# Compressing the Channels in the Crystal Structure of Copper Squarate Metal-Organic Framework

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## Abstract

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## 1. Introduction

## 2. Methods

## 3. Results

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Computed crystal structure of copper squarate: view of a 2 × 2 × 2 supercell from [0 0 1] direction. Color code: Cu—orange; C—gray; O—red.

**Figure 2.**A channel in the crystal structure of copper squarate displayed by means of the corresponding solvent-accessible surface in a 1 $\times $ 1 $\times $ 5 supercell.

**Figure 3.**Two-dimensional projections on the xy plane of the tridimensional representations of the elastic properties of copper squarate as a function of the orientation of the applied stress: (

**A**) Compressibility; (

**B**) Young modulus; (

**C**) Maximum shear modulus; (

**D**) Maximum (blue) and minimum (red) Poisson’s ratios. The labels of the marks in the vertical axis are exactly the same as those of the horizontal one. In the plots, negative values are displayed in red.

**Figure 4.**Two-dimensional projections on the xz plane of the tridimensional representations of the elastic properties of copper squarate as a function of the orientation of the applied stress: (

**A**) Compressibility; (

**B**) Young modulus; (

**C**) Maximum shear modulus; (

**D**) Maximum (blue) and minimum (red) Poisson’s ratios. The labels of the marks in the vertical axis are exactly the same as those of the horizontal one. In the plots, negative values are displayed in red.

**Figure 5.**(

**A**) Computed unit cell volume of copper squarate as a function of the applied isotropic pressure; (

**B**) a lattice parameter; (

**C**) b lattice parameter; (

**D**) c lattice parameter; (

**E**) Compressibility along [1 0 0] crystallographic direction, ${k}_{a}=-1/a\xb7{\left(\partial a/\partial P\right)}_{P}$.

**Figure 6.**(

**A**) Computed unit cell volume of copper squarate as a function of the external stress applied along the [1 0 0] crystallographic direction; (

**B**) a lattice parameter; (

**C**) b lattice parameter; (

**D**) c lattice parameter; (

**E**) Volumetric compressibility, ${k}_{V}=-1/V\xb7{\left(\partial V/\partial P\right)}_{P}$.

**Figure 7.**The structure of copper squarate under increasing isotropic pressures. View of a 2 $\times $ 1 $\times $ 1 supercell from [0 0 1] direction showing two structural channels at different pressures: P = 0.0, 1.0, 1.5, 2.0 and 3.0 GPa. The meaning of the width of a channel (${\omega}_{ch}$ ) as measured by the distance between two opposite oxygen atoms is illustrated in the structure at P = 0.0 GPa. The values of ${\omega}_{ch}$ are 8.154, 8.300, 8.810, 9.193 and 9.277 $\AA $, respectively.

**Figure 8.**The structure of copper squarate under different stresses applied along [1 0 0] direction. View of a 2 $\times $ 1 $\times $ 1 supercell showing two structural channels at different stresses: P = −0.17, –0.08, 0.0, 0.08 and 0.17 GPa.

Parameter | $\mathit{\alpha}$$\left(\mathbf{\AA}\right)$ | $\mathit{b}$$\left(\mathbf{\AA}\right)$ | $\mathit{c}$$\left(\mathbf{\AA}\right)$ | $\mathit{\alpha}\left(\mathbf{deg}\right)$ | $\mathit{\beta}\left(\mathbf{deg}\right)$ | $\mathit{\gamma}\left(\mathbf{deg}\right)$ | $\mathbf{Vol}.\left({\mathbf{\AA}}^{3}\right)$ | $\mathit{\rho}$$(\mathbf{gr}/\mathbf{c}{\mathbf{m}}^{3})$ |
---|---|---|---|---|---|---|---|---|

PBE | 11.1926 | 9.1271 | 5.7595 | 90.0 | 116.07 | 90.0 | 528.5049 | 2.207 |

PBE + disp | 11.1578 | 9.1640 | 5.5982 | 90.0 | 117.78 | 90.0 | 506.4448 | 2.303 |

B3LYP | 11.1829 | 9.2835 | 5.9160 | 90.0 | 114.88 | 90.0 | 557.1953 | 2.093 |

PBEsol | 11.0961 | 9.0074 | 5.6076 | 90.0 | 116.26 | 90.0 | 502.6355 | 2.320 |

Exp. [25] | 10.6869(4) | 8.9394(4) | 5.6747(1) | 90.0 | 117.60(2) | 90.0 | 480.4546 | 2.427 |

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**MDPI and ACS Style**

Colmenero, F.; Lobato, Á.; Timón, V.
Compressing the Channels in the Crystal Structure of Copper Squarate Metal-Organic Framework. *Solids* **2022**, *3*, 374-384.
https://doi.org/10.3390/solids3020026

**AMA Style**

Colmenero F, Lobato Á, Timón V.
Compressing the Channels in the Crystal Structure of Copper Squarate Metal-Organic Framework. *Solids*. 2022; 3(2):374-384.
https://doi.org/10.3390/solids3020026

**Chicago/Turabian Style**

Colmenero, Francisco, Álvaro Lobato, and Vicente Timón.
2022. "Compressing the Channels in the Crystal Structure of Copper Squarate Metal-Organic Framework" *Solids* 3, no. 2: 374-384.
https://doi.org/10.3390/solids3020026