The structural phase transitions of MF_3 (M=Al, Cr, V, Fe, Ti, Sc) metal trifluorides are studied within a simple Landau theory consisting of tilts of rigid MF_6 octahedra associated with soft antiferrodistoritive optic modes that are coupled to long-wavelength strain generating acoustic phonons. We calculate the temperature and pressure dependence of several quantities such as the spontaneous distortions, volume expansion and shear strains as well as T-P phase diagrams. By contrasting our

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... to experiments we quantify the deviations from mean-field behavior and found that the tilt fluctuations of the MF_6 octahedra increase with metal cation size. We apply our model to predict giant barocaloric effects in Sc substituted TiF_3 of up to about 15 JK^-1kg^-1 for modest hydrostatic compressions of 0.2 GPa. The effect extends over a wide temperature range of over 140 K (including room temperature) due to a large predicted rate dT_c/dP = 723 K GPa^-1, which exceeds those of typical barocaloric materials. Our results suggest that open lattice frameworks such as the trifluorides are an attractive platform to search for giant barocaloric effects.