Calculation of the Refractive Index of Metal-Organic Frameworks Using Empirical Electronic Polarizabilities

The prediction of optical properties from the chemical composition is of great value in developing new materials for optical applications. In this study, an approach for the calculation of the refractive index (RI) of hybrid materials from empirical polarizabilities is presented. Metal–organic frameworks (MOFs) are a prominent class of hybrid inorganic–organic materials with a modular design. This allows the fine-tuning of their optical properties. For the calculation of the RI of hybrid materials like MOFs using empirical electronic polarizabilities, a fragmentation is required. In this process, the MOF is split into its modular components, the linkers and the inorganic building units (IBUs). The electronic polarizabilities of the linkers are calculated using refractivities obtained from organic compounds. To calculate the electronic polarizabilities of the IBUs, the electronic polarizabilities of ions derived from minerals are used. With a combination of these values the MOF’s RI is calculated. Therefore, the Anderson-Eggleton equation is used with an optimized c parameter. This approach was applied to a set of 19 MOFs including Zr-based MOFs and zeolitic imidazolate frameworks (ZIFs). In a first step, the calculated polarizability values of the modular components were compared to theoretical polarizability values obtained from density functional theory (DFT) calculations. In addition, the predicted RI values are validated using HSE06 hybrid DFT calculations and available high quality experimental data. The examination of the MOF set highlighted the use of empirical electronic polarizabilities as a facile approach allowing quantitative predictions of the RI with a mean deviation from the periodic DFT calculations of 1.60%.