Adsorption Energies

Adsorption Energies#

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 ( $E_{ads}$ ) is defined as:

\begin{matrix} (1) & E_{ads} = E_{MOF + CO 2} - E_{MOF} - E_{CO 2} \end{matrix}

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

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.

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-1p1")
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()

../../_images/1bc2dace0cab255f6fbec12f630170db9bcb837b8d23bf087fcfddfd8d5d110f.png

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: -0.459 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, $E_{MOF}$ , 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: $E_{MOF} (r_{MOF})$

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 01:39:47    -1077.274064        0.206406

BFGS:    1 01:39:47    -1077.276780        0.152729

BFGS:    2 01:39:48    -1077.281940        0.169926

BFGS:    3 01:39:48    -1077.284769        0.155780

BFGS:    4 01:39:48    -1077.288838        0.108779

BFGS:    5 01:39:48    -1077.291023        0.086441

BFGS:    6 01:39:49    -1077.293361        0.093435

BFGS:    7 01:39:49    -1077.295415        0.100095

BFGS:    8 01:39:49    -1077.297831        0.102518

BFGS:    9 01:39:49    -1077.300016        0.091608

BFGS:   10 01:39:50    -1077.302011        0.078980

BFGS:   11 01:39:50    -1077.304140        0.105576

BFGS:   12 01:39:50    -1077.306720        0.087929

BFGS:   13 01:39:50    -1077.309519        0.086369

BFGS:   14 01:39:51    -1077.312262        0.086852

BFGS:   15 01:39:51    -1077.314701        0.106260

BFGS:   16 01:39:51    -1077.316988        0.106196

BFGS:   17 01:39:51    -1077.319482        0.085481

BFGS:   18 01:39:52    -1077.322265        0.109655

BFGS:   19 01:39:52    -1077.325133        0.148706

BFGS:   20 01:39:52    -1077.327768        0.125920

BFGS:   21 01:39:52    -1077.329919        0.069115

BFGS:   22 01:39:52    -1077.331953        0.087283

BFGS:   23 01:39:53    -1077.334270        0.125252

BFGS:   24 01:39:53    -1077.336837        0.166678

BFGS:   25 01:39:53    -1077.339540        0.145561

BFGS:   26 01:39:53    -1077.342146        0.087615

BFGS:   27 01:39:54    -1077.344543        0.076205

BFGS:   28 01:39:54    -1077.346890        0.148949

BFGS:   29 01:39:54    -1077.349788        0.170234

BFGS:   30 01:39:54    -1077.352532        0.109299

BFGS:   31 01:39:55    -1077.354749        0.070312

BFGS:   32 01:39:55    -1077.356775        0.089657

BFGS:   33 01:39:55    -1077.358660        0.124320

BFGS:   34 01:39:55    -1077.360601        0.108063

BFGS:   35 01:39:56    -1077.362472        0.068663

BFGS:   36 01:39:56    -1077.364167        0.070245

BFGS:   37 01:39:56    -1077.365713        0.105391

BFGS:   38 01:39:56    -1077.367258        0.104402

BFGS:   39 01:39:57    -1077.368765        0.062637

BFGS:   40 01:39:57    -1077.370126        0.057785

BFGS:   41 01:39:57    -1077.371344        0.063997

BFGS:   42 01:39:57    -1077.372385        0.066973

BFGS:   43 01:39:58    -1077.373365        0.057745

BFGS:   44 01:39:58    -1077.374396        0.042126

Energy of empty MOF: -1077.374 eV

Next, we add the H₂O guest molecule and relax the MOF + adsorbate to obtain $E_{MOF + H 2 O} (r_{MOF + H 2 O})$ .

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 01:39:58    -1091.565588        1.145035

