Estimate of the vibrational contribution to the entropy change associated with the spin transition in the d⁴ systems [Mn^III(pyrol) ₃tren] and [Cr^II(depe)₂I₂]

The vibrational contribution to ΔS of the low-spin ( ³T₁) to high-spin (⁵E) spin transition in two 3d⁴ octahedral systems [Mn^III(pyrol)₃tren] and [Cr(depe)₂I₂] have been estimated by means of DFT calculations (B3LYP/CEP-31G) of the vibrational normal-modes frequencies. The obtained value at the transition temperature for the Mn(iii) complex is ΔS_vib(44 K) = 6.3 J K^-1 mol^-1, which is comparable with the proposed Jahn-Teller contribution of R 1n3 = 9.1 J K ^-1 mol^-1 and which is approximately half of the experimentally determined 13.8 J K^-1 mol^-1. The corresponding value for the Cr(ii) complex is ΔS_vib(171.45 K) = 46.5 J K^-1 mol^-1, as compared to the experimental value of 39.45 J K^-1 mol^-1. The analysis of the vibrational normal modes reveals that for the d⁴ systems under study, contrary to Fe(ii) d⁶ systems, not all metal-ligand stretching vibrations make a contribution. For the Mn(iii) complex, the only vibration that contributes to ΔS_vib involve the nitrogens occupying the Jahn-Teller axis, while in the case of Cr(ii) the contributing vibrations involve the Cr-I bonds. Low-frequency modes due to ring vibrations, metal-ligand bending and movement of the molecule as a whole also contribute to the vibrational entropy associated with the spin transition. This journal is