Low-temperature anomaly in heat capacity due to overlapping the spectrums in molecular crystals

Investigations of dynamic and thermodynamic properties for a molecular crystal tris-hexafluoroacetylacetonate-iron $Fe(O_2C_5HF_6)_3$ are presented. Heat capacity $C_p(T)$ has been measured by adiabatic calorimetry method in the temperature range $4.8-321 K$. An anomaly with a maximum at $T_c = 44.6 K$ has been discovered. Intermolecular vibrations spectrum was calculated by lattice dynamics method in quasiharmonic approximation. Intramolecular frequencies are found by solving the Schr\"odinger equation in approach of small harmonic oscillations. In the frequency interval $\approx 30-70 cm^{-1}$ overlapping the spectrums intra- and intermolecular oscillations has been found. The good agreement for calculated and experimental $C_p(T)$ occurred to be possible for two sets of the force constants. These sets describe two phases above and below $T_c$. The difference between phases is connected with freezing of rotation $CF_3$ groups. It has been concluded that the interaction between different modes leads to phase transition and anomaly in heat capacity.