# Metal-Organic Framework Breathing in Electric Field: A Theoretical Study

## TL;DR

This theoretical study models the electrically induced breathing behavior of Metal-Organic Frameworks using a 2D lattice approach, revealing hysteresis and structural transitions consistent with molecular dynamics simulations.

## Contribution

It introduces a theoretical framework for MOF breathing under electric fields, incorporating electrostatic and elastic energies with symmetry considerations.

## Key findings

- Hysteresis observed in structural transition regions.
- Electric field influences unit cell parameters and polarization.
- Qualitative agreement with molecular dynamics simulations.

## Abstract

In this manuscript, we study the electrically induced breathing of Metal-Organic Framework (MOF) within a 2D lattice model. The Helmholtz free energy of the MOF in electric field consists of two parts: the electrostatic energy of the dielectric body in the external electric field and elastic energy of the framework. The first contribution is calculated from the first principles of statistical mechanics with an account of MOF symmetry. By minimizing the obtained free energy and solving the resulting system of equations, we obtain the local electric field and the parameter of the unit cell (angle $\alpha$). The paper also studies the cross-section area of the unit cell and the polarization as functions of the external electric field. We obtain the hysteresis in the region of the structural transition of the framework. Our results are in qualitative agreement with the literature data of the molecular dynamics (MD) simulation of MIL-53(Cr).