# Extending Libraries of Extremely Localized Molecular Orbitals to Metal Organic Frameworks: A Preliminary Investigation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{3}(BTC)

_{2}}

_{n}, with BTC=1,3,5-benzenetricarboxylate) to quickly calculate electrostatic potential maps in the small and large cavities inside the network. On the basis of the obtained results, we envisage further improvements and applications of this strategy, which can be also seen as a starting point to perform less computationally expensive quantum mechanical calculations on metal organic frameworks with the goal of investigating transformation phenomena such as chemisorption.

## 1. Introduction

## 2. Theoretical and Computational Details

#### 2.1. Extremely Localized Molecular Orbitals and ELMO Libraries

#### 2.2. ELMO-Protocol for MOFs

_{3}(BTC)

_{2}}

_{n}(where BTC stands for 1,3,5-benzenetricarboxylate), which is also commonly known as HKUST-1 (see Figure 2) [108,109]. Since the current ELMO libraries cover only the basic fragments of the twenty natural amino acids, it was primarily necessary to obtain tailor-made ELMOs computed on suitable model molecules of the MOF subunits.

- Construct a library of ELMOs describing the elementary fragments of the most common linkers employed for MOFs design.
- For each MOF crystal structure, perform ad hoc QM/ELMO calculations on model systems consisting of a SBU (at QM level) and the connected linkers (using ELMOs computed at step 1).
- The ELMOs for the linkers (see point 1) and the localized molecular orbitals for the SBU (obtained from point 2) will be finally transferred to the symmetry-related positions of the crystal structure using the ELMOdb program [61], thus quickly obtaining an approximate wavefunction/electron density for the periodic system.

## 3. Results and Discussion

## 4. Conclusions and Perspectives

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Examples of extremely localized molecular orbitals computed for acetamide (see panel (

**A**)) using a localization scheme corresponding to the Lewis diagram of the molecule: (

**B**) ELMO describing the lone pair of the nitrogen atom, (

**C**) ELMO associated with one of the two N-H bonds, (

**D**) ELMO corresponding to the N-C bond, (

**E**) ELMO describing the C-C bond, (

**F**) ELMO associated with one of the three C-H bonds, (

**G**,

**H**) ELMOs corresponding to the C=O double bond ($\sigma $ and $\pi $ orbitals, respectively), (

**I**,

**J**) ELMOs for the lone pairs of the oxygen atom. All the orbitals were computed with the cc-pVDZ basis set and were plotted considering a 0.15 a.u. isosurface.

**Figure 2.**Crystal structure of {Cu

_{3}(BTC)

_{2}}

_{n}(HKUST-1): (

**left**panel) unit-cell content with large and small cavities highlighted by ochre and blue spheres, respectively; (

**right**panel) paddlewheel model system for the QM/ELMO calculations.

**Figure 3.**NCI plots at different levels of theory with basis set 6-311G(2d,2p) for the model system extracted from the HKUST-1 experimental crystal structure with water chemisorption degree of 14.3(6)%. All the reduced-density gradient isosurfaces correspond to the 0.4 a.u. isovalue and are colored according to the BGR (blue-green-red) scheme over the range −5.0 a.u < $\mathrm{sign}\left({\lambda}_{2}\right)\rho $ < 5.0 a.u.

**Figure 4.**Zoom on the Cu-Cu subunit of the NCI plots depicted in Figure 3. All the reduced-density gradient isosurfaces correspond to the 0.4 a.u. isovalue and are colored according to the BGR (blue-green-red) scheme over the range −5.0 a.u < $\mathrm{sign}\left({\lambda}_{2}\right)\rho $ < 5.0 a.u.

**Figure 5.**Electrostatic potential maps at different levels of theory with basis set 6-311G(2d,2p) for the model system extracted from the HKUST-1 experimental crystal structure with a water chemisorption degree of 14.3(6)%. The electrostatic potentials were plotted on the corresponding 0.05 a.u. electron density isosurfaces according to the RWB (red-white-blue) scheme over the range [−0.1 a.u., 0.1 a.u.].

**Figure 6.**Electrostatic potential maps for the large cavity of HKUST-1 (

**A**) without water molecules and (

**B**) in the presence of water molecules, plotted both on the 0.05 a.u. isosurface of the electron density and as isocontour lines in the middle of the pore. The color scale for the maps is given on the right-hand side of the figure.

**Figure 7.**Electrostatic potential maps for the small cavity of HKUST-1 (

**A**) without water molecules and (

**B**) in the presence of water molecules, plotted both on the 0.05 a.u. isosurface of the electron density and as isocontour lines in the middle of the pore. The color scale for the maps is given on the right-hand side of the figure.

**Table 1.**Properties at the bond critical point between the Cu atoms and between the Cu and O atoms, as obtained from the calculations performed at different levels of theory with basis set 6-311G(2d,2p) on the model system extracted from the HKUST-1 experimental crystal structure with a water chemisorption degree of 14.3(6)%.