BFGS:    1 01:39:59    -1091.585062        0.314149

BFGS:    2 01:39:59    -1091.590212        0.243429

BFGS:    3 01:39:59    -1091.608171        0.237254

BFGS:    4 01:39:59    -1091.614633        0.227932

BFGS:    5 01:40:00    -1091.625217        0.186813

BFGS:    6 01:40:00    -1091.632355        0.178921

BFGS:    7 01:40:00    -1091.640630        0.175038

BFGS:    8 01:40:00    -1091.648041        0.184528

BFGS:    9 01:40:01    -1091.656144        0.160912

BFGS:   10 01:40:01    -1091.663841        0.178473

BFGS:   11 01:40:01    -1091.672298        0.188756

BFGS:   12 01:40:01    -1091.682088        0.157566

BFGS:   13 01:40:02    -1091.692983        0.177231

BFGS:   14 01:40:02    -1091.704439        0.158181

BFGS:   15 01:40:02    -1091.715512        0.191696

BFGS:   16 01:40:02    -1091.725712        0.197831

BFGS:   17 01:40:03    -1091.735331        0.163695

BFGS:   18 01:40:03    -1091.745539        0.151478

BFGS:   19 01:40:03    -1091.754027        0.170794

BFGS:   20 01:40:03    -1091.761500        0.153326

BFGS:   21 01:40:04    -1091.767892        0.152617

BFGS:   22 01:40:04    -1091.774205        0.166014

BFGS:   23 01:40:04    -1091.780886        0.135356

BFGS:   24 01:40:05    -1091.788355        0.180989

BFGS:   25 01:40:05    -1091.794283        0.204480

BFGS:   26 01:40:05    -1091.800638        0.131343

BFGS:   27 01:40:05    -1091.806519        0.189936

BFGS:   28 01:40:06    -1091.812303        0.199082

BFGS:   29 01:40:06    -1091.817181        0.151631

BFGS:   30 01:40:06    -1091.822210        0.100074

BFGS:   31 01:40:06    -1091.826300        0.125182

BFGS:   32 01:40:07    -1091.832529        0.177259

BFGS:   33 01:40:07    -1091.837117        0.246105

BFGS:   34 01:40:07    -1091.842046        0.112816

BFGS:   35 01:40:07    -1091.845773        0.331133

BFGS:   36 01:40:08    -1091.850859        0.173914

BFGS:   37 01:40:08    -1091.858471        0.159588

BFGS:   38 01:40:08    -1091.865280        0.141787

BFGS:   39 01:40:08    -1091.872006        0.139607

BFGS:   40 01:40:09    -1091.878240        0.266114

BFGS:   41 01:40:09    -1091.879824        0.597780

BFGS:   42 01:40:09    -1091.887409        0.530006

BFGS:   43 01:40:09    -1091.893885        0.247738

BFGS:   44 01:40:10    -1091.900308        0.178915

BFGS:   45 01:40:10    -1091.915874        0.233623

BFGS:   46 01:40:10    -1091.924363        0.389300

BFGS:   47 01:40:10    -1091.937921        0.267920

BFGS:   48 01:40:11    -1091.953105        0.451334

BFGS:   49 01:40:11    -1091.972261        0.650966

BFGS:   50 01:40:11    -1091.965140        1.527650

BFGS:   51 01:40:11    -1092.005189        0.412145

BFGS:   52 01:40:12    -1092.020963        0.279931

BFGS:   53 01:40:12    -1092.069785        0.308777

BFGS:   54 01:40:12    -1092.085938        0.302366

BFGS:   55 01:40:12    -1092.118688        0.691811

BFGS:   56 01:40:13    -1092.123713        0.369363

BFGS:   57 01:40:13    -1092.139152        0.209754

BFGS:   58 01:40:13    -1092.151227        0.237076

BFGS:   59 01:40:14    -1092.168240        0.349448

BFGS:   60 01:40:14    -1092.178640        0.385496

BFGS:   61 01:40:14    -1092.189915        0.336816

BFGS:   62 01:40:14    -1092.200339        0.255397

BFGS:   63 01:40:15    -1092.213032        0.183374

BFGS:   64 01:40:15    -1092.222258        0.193552

BFGS:   65 01:40:15    -1092.230834        0.158116

BFGS:   66 01:40:15    -1092.237093        0.104141

BFGS:   67 01:40:16    -1092.242582        0.112126

BFGS:   68 01:40:16    -1092.248284        0.143935

BFGS:   69 01:40:16    -1092.253348        0.149438

BFGS:   70 01:40:16    -1092.258586        0.116323

BFGS:   71 01:40:17    -1092.263462        0.101921

BFGS:   72 01:40:17    -1092.267491        0.133185

BFGS:   73 01:40:17    -1092.271215        0.149521

BFGS:   74 01:40:17    -1092.274783        0.132079

BFGS:   75 01:40:18    -1092.278109        0.111358

BFGS:   76 01:40:18    -1092.281503        0.096331

BFGS:   77 01:40:18    -1092.284606        0.094698

BFGS:   78 01:40:18    -1092.287030        0.095055

BFGS:   79 01:40:19    -1092.289597        0.079531

BFGS:   80 01:40:19    -1092.291638        0.071188

BFGS:   81 01:40:19    -1092.293462        0.072202

BFGS:   82 01:40:19    -1092.294991        0.080777

BFGS:   83 01:40:20    -1092.296340        0.081011

BFGS:   84 01:40:20    -1092.297769        0.076610

BFGS:   85 01:40:20    -1092.299244        0.082901

BFGS:   86 01:40:20    -1092.301079        0.071464

BFGS:   87 01:40:21    -1092.302674        0.061577

BFGS:   88 01:40:21    -1092.304527        0.056023

BFGS:   89 01:40:21    -1092.306063        0.064720

BFGS:   90 01:40:21    -1092.307444        0.054114

BFGS:   91 01:40:22    -1092.308748        0.053171

BFGS:   92 01:40:22    -1092.309763        0.061913

BFGS:   93 01:40:22    -1092.310655        0.061019

BFGS:   94 01:40:23    -1092.311391        0.054056

BFGS:   95 01:40:23    -1092.312157        0.044976

Energy of MOF + H2O: -1092.312 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 $E_{MOF} (r_{MOF + H 2 O})$ .

