Calculation of the infrared frequency and the damping constant (full width at half maximum) for metal organic frameworks

The ρ(NH₂) infrared (IR) frequencies and the corresponding full width at half maximum (FWHM) values for (CH₃)₂NH₂Fe^III M ^II(HCOO)₆ (DMFeM, M = Ni, Zn, Cu, Fe, and Mg) are analyzed at various temperatures by using the experimental data from the literature. For the analysis of the IR frequencies of the ρ(NH₂) mode which is associated with the structural phase transitions in those metal structures, the temperature dependence of the mode frequency is assumed as an order parameter and the IR frequencies are calculated by using the molecular field theory. Also, the temperature dependence of the IR frequencies and of the damping constant as calculated from the models of pseudospin (dynamic disorder of dimethylammonium (DMA⁺) cations)–phonon coupling (PS) and of the energy fluctuation (EF), is fitted to the observed data for the wavenumber and FWHM of the ρ(NH₂) IR mode of the niccolites studied here. We find that the observed behavior of the IR frequencies and the FWHM of this mode can be described adequately by the models studied for the crystalline structures of interest. This method of calculating the frequencies (IR and Raman) and FWHM of modes which are responsible for the phase transitions can also be applied to some other metal organic frameworks. (paper)