^{(a)}

Interaction | Spin State | Calculation | ${\mathit{\rho}}_{\mathit{b}\mathit{c}\mathit{p}}$ | ${\nabla}^{\mathit{2}}{\mathit{\rho}}_{\mathit{b}\mathit{c}\mathit{p}}$ | $\left|{\mathit{V}}_{\mathit{b}\mathit{c}\mathit{p}}\right|/{\mathit{G}}_{\mathit{b}\mathit{c}\mathit{p}}$ | $-{\mathit{K}}_{\mathit{b}\mathit{c}\mathit{p}}$ | $\mathit{D}\mathit{I}$ |
---|---|---|---|---|---|---|---|

Cu-Cu | Diamagnetic | B3LYP/ELMO | 0.029 | 0.075 | 1.344 | −0.0098 | 1.031 |

Standard B3LYP | 0.036 | 0.069 | 1.423 | −0.0127 | 0.426 | ||

Anti-Ferromagnetic | B3LYP/ELMO | 0.029 | 0.074 | 1.348 | −0.0099 | 0.100 | |

Standard B3LYP | 0.035 | 0.070 | 1.410 | −0.0122 | 0.146 | ||

Ferromagnetic | B3LYP/ELMO | 0.029 | 0.074 | 1.348 | −0.0099 | 0.100 | |

Standard B3LYP | 0.035 | 0.070 | 1.409 | −0.0121 | 0.144 | ||

Cu-O | Diamagnetic | B3LYP/ELMO | 0.066 | 0.614 | 0.956 | 0.0065 | 0.227 |

Standard B3LYP | 0.095 | 0.462 | 1.140 | −0.0189 | 0.429 | ||

Anti-Ferromagnetic | B3LYP/ELMO | 0.065 | 0.626 | 0.943 | 0.0084 | 0.233 | |

Standard B3LYP | 0.093 | 0.477 | 1.127 | −0.0174 | 0.466 | ||

Ferromagnetic | B3LYP/ELMO | 0.065 | 0.626 | 0.943 | 0.0084 | 0.233 | |

Standard B3LYP | 0.093 | 0.478 | 1.127 | −0.0173 | 0.466 |

^{(a)}${\rho}_{bcp}$ and ${\nabla}^{2}{\rho}_{bcp}$ are, respectively, the electron density (e/bohr

^{3}) and the Laplacian of the electron density (e/bohr

^{5}) at the bond critical point; $\left|{V}_{bcp}\right|/{G}_{bcp}$ is the ratio between the potential and the kinetic energy density at the bond critical point; $-{K}_{bcp}$ is the total bond energy density at the bond critical point (hartree/bohr

^{3}); and DI is the delocalization index (electron pairs shared between two atoms).

**Table 2.**Bader charges and volumes (0.001 e/bohr

^{3}isosurface) for the Cu and O atoms, as obtained from calculations performed at different levels of theory with basis set 6-311G(2d,2p) on the model system extracted from the HKUST-1 experimental crystal structure with a water chemisorption degree of 14.3(6)%.

^{(a)}

Spin State | Calculation | ${\mathit{q}}_{\mathit{C}\mathit{u}\mathit{1}}$ | ${\mathit{q}}_{\mathit{C}\mathit{u}\mathbf{2}}$ | ${\mathit{q}}_{\mathit{O}}$ | ${\mathit{V}}_{\mathit{C}\mathit{u}\mathit{1}}$ | ${\mathit{V}}_{\mathit{C}\mathit{u}\mathit{2}}$ | ${\mathit{V}}_{\mathit{O}}$ |
---|---|---|---|---|---|---|---|

Diamagnetic | B3LYP/ELMO | 1.79 | 1.79 | −1.42 | 61.50 | 61.50 | 109.45 |

Standard B3LYP | 1.10 | 1.10 | −1.13 | 75.03 | 75.03 | 104.62 | |

Anti-Ferromagnetic | B3LYP/ELMO | 1.79 | 1.79 | −1.42 | 61.52 | 61.52 | 109.46 |

Standard B3LYP | 1.20 | 1.20 | −1.16 | 73.41 | 73.41 | 104.95 | |

Ferromagnetic | B3LYP/ELMO | 1.79 | 1.79 | −1.42 | 61.52 | 61.52 | 109.46 |

Standard B3LYP | 1.21 | 1.21 | −1.16 | 73.35 | 73.35 | 104.97 |

^{(a)}Charges in electrons (e) and volumes in bohr

^{3}.

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**MDPI and ACS Style**

Wieduwilt, E.K.; Macetti, G.; Scatena, R.; Macchi, P.; Genoni, A. Extending Libraries of Extremely Localized Molecular Orbitals to Metal Organic Frameworks: A Preliminary Investigation. *Crystals* **2021**, *11*, 207.
https://doi.org/10.3390/cryst11020207

**AMA Style**

Wieduwilt EK, Macetti G, Scatena R, Macchi P, Genoni A. Extending Libraries of Extremely Localized Molecular Orbitals to Metal Organic Frameworks: A Preliminary Investigation. *Crystals*. 2021; 11(2):207.
https://doi.org/10.3390/cryst11020207

**Chicago/Turabian Style**

Wieduwilt, Erna K., Giovanni Macetti, Rebecca Scatena, Piero Macchi, and Alessandro Genoni. 2021. "Extending Libraries of Extremely Localized Molecular Orbitals to Metal Organic Frameworks: A Preliminary Investigation" *Crystals* 11, no. 2: 207.
https://doi.org/10.3390/cryst11020207