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: -1077.091 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 $r_{MOF + H 2 O}$ 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 01:40:23    -1077.090842        0.986442

BFGS:    1 01:40:23    -1077.123006        0.873281

BFGS:    2 01:40:24    -1077.172142        0.818488

BFGS:    3 01:40:24    -1077.210928        0.524014

BFGS:    4 01:40:24    -1077.230435        0.438096

BFGS:    5 01:40:24    -1077.246901        0.281661

BFGS:    6 01:40:25    -1077.257650        0.260293

BFGS:    7 01:40:25    -1077.266931        0.248066

BFGS:    8 01:40:25    -1077.276498        0.223251

BFGS:    9 01:40:25    -1077.283446        0.156257

BFGS:   10 01:40:26    -1077.288391        0.140787

BFGS:   11 01:40:26    -1077.292383        0.135912

BFGS:   12 01:40:26    -1077.295841        0.155181

BFGS:   13 01:40:26    -1077.300817        0.165285

BFGS:   14 01:40:27    -1077.305075        0.147316

BFGS:   15 01:40:27    -1077.309342        0.132313

BFGS:   16 01:40:27    -1077.313278        0.159774

BFGS:   17 01:40:27    -1077.317558        0.162286

BFGS:   18 01:40:28    -1077.322187        0.150076

BFGS:   19 01:40:28    -1077.325886        0.124297

BFGS:   20 01:40:28    -1077.328480        0.117647

BFGS:   21 01:40:28    -1077.330847        0.112662

BFGS:   22 01:40:29    -1077.333412        0.120923

BFGS:   23 01:40:29    -1077.336332        0.113709

BFGS:   24 01:40:29    -1077.339196        0.097602

BFGS:   25 01:40:29    -1077.341490        0.088436

BFGS:   26 01:40:30    -1077.343554        0.081498

BFGS:   27 01:40:30    -1077.345213        0.071598

BFGS:   28 01:40:30    -1077.347019        0.083949

BFGS:   29 01:40:30    -1077.348591        0.100711

BFGS:   30 01:40:31    -1077.350343        0.077874

BFGS:   31 01:40:31    -1077.351663        0.052155

BFGS:   32 01:40:31    -1077.352979        0.061598

BFGS:   33 01:40:31    -1077.354324        0.079844

BFGS:   34 01:40:32    -1077.355739        0.085233

BFGS:   35 01:40:32    -1077.357378        0.074236

BFGS:   36 01:40:32    -1077.358918        0.069354

BFGS:   37 01:40:32    -1077.360228        0.072352

BFGS:   38 01:40:33    -1077.361457        0.074052

BFGS:   39 01:40:33    -1077.362876        0.087442

BFGS:   40 01:40:33    -1077.364028        0.069788

BFGS:   41 01:40:33    -1077.365151        0.052757

BFGS:   42 01:40:34    -1077.366261        0.063634

BFGS:   43 01:40:34    -1077.367399        0.068825

BFGS:   44 01:40:34    -1077.368753        0.079137

BFGS:   45 01:40:34    -1077.370054        0.048170

Energy of re-relaxed empty MOF: -1077.370 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 ( $E_{MOF}$ 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: -0.689 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 $E_{int}$ and $E_{MOF, deform}$ , respectively, as

\begin{matrix} (2) & E_{int} = E_{MOF + H 2 O} (r_{MOF + H 2 O}) - E_{MOF} (r_{MOF + H 2 O}) - E_{H 2 O} (r_{MOF + H 2 O}) \end{matrix}

\begin{matrix} (3) & E_{MOF, deform} = E_{MOF} (r_{MOF + H 2 O}) - E_{MOF} (r_{MOF}) \end{matrix}

$E_{int}$ describes host host–guest interactions for the MOF in the adsorbed state only. $E_{MOF, deform}$ 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

\begin{matrix} (4) & E_{ads} = E_{int} + E_{MOF, deform} \end{matrix}

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: -0.9726162552831692

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

E_mof_deform: 0.2835540771484375

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

E_ads: -0.6890621781347317

$E_{int}$ is equivalent to $E_{ads}$ 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.

Adsorption Energies

Contents

Adsorption Energies#

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#