Vibrational properties and cooperativity of the 3D spin crossover network [Fe(pyrazine)][Pt(CN)₄]

Nuclear inelastic scattering of synchrotron radiation has been used to determine the phonon density of vibrational states (pDOS) for the high-spin and low-spin phases of the hydrated and dehydrated isomer of the spin crossover polymer [Fe(pyrazine)][Pt(CN)₄]. Density functional theory calculations have been performed for molecular models of the 3D polymeric system. The models contain 15 Fe(ii)/Zn(ii) centres and allowed the assignment of the observed bands to the corresponding vibrational modes. Thermodynamic parameters like the mean force constant and the vibrational entropy but also sound velocities of the molecular lattices in both spin states have been derived from the pDOS. Modelling of the low-spin and high-spin centres in the environment or matrix of different spins has revealed the enthalpic and entropic components of the intramolecular cooperativity. In contrast to the 1D spin crossover systems (Rackwitz, et al., Phys. Chem. Chem. Phys., 2013, 15, 15450) based on the rigid 1,2,4-triazole derivatives the distortion of the low-spin iron Fe(ii) centre by the matrix of high-spin Fe(ii) (modelled as Zn(ii)) occurs only in two dimensions, defined by the [M(CN)₄]^2- sheets, rather than concerning all six Fe-N bonds, as in 1D systems. The enthalpic intramolecular cooperativity has been determined to be 15 kJ mol^-1 which is lower than that in 1D systems (20-30 kJ mol^-1). Yet, the entropic contribution stabilizes the low-spin state in a low-spin matrix, a behaviour which is opposite to what was found for the 1D systems.