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 06:57:39    -1077.368916        0.129115

BFGS:    1 06:57:40    -1077.370392        0.075188

BFGS:    2 06:57:41    -1077.372342        0.145326

BFGS:    3 06:57:42    -1077.374554        0.111789

BFGS:    4 06:57:44    -1077.376091        0.074286

BFGS:    5 06:57:45    -1077.377457        0.063781

BFGS:    6 06:57:46    -1077.378943        0.080817

BFGS:    7 06:57:47    -1077.380753        0.096874

BFGS:    8 06:57:49    -1077.382637        0.078411

BFGS:    9 06:57:50    -1077.384448        0.086861

BFGS:   10 06:57:50    -1077.386286        0.083326

BFGS:   11 06:57:53    -1077.388394        0.083968

BFGS:   12 06:57:56    -1077.390742        0.069073

BFGS:   13 06:57:57    -1077.393127        0.076017

BFGS:   14 06:57:58    -1077.395559        0.084334

BFGS:   15 06:57:59    -1077.398143        0.079950

BFGS:   16 06:58:02    -1077.400826        0.079988

BFGS:   17 06:58:05    -1077.403369        0.067388

BFGS:   18 06:58:06    -1077.405674        0.070439

BFGS:   19 06:58:07    -1077.407932        0.087926

BFGS:   20 06:58:08    -1077.410399        0.083985

BFGS:   21 06:58:09    -1077.413124        0.059740

BFGS:   22 06:58:09    -1077.415974        0.072024

BFGS:   23 06:58:12    -1077.418817        0.067762

BFGS:   24 06:58:13    -1077.421562        0.069897

BFGS:   25 06:58:13    -1077.424152        0.067318

BFGS:   26 06:58:14    -1077.426523        0.060818

BFGS:   27 06:58:16    -1077.428603        0.069330

BFGS:   28 06:58:18    -1077.430417        0.060328

BFGS:   29 06:58:20    -1077.431996        0.051475

BFGS:   30 06:58:22    -1077.433388        0.056308

BFGS:   31 06:58:25    -1077.434618        0.057611

BFGS:   32 06:58:25    -1077.435741        0.046106
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 06:58:26    -1091.661288        1.120236

