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'.

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 for the first time

W1007 02:59:59.613000 9587 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.

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 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 03:00:59    -1077.361728        0.157085

BFGS:    1 03:01:00    -1077.363819        0.092716

BFGS:    2 03:01:01    -1077.366761        0.102512

BFGS:    3 03:01:03    -1077.369806        0.112174

BFGS:    4 03:01:03    -1077.372809        0.108710

BFGS:    5 03:01:06    -1077.375104        0.081817

BFGS:    6 03:01:07    -1077.377097        0.059926

BFGS:    7 03:01:08    -1077.379165        0.081631

BFGS:    8 03:01:09    -1077.381439        0.086745

BFGS:    9 03:01:10    -1077.383768        0.074753

BFGS:   10 03:01:10    -1077.386165        0.097186

BFGS:   11 03:01:13    -1077.388725        0.102922

BFGS:   12 03:01:17    -1077.391370        0.102110

BFGS:   13 03:01:19    -1077.393886        0.092764

BFGS:   14 03:01:20    -1077.396292        0.108275

BFGS:   15 03:01:20    -1077.398863        0.132848

BFGS:   16 03:01:21    -1077.401809        0.117695

BFGS:   17 03:01:21    -1077.404709        0.076294

BFGS:   18 03:01:22    -1077.407170        0.077397

BFGS:   19 03:01:23    -1077.409312        0.096906

BFGS:   20 03:01:24    -1077.411621        0.094306

BFGS:   21 03:01:24    -1077.414302        0.096983

BFGS:   22 03:01:25    -1077.417217        0.103968

BFGS:   23 03:01:25    -1077.420047        0.076053

BFGS:   24 03:01:26    -1077.422612        0.092562

BFGS:   25 03:01:26    -1077.424985        0.075280

BFGS:   26 03:01:28    -1077.427307        0.088241

BFGS:   27 03:01:28    -1077.429531        0.086665

BFGS:   28 03:01:29    -1077.431508        0.069691

BFGS:   29 03:01:31    -1077.433203        0.064779

BFGS:   30 03:01:34    -1077.434718        0.050624

BFGS:   31 03:01:35    -1077.436141        0.067221

BFGS:   32 03:01:37    -1077.437481        0.061927

BFGS:   33 03:01:37    -1077.438758        0.054399

BFGS:   34 03:01:37    -1077.440062        0.040901
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 03:01:38    -1091.648156        1.137715

