Spin crossover in the CsFeII[CrIII(CN)6] Prussian blue analog: Phonons and thermodynamics from hybrid functionals

Solid-state lattice-dynamics calculations within the hybrid density-functional approach are applied to the study of the thermally induced Fe2+ low spin(LS; S=0) double left right arrow high spin(HS; S=2) crossover (SCO) in the extended network of the CsFe[Cr(CN)(6)] Prussian blue analog. The variations in the thermodynamic parameters defining the SCO transition with the Fock exchange content (F-0) of the functional are obtained and discussed, where, in keeping with the findings of previous studies of isolated complexes, it is found that an admixture F-0 approximate to 14% provides reliable values. The transition is shown to be dominated by the entropy difference, Delta S, associated with the softening of low-frequency vibrational (vib) modes in the HS state, as has been suggested previously for a wide range of SCO materials, more than half of Delta S-vib deriving from modes with wave numbers of 250 cm(-1) or less. Analysis of the influence of the spectroscopic selection rules upon the apparent SCO thermodynamics reveals that determinations based solely upon infrared or Raman frequencies, or upon their combination, lead to significant errors. The effect upon the SCO transition of the electronic entropy associated with the degenerate Fe2+ HS (e(g)(2)t(2g)(4)) configurations is also detailed, evidence for the existence of an associated dynamic Jahn-Teller distortion being presented. Optimized structures, bulk moduli, Gamma-point vibