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-1p2p1")
calc = FAIRChemCalculator(predictor, task_name="odac")

Warp 1.18.0 initialized:
   CUDA Toolkit 13.4, Driver 13.1
   Devices:
     "cpu"      : "x86_64"
     "cuda:0"   : "Tesla T4" (16 GiB, sm_75, mempool enabled)
   Kernel cache:
     /home/runner/.cache/warp/1.18.0

WARNING:root:device was not explicitly set, using device='cuda'.

WARNING:root:UMA Nitro cannot serve this request: nitro mode supports only CUDA compute capability 8.x-12.x, not 7.5.

WARNING:root:Now running with nitro=False, execution_mode='umas_fast_gpu' (TF32).

WARNING:root:Running in a reduced-precision mode: some values, such as higher-order derivatives and phonon calculations, will be less accurate. For standard FP32 precision, use inference_settings='high-precision'.

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")

WARNING:root:Model is being compiled. This might take a while the first time.

WARNING:root:Running (unknown commit) with inference settings: multigpu

W1027 22:03:57.516000 9750 site-packages/torch/_logging/_internal.py:1345] [0/0] Profiler record function <class 'torch.autograd.profiler.record_function'> will be ignored

WARNING:root:The UMA fast path (merge_mole + compile) is only available for fixed composition, task, charge, and spin. This is optimized for MD applications. Falling back to a less optimized version for subsequent evaluations. Reason: 'Compositions differ from merged model'.
Use inference_settings='batch' for heterogeneous batched evaluations.

WARNING:root:Now running with merge_mole=False, compile=False, execution_mode='general' (TF32).

Adsorption energy of CO2 in Mg-MOF-74: -0.482 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 geometry 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 22:04:54    -1077.361727        0.157084

BFGS:    1 22:04:54    -1077.363819        0.092716

BFGS:    2 22:04:56    -1077.366761        0.102510

BFGS:    3 22:04:57    -1077.369805        0.112169

BFGS:    4 22:05:01    -1077.372811        0.108720

BFGS:    5 22:05:02    -1077.375103        0.081800

BFGS:    6 22:05:02    -1077.377096        0.059922

BFGS:    7 22:05:05    -1077.379166        0.081639

BFGS:    8 22:05:05    -1077.381439        0.086789

BFGS:    9 22:05:08    -1077.383770        0.074891

BFGS:   10 22:05:10    -1077.386161        0.097254

BFGS:   11 22:05:13    -1077.388719        0.102982

BFGS:   12 22:05:14    -1077.391364        0.103654

BFGS:   13 22:05:16    -1077.393878        0.092150

BFGS:   14 22:05:16    -1077.396289        0.108202

BFGS:   15 22:05:17    -1077.398861        0.132714

BFGS:   16 22:05:17    -1077.401808        0.117633

BFGS:   17 22:05:17    -1077.404709        0.076484

BFGS:   18 22:05:18    -1077.407172        0.077310

BFGS:   19 22:05:19    -1077.409308        0.096843

BFGS:   20 22:05:19    -1077.411622        0.094293

BFGS:   21 22:05:19    -1077.414302        0.097035
BFGS:   22 22:05:19    -1077.417215        0.104005

BFGS:   23 22:05:20    -1077.420047        0.076152

BFGS:   24 22:05:20    -1077.422612        0.092551

BFGS:   25 22:05:24    -1077.424984        0.075289

BFGS:   26 22:05:25    -1077.427308        0.088279

BFGS:   27 22:05:25    -1077.429529        0.086770

BFGS:   28 22:05:26    -1077.431508        0.069720

BFGS:   29 22:05:26    -1077.433200        0.064812

BFGS:   30 22:05:27    -1077.434720        0.050630

BFGS:   31 22:05:31    -1077.436135        0.067306

BFGS:   32 22:05:33    -1077.437480        0.061921

BFGS:   33 22:05:35    -1077.438762        0.054473

BFGS:   34 22:05:36    -1077.440056        0.040897
Energy of empty MOF: -1077.440 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 22:05:36    -1091.648157        1.137715

