Estimate of the vibrational contribution to the entropy change associated with the spin transition in the d4 systems [MnIII(pyrol)3tren] and [CrII(depe)2I2]

Abstract

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 ln3 = 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.