BFGS:    1 06:58:28    -1091.679631        0.313939

BFGS:    2 06:58:29    -1091.683944        0.232091

BFGS:    3 06:58:31    -1091.695506        0.302433

BFGS:    4 06:58:32    -1091.701044        0.210470

BFGS:    5 06:58:33    -1091.707222        0.171338

BFGS:    6 06:58:34    -1091.712981        0.183077

BFGS:    7 06:58:35    -1091.720515        0.262585

BFGS:    8 06:58:36    -1091.727862        0.203020

BFGS:    9 06:58:38    -1091.735396        0.175080

BFGS:   10 06:58:39    -1091.743449        0.214429

BFGS:   11 06:58:40    -1091.752655        0.253306

BFGS:   12 06:58:41    -1091.762640        0.232716

BFGS:   13 06:58:42    -1091.773122        0.197351

BFGS:   14 06:58:43    -1091.784456        0.164014

BFGS:   15 06:58:45    -1091.796074        0.252699

BFGS:   16 06:58:45    -1091.806471        0.270282

BFGS:   17 06:58:46    -1091.815239        0.186038

BFGS:   18 06:58:47    -1091.822968        0.130861

BFGS:   19 06:58:47    -1091.830277        0.119955

BFGS:   20 06:58:49    -1091.837497        0.139375

BFGS:   21 06:58:51    -1091.844738        0.154519

BFGS:   22 06:58:52    -1091.851980        0.162026

BFGS:   23 06:58:52    -1091.858862        0.162918

BFGS:   24 06:58:53    -1091.864410        0.148798

BFGS:   25 06:58:54    -1091.868569        0.444903

BFGS:   26 06:58:55    -1091.873918        0.213461

BFGS:   27 06:58:56    -1091.879791        0.111733

BFGS:   28 06:58:57    -1091.884374        0.088918

BFGS:   29 06:58:58    -1091.888649        0.156420

BFGS:   30 06:59:01    -1091.893166        0.141394

BFGS:   31 06:59:03    -1091.899367        0.186927

BFGS:   32 06:59:05    -1091.905195        0.192753

BFGS:   33 06:59:06    -1091.907726        0.506736

BFGS:   34 06:59:06    -1091.913695        0.142511

BFGS:   35 06:59:07    -1091.918977        0.123537

BFGS:   36 06:59:08    -1091.927471        0.128361

BFGS:   37 06:59:09    -1091.933435        0.351424

BFGS:   38 06:59:11    -1091.938710        0.238493

BFGS:   39 06:59:12    -1091.945889        0.349652

BFGS:   40 06:59:13    -1091.952175        0.202790

BFGS:   41 06:59:14    -1091.957069        0.537613

BFGS:   42 06:59:15    -1091.965228        0.260100

BFGS:   43 06:59:16    -1091.977943        0.221804

BFGS:   44 06:59:17    -1091.987808        0.261329

BFGS:   45 06:59:18    -1092.002629        0.278246

BFGS:   46 06:59:19    -1092.015380        0.209752

BFGS:   47 06:59:20    -1092.010111        1.315145

BFGS:   48 06:59:21    -1092.044970        0.207968

BFGS:   49 06:59:22    -1092.059866        0.236342

BFGS:   50 06:59:23    -1092.095243        0.533745

BFGS:   51 06:59:24    -1092.112353        0.248960

BFGS:   52 06:59:25    -1092.133667        0.353575

BFGS:   53 06:59:26    -1092.155863        0.456054

BFGS:   54 06:59:27    -1092.167969        0.362343

BFGS:   55 06:59:29    -1092.183025        0.359043

BFGS:   56 06:59:31    -1092.198402        0.298786

BFGS:   57 06:59:33    -1092.213785        0.241418

BFGS:   58 06:59:33    -1092.224196        0.308912

BFGS:   59 06:59:34    -1092.238496        0.366594

BFGS:   60 06:59:35    -1092.250596        0.335279

BFGS:   61 06:59:35    -1092.259845        0.228000

BFGS:   62 06:59:36    -1092.267397        0.144493

BFGS:   63 06:59:37    -1092.274087        0.117572

BFGS:   64 06:59:38    -1092.279949        0.108475

BFGS:   65 06:59:38    -1092.285333        0.106156

BFGS:   66 06:59:39    -1092.290431        0.154971

BFGS:   67 06:59:40    -1092.295332        0.144615

BFGS:   68 06:59:43    -1092.299781        0.099191

BFGS:   69 06:59:44    -1092.303788        0.116816

BFGS:   70 06:59:45    -1092.307717        0.126437

BFGS:   71 06:59:46    -1092.311868        0.161737

BFGS:   72 06:59:47    -1092.316230        0.160021

BFGS:   73 06:59:48    -1092.320427        0.149313

BFGS:   74 06:59:50    -1092.324075        0.094865

BFGS:   75 06:59:51    -1092.327339        0.100525

BFGS:   76 06:59:52    -1092.330436        0.113257

BFGS:   77 06:59:54    -1092.333205        0.077734

BFGS:   78 06:59:56    -1092.335301        0.051398

BFGS:   79 06:59:59    -1092.336868        0.066442

BFGS:   80 06:59:59    -1092.338223        0.072968

BFGS:   81 07:00:00    -1092.339563        0.064097

BFGS:   82 07:00:03    -1092.340928        0.062198

BFGS:   83 07:00:03    -1092.342314        0.082883

BFGS:   84 07:00:06    -1092.343689        0.092175

BFGS:   85 07:00:06    -1092.345045        0.092405

BFGS:   86 07:00:08    -1092.346386        0.067563

BFGS:   87 07:00:08    -1092.347678        0.057815

BFGS:   88 07:00:09    -1092.348818        0.052588

BFGS:   89 07:00:11    -1092.349766        0.040936
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 07:00:12    -1077.149979        1.020758

BFGS:    1 07:00:13    -1077.191349        0.894265

BFGS:    2 07:00:14    -1077.241897        0.662140

BFGS:    3 07:00:14    -1077.289354        0.480717

BFGS:    4 07:00:15    -1077.307123        0.355594

BFGS:    5 07:00:16    -1077.323809        0.302568

BFGS:    6 07:00:17    -1077.337513        0.319681

BFGS:    7 07:00:18    -1077.349730        0.252128

BFGS:    8 07:00:19    -1077.356911        0.131622

BFGS:    9 07:00:20    -1077.361701        0.128422

BFGS:   10 07:00:21    -1077.366151        0.174366

BFGS:   11 07:00:22    -1077.370830        0.161376

BFGS:   12 07:00:24    -1077.375530        0.140726

BFGS:   13 07:00:25    -1077.380179        0.131400

BFGS:   14 07:00:26    -1077.384726        0.148871

BFGS:   15 07:00:26    -1077.388609        0.123356

BFGS:   16 07:00:27    -1077.391667        0.092646

BFGS:   17 07:00:28    -1077.394388        0.089444

BFGS:   18 07:00:30    -1077.397130        0.113657

BFGS:   19 07:00:31    -1077.399853        0.117222

BFGS:   20 07:00:32    -1077.402525        0.104061

BFGS:   21 07:00:33    -1077.405155        0.104677

BFGS:   22 07:00:34    -1077.407705        0.090360

BFGS:   23 07:00:35    -1077.410088        0.097459

BFGS:   24 07:00:36    -1077.412228        0.074967

BFGS:   25 07:00:38    -1077.414167        0.081961

BFGS:   26 07:00:39    -1077.415916        0.082078

BFGS:   27 07:00:40    -1077.417398        0.079457

BFGS:   28 07:00:41    -1077.418632        0.049228
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: -0.541 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: -0.8270156798213417

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

E_mof_deform: 0.2857624145265163

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

E_ads: -0.5412532652948254

$E_{\mathrm{int}}$ 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
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¶