333179

BFGS:   54 22:08:31    -1092.156493        0.912261

BFGS:   55 22:08:32    -1092.172969        0.431741

BFGS:   56 22:08:32    -1092.189890        0.301060

BFGS:   57 22:08:33    -1092.202470        0.332100

BFGS:   58 22:08:33    -1092.218215        0.268899

BFGS:   59 22:08:34    -1092.230694        0.369342

BFGS:   60 22:08:34    -1092.242541        0.443352

BFGS:   61 22:08:34    -1092.252815        0.478377

BFGS:   62 22:08:35    -1092.262496        0.343131

BFGS:   63 22:08:35    -1092.269583        0.204660

BFGS:   64 22:08:36    -1092.275736        0.110861

BFGS:   65 22:08:37    -1092.280762        0.139288

BFGS:   66 22:08:38    -1092.286276        0.167535

BFGS:   67 22:08:38    -1092.291712        0.159331

BFGS:   68 22:08:39    -1092.296359        0.145826

BFGS:   69 22:08:40    -1092.300569        0.124612

BFGS:   70 22:08:41    -1092.304774        0.177232

BFGS:   71 22:08:41    -1092.309131        0.168547

BFGS:   72 22:08:42    -1092.313406        0.138185

BFGS:   73 22:08:42    -1092.317422        0.176872

BFGS:   74 22:08:42    -1092.321573        0.222797

BFGS:   75 22:08:43    -1092.325494        0.184534

BFGS:   76 22:08:43    -1092.328641        0.095670

BFGS:   77 22:08:44    -1092.331388        0.108256

BFGS:   78 22:08:45    -1092.333870        0.109472

BFGS:   79 22:08:45    -1092.335866        0.112136

BFGS:   80 22:08:45    -1092.337376        0.082561

BFGS:   81 22:08:46    -1092.338633        0.065768

BFGS:   82 22:08:46    -1092.339897        0.093907

BFGS:   83 22:08:47    -1092.341339        0.095378

BFGS:   84 22:08:47    -1092.342808        0.066368

BFGS:   85 22:08:47    -1092.344186        0.044345
Energy of MOF + H2O: -1092.344 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: -1077.147 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 22:08:48    -1077.146911        1.030721

BFGS:    1 22:08:48    -1077.188619        0.901668

BFGS:    2 22:08:48    -1077.241168        0.661203

BFGS:    3 22:08:49    -1077.289408        0.501442

BFGS:    4 22:08:50    -1077.308254        0.373323

BFGS:    5 22:08:50    -1077.325556        0.316585

BFGS:    6 22:08:50    -1077.339792        0.323845

BFGS:    7 22:08:51    -1077.352527        0.251422

BFGS:    8 22:08:51    -1077.360011        0.124480

BFGS:    9 22:08:52    -1077.364900        0.132298

BFGS:   10 22:08:52    -1077.369500        0.177613

BFGS:   11 22:08:53    -1077.374454        0.155020

BFGS:   12 22:08:56    -1077.379418        0.142361

BFGS:   13 22:08:56    -1077.384296        0.131527

BFGS:   14 22:08:57    -1077.389019        0.144056

BFGS:   15 22:08:58    -1077.392970        0.125976

BFGS:   16 22:08:59    -1077.396005        0.099481

BFGS:   17 22:09:00    -1077.398631        0.092586

BFGS:   18 22:09:00    -1077.401216        0.108571

BFGS:   19 22:09:01    -1077.403778        0.112314

BFGS:   20 22:09:02    -1077.406340        0.101940

BFGS:   21 22:09:03    -1077.408905        0.104594

BFGS:   22 22:09:03    -1077.411384        0.086669

BFGS:   23 22:09:05    -1077.413615        0.093190

BFGS:   24 22:09:06    -1077.415557        0.073747

BFGS:   25 22:09:06    -1077.417345        0.079264

BFGS:   26 22:09:06    -1077.419014        0.084089

BFGS:   27 22:09:07    -1077.420420        0.077216

BFGS:   28 22:09:08    -1077.421563        0.053781

BFGS:   29 22:09:08    -1077.422641        0.062959

BFGS:   30 22:09:10    -1077.423809        0.074648

BFGS:   31 22:09:10    -1077.424958        0.074721

BFGS:   32 22:09:10    -1077.425958        0.048876
Energy of re-relaxed empty MOF: -1077.426 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: -0.534 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: -0.8226882889508413

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

E_mof_deform: 0.28883024178003325

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

E_ads: -0.5338580471708081

$E_{\mathrm{int}}$ 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¶