BFGS:    1 22:05:36    -1091.667006        0.323337

BFGS:    2 22:05:37    -1091.671332        0.231188

BFGS:    3 22:05:37    -1091.684672        0.293404

BFGS:    4 22:05:37    -1091.690923        0.233438

BFGS:    5 22:05:37    -1091.698612        0.197352

BFGS:    6 22:05:38    -1091.705230        0.197438

BFGS:    7 22:05:38    -1091.713828        0.253893

BFGS:    8 22:05:38    -1091.721813        0.223165

BFGS:    9 22:05:39    -1091.730000        0.200523

BFGS:   10 22:05:39    -1091.738725        0.221101

BFGS:   11 22:05:41    -1091.748961        0.290274

BFGS:   12 22:05:42    -1091.760313        0.285064

BFGS:   13 22:05:42    -1091.772073        0.191162

BFGS:   14 22:05:42    -1091.783890        0.190939

BFGS:   15 22:05:43    -1091.795383        0.272141

BFGS:   16 22:05:43    -1091.806223        0.314329

BFGS:   17 22:05:44    -1091.815600        0.230961

BFGS:   18 22:05:46    -1091.823825        0.138286

BFGS:   19 22:05:50    -1091.831509        0.132151

BFGS:   20 22:05:52    -1091.839423        0.146276

BFGS:   21 22:05:54    -1091.847564        0.154044

BFGS:   22 22:05:54    -1091.855795        0.170335

BFGS:   23 22:05:55    -1091.863479        0.150795

BFGS:   24 22:05:57    -1091.870203        0.177467

BFGS:   25 22:05:59    -1091.876215        0.271320

BFGS:   26 22:06:00    -1091.880606        0.307588

BFGS:   27 22:06:01    -1091.883678        0.564534

BFGS:   28 22:06:01    -1091.890124        0.162659

BFGS:   29 22:06:02    -1091.894710        0.097671

BFGS:   30 22:06:06    -1091.901064        0.124770

BFGS:   31 22:06:09    -1091.906084        0.227916

BFGS:   32 22:06:12    -1091.912303        0.176272

BFGS:   33 22:06:12    -1091.919348        0.131771

BFGS:   34 22:06:14    -1091.924831        0.168383

BFGS:   35 22:06:15    -1091.929644        0.294082

BFGS:   36 22:06:18    -1091.926169        0.924655

BFGS:   37 22:06:18    -1091.939384        0.121863

BFGS:   38 22:06:18    -1091.944028        0.104041

BFGS:   39 22:06:21    -1091.955875        0.249834

BFGS:   40 22:06:21    -1091.960026        0.248983

BFGS:   41 22:06:23    -1091.974412        0.263744

BFGS:   42 22:06:23    -1091.981631        0.131881

BFGS:   43 22:06:24    -1091.984498        0.792926

BFGS:   44 22:06:24    -1091.998011        0.164621

BFGS:   45 22:06:25    -1092.006805        0.203590

BFGS:   46 22:06:25    -1092.030106        0.473526

BFGS:   47 22:06:26    -1092.040989        0.183707

BFGS:   48 22:06:26    -1092.065414        0.248444

BFGS:   49 22:06:28    -1092.090531        0.380776

BFGS:   50 22:06:28    -1092.097876        1.131959

BFGS:   51 22:06:29    -1092.120389        0.460874

BFGS:   52 22:06:29    -1092.142659        0.389019

BFGS:   53 22:06:29    -1092.160367        0.359601

BFGS:   54 22:06:30    -1092.178404        0.271300

BFGS:   55 22:06:31    -1092.191369        0.512656

BFGS:   56 22:06:34    -1092.207031        0.679580

BFGS:   57 22:06:34    -1092.222595        0.687631

BFGS:   58 22:06:34    -1092.235564        0.423301

BFGS:   59 22:06:37    -1092.247942        0.160092

BFGS:   60 22:06:39    -1092.259184        0.157131

BFGS:   61 22:06:42    -1092.267919        0.182829

BFGS:   62 22:06:45    -1092.274801        0.120554

BFGS:   63 22:06:46    -1092.280008        0.093289

BFGS:   64 22:06:49    -1092.284890        0.125578

BFGS:   65 22:06:50    -1092.289714        0.112042

BFGS:   66 22:06:52    -1092.294385        0.123275

BFGS:   67 22:06:53    -1092.298931        0.135737

BFGS:   68 22:06:54    -1092.303558        0.233423

BFGS:   69 22:06:55    -1092.308260        0.264182

BFGS:   70 22:06:55    -1092.312664        0.208955

