Structural properties of metal-organic frameworks within the density-functional based tight-binding method

Density-functional based tight-binding (DFTB) is a powerful method to describe large molecules and materials. Metal-organic frameworks (MOFs), materials with interesting catalytic properties and with very large surface areas, have been developed and have become commercially available. Unit cells of MOFs typically include hundreds of atoms, which make the application of standard density-functional methods computationally very expensive, sometimes even unfeasible. The aim of this paper is to prepare and to validate the self-consistent charge-DFTB (SCC-DFTB) method for MOFs containing Cu, Zn, and Al metal centers. The method has been validated against full hybrid density-functional calculations for model clusters, against gradient corrected density-functional calculations for supercells, and against experiment. Moreover, the modular concept of MOF chemistry has been discussed on the basis of their electronic properties. We concentrate on MOFs comprising three common connector units: copper paddlewheels (HKUST-1), zinc oxide Zn₄O tetrahedron (MOF-5, MOF-177, DUT-6 (MOF-205)), and aluminum oxide AlO₄(OH)₂ octahedron (MIL-53). We show that SCC-DFTB predicts structural parameters with a very good accuracy (with less than 5% deviation, even for adsorbed CO and H₂O on HKUST-1), while adsorption energies differ by 12kJmol^-1 or less for CO and water compared to DFT benchmark calculations.