Analytical Approach to Screen Semiconducting MOFs Using Bloch Mode Analysis and Spectroscopic Measurements

A rapid and simple analytical approach is developed to screen the semiconducting properties of metal organic frameworks (MOFs) by modeling the band structure and predicting the density of state of isoreticular MOFs (IRMOFs). One can consider the periodic arrangement of metal nodes linked by organic subunits as a 1D periodic array crystal model, which can be aligned with any unit-cell axis included in the IRMOF's primitive cubic lattice. In such a structure, each valence electron of a metal atom feels the potential field of the entire periodic array. We allocate the 1D periodic array in a crystal unit cell to three IRMOFs-n (n = 1, 8, and 10) of the Zn₄O(L)₃ IRMOF series and apply the model to their crystal lattices with unit-cell constants a = 25.66, 30.09, and 34.28 Å, respectively. By solving Schrödinger's equation with a Kronig-Penney periodic potential and fitting the computed energy spectra to IRMOFs' experimental spectroscopic data, we model electronic band structures and obtain densities of state. The band diagram of each IRMOF reveals the nature of its electronic structures and density of state, allowing one to identify its n- or p-type semiconducting behavior. This novel analytical approach serves as a predictive and rapid screening tool to search the MOF database to identify potential semiconducting MOFs.