BFGS:   71 22:06:55    -1092.316594        0.098742

BFGS:   72 22:06:56    -1092.320084        0.085691

BFGS:   73 22:06:56    -1092.323370        0.087570

BFGS:   74 22:06:58    -1092.326317        0.091063

BFGS:   75 22:06:58    -1092.328913        0.072368

BFGS:   76 22:06:58    -1092.331195        0.083745

BFGS:   77 22:06:59    -1092.333414        0.096796

BFGS:   78 22:07:01    -1092.335551        0.087634

BFGS:   79 22:07:02    -1092.337547        0.066482

BFGS:   80 22:07:03    -1092.339352        0.103987

BFGS:   81 22:07:04    -1092.341101        0.145929

BFGS:   82 22:07:07    -1092.342959        0.145695

BFGS:   83 22:07:10    -1092.344928        0.106599

BFGS:   84 22:07:13    -1092.346843        0.051569

BFGS:   85 22:07:14    -1092.348572        0.072896

BFGS:   86 22:07:14    -1092.350101        0.109374

BFGS:   87 22:07:16    -1092.351467        0.075661

BFGS:   88 22:07:19    -1092.352654        0.047172
Energy of MOF + H2O: -1092.353 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: -1077.124 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 22:07:19    -1077.124456        1.249112

BFGS:    1 22:07:21    -1077.176465        1.034951

BFGS:    2 22:07:21    -1077.238391        0.694201

BFGS:    3 22:07:24    -1077.282887        0.444090

BFGS:    4 22:07:25    -1077.302237        0.369405

BFGS:    5 22:07:26    -1077.319342        0.344145

BFGS:    6 22:07:29    -1077.334904        0.330357

BFGS:    7 22:07:30    -1077.346959        0.246280

BFGS:    8 22:07:31    -1077.354422        0.146094

BFGS:    9 22:07:32    -1077.359574        0.150676

BFGS:   10 22:07:32    -1077.364407        0.187989

BFGS:   11 22:07:32    -1077.369508        0.170277

BFGS:   12 22:07:33    -1077.374687        0.143982

BFGS:   13 22:07:33    -1077.379769        0.124602

BFGS:   14 22:07:34    -1077.384653        0.140744

BFGS:   15 22:07:35    -1077.388976        0.110850

BFGS:   16 22:07:36    -1077.392561        0.090428

BFGS:   17 22:07:36    -1077.395769        0.092970

BFGS:   18 22:07:36    -1077.398952        0.108345

BFGS:   19 22:07:39    -1077.402116        0.114093

BFGS:   20 22:07:40    -1077.405256        0.103801

BFGS:   21 22:07:42    -1077.408397        0.105788

BFGS:   22 22:07:44    -1077.411466        0.096627

BFGS:   23 22:07:45    -1077.414359        0.099751

BFGS:   24 22:07:45    -1077.417052        0.080846

BFGS:   25 22:07:48    -1077.419559        0.080246

BFGS:   26 22:07:49    -1077.421788        0.076751

BFGS:   27 22:07:50    -1077.423636        0.076364

BFGS:   28 22:07:52    -1077.425185        0.051853

BFGS:   29 22:07:54    -1077.426672        0.071259

BFGS:   30 22:07:57    -1077.428243        0.079763

BFGS:   31 22:07:58    -1077.429745        0.074225

BFGS:   32 22:08:01    -1077.431051        0.049147
Energy of re-relaxed empty MOF: -1077.431 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: -0.542 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–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: -0.8573709850175231

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

E_mof_deform: 0.3156003030710508

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

E_ads: -0.5417706819464723

$E_{\mathrm{int}}$ 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¶

The Open DAC 2023 Dataset and Challenges for Sorbent Discovery in Direct Air Capture. (2024). 10.1021/acscentsci.3c01629
Carbon Dioxide Adsorption in Mg-MOF-74. (2015). 10.1039/C4SC02064B
Carbon Dioxide Adsorption in Mg-MOF-74. (2014). 10.1039/C3SC51319J
Carbon Dioxide Adsorption in Mg-MOF-74. (2018). 10.1021/acs.jpcc.8b00938
Framework Flexibility in Metal-Organic Frameworks. (2017). 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¶