BFGS:    1 03:01:39    -1091.667005        0.323337

BFGS:    2 03:01:42    -1091.671332        0.231188

BFGS:    3 03:01:46    -1091.684672        0.293447

BFGS:    4 03:01:48    -1091.690921        0.233354

BFGS:    5 03:01:51    -1091.698610        0.197337

BFGS:    6 03:01:55    -1091.705228        0.197557

BFGS:    7 03:01:56    -1091.713826        0.253841

BFGS:    8 03:01:56    -1091.721811        0.222957

BFGS:    9 03:02:00    -1091.729995        0.200693

BFGS:   10 03:02:01    -1091.738721        0.221133

BFGS:   11 03:02:02    -1091.748961        0.290418

BFGS:   12 03:02:02    -1091.760310        0.285148

BFGS:   13 03:02:03    -1091.772074        0.191192

BFGS:   14 03:02:04    -1091.783889        0.190957

BFGS:   15 03:02:04    -1091.795379        0.272311

BFGS:   16 03:02:05    -1091.806226        0.314385

BFGS:   17 03:02:05    -1091.815598        0.230622

BFGS:   18 03:02:06    -1091.823823        0.138258

BFGS:   19 03:02:07    -1091.831508        0.132802

BFGS:   20 03:02:07    -1091.839420        0.145287

BFGS:   21 03:02:08    -1091.847562        0.153910

BFGS:   22 03:02:10    -1091.855785        0.170223

BFGS:   23 03:02:10    -1091.863478        0.151220

BFGS:   24 03:02:11    -1091.869871        0.291391

BFGS:   25 03:02:12    -1091.873210        0.346870

BFGS:   26 03:02:13    -1091.879866        0.281666

BFGS:   27 03:02:13    -1091.884996        0.293107

BFGS:   28 03:02:14    -1091.891702        0.254318

BFGS:   29 03:02:17    -1091.896283        0.169706

BFGS:   30 03:02:17    -1091.902429        0.165910

BFGS:   31 03:02:18    -1091.908684        0.184083

BFGS:   32 03:02:19    -1091.903131        0.970479

BFGS:   33 03:02:20    -1091.917586        0.232307

BFGS:   34 03:02:21    -1091.921236        0.186875

BFGS:   35 03:02:21    -1091.929301        0.559320

BFGS:   36 03:02:22    -1091.934649        0.107758

BFGS:   37 03:02:23    -1091.939357        0.113791

BFGS:   38 03:02:23    -1091.951233        0.202961

BFGS:   39 03:02:23    -1091.955511        0.255386

BFGS:   40 03:02:24    -1091.965732        0.275891

BFGS:   41 03:02:25    -1091.973826        0.278334

BFGS:   42 03:02:25    -1091.983656        0.127159

BFGS:   43 03:02:26    -1091.981491        1.028268

BFGS:   44 03:02:26    -1091.998888        0.182957

BFGS:   45 03:02:29    -1092.006735        0.170926

BFGS:   46 03:02:30    -1092.031134        0.611769

BFGS:   47 03:02:30    -1092.043195        0.201287

BFGS:   48 03:02:31    -1092.060177        0.224321

BFGS:   49 03:02:31    -1092.089467        0.361747

BFGS:   50 03:02:32    -1092.107736        0.774038

BFGS:   51 03:02:32    -1092.124024        0.478346

BFGS:   52 03:02:33    -1092.154814        0.381700

BFGS:   53 03:02:34    -1092.167540        0.301699

BFGS:   54 03:02:34    -1092.182629        0.356056

BFGS:   55 03:02:35    -1092.197770        0.627775

BFGS:   56 03:02:35    -1092.213467        0.712987

BFGS:   57 03:02:36    -1092.228885        0.521702

BFGS:   58 03:02:36    -1092.242795        0.222555

BFGS:   59 03:02:39    -1092.254508        0.140366

BFGS:   60 03:02:40    -1092.264164        0.165742

BFGS:   61 03:02:40    -1092.271887        0.125280

BFGS:   62 03:02:41    -1092.277466        0.102071

BFGS:   63 03:02:41    -1092.282340        0.122535

BFGS:   64 03:02:42    -1092.287140        0.142831

BFGS:   65 03:02:43    -1092.291954        0.123931

BFGS:   66 03:02:43    -1092.296538        0.142895

BFGS:   67 03:02:44    -1092.301229        0.220773

BFGS:   68 03:02:44    -1092.306129        0.247880

BFGS:   69 03:02:45    -1092.310826        0.208348

BFGS:   70 03:02:46    -1092.314869        0.098626

BFGS:   71 03:02:46    -1092.318484        0.091698

BFGS:   72 03:02:49    -1092.321843        0.075553

BFGS:   73 03:02:50    -1092.324946        0.078337

BFGS:   74 03:02:50    -1092.327617        0.069815

BFGS:   75 03:02:51    -1092.329989        0.083589

BFGS:   76 03:02:51    -1092.332245        0.096711

BFGS:   77 03:02:52    -1092.334466        0.085656

BFGS:   78 03:02:53    -1092.336511        0.072525

BFGS:   79 03:02:53    -1092.338342        0.100801

BFGS:   80 03:02:56    -1092.340115        0.146292

BFGS:   81 03:02:57    -1092.341984        0.143164

BFGS:   82 03:02:57    -1092.343951        0.105547

BFGS:   83 03:02:58    -1092.345906        0.054866

BFGS:   84 03:02:59    -1092.347718        0.064837

BFGS:   85 03:03:00    -1092.349363        0.095342

BFGS:   86 03:03:00    -1092.350828        0.067640

BFGS:   87 03:03:02    -1092.352074        0.041764
Energy of MOF + H2O: -1092.352 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: -1077.126 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 03:03:02    -1077.125631        1.242060

BFGS:    1 03:03:05    -1077.177332        1.030568

BFGS:    2 03:03:05    -1077.239276        0.691275

BFGS:    3 03:03:06    -1077.283608        0.444915

BFGS:    4 03:03:09    -1077.302940        0.365988

BFGS:    5 03:03:12    -1077.320068        0.342455

BFGS:    6 03:03:13    -1077.335710        0.329826

BFGS:    7 03:03:13    -1077.347778        0.244605

BFGS:    8 03:03:13    -1077.355188        0.143468

BFGS:    9 03:03:14    -1077.360298        0.149044

BFGS:   10 03:03:17    -1077.365141        0.188222

BFGS:   11 03:03:20    -1077.370249        0.171478

BFGS:   12 03:03:21    -1077.375429        0.145427

BFGS:   13 03:03:22    -1077.380506        0.122569

BFGS:   14 03:03:22    -1077.385394        0.141314

BFGS:   15 03:03:22    -1077.389735        0.112399

BFGS:   16 03:03:24    -1077.393318        0.088372

BFGS:   17 03:03:24    -1077.396494        0.091595

BFGS:   18 03:03:25    -1077.399653        0.107278

BFGS:   19 03:03:28    -1077.402794        0.114057

BFGS:   20 03:03:30    -1077.405922        0.103159

BFGS:   21 03:03:32    -1077.409038        0.106028

BFGS:   22 03:03:33    -1077.412086        0.094571

BFGS:   23 03:03:34    -1077.414947        0.098399

BFGS:   24 03:03:35    -1077.417604        0.080500

BFGS:   25 03:03:35    -1077.420070        0.080954

BFGS:   26 03:03:36    -1077.422270        0.076457

BFGS:   27 03:03:37    -1077.424090        0.076859

BFGS:   28 03:03:37    -1077.425624        0.051165

BFGS:   29 03:03:38    -1077.427087        0.070819

BFGS:   30 03:03:38    -1077.428641        0.079939

BFGS:   31 03:03:39    -1077.430131        0.075364

BFGS:   32 03:03:39    -1077.431433        0.050538

BFGS:   33 03:03:40    -1077.432639        0.052611

BFGS:   34 03:03:42    -1077.433962        0.056413

BFGS:   35 03:03:42    -1077.435446        0.086223

BFGS:   36 03:03:42    -1077.436965        0.082802

BFGS:   37 03:03:43    -1077.438323        0.066014

BFGS:   38 03:03:43    -1077.439580        0.068227

BFGS:   39 03:03:44    -1077.440801        0.056699

BFGS:   40 03:03:45    -1077.442278        0.058103

BFGS:   41 03:03:45    -1077.443234        0.057014

BFGS:   42 03:03:46    -1077.444516        0.054631

BFGS:   43 03:03:47    -1077.445616        0.056188

BFGS:   44 03:03:50    -1077.446629        0.044178
Energy of re-relaxed empty MOF: -1077.447 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: -0.8554720883534994

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

E_mof_deform: 0.31443114251214865

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

E_ads: -0.5410409458413508

$E_{\mathrm{int}}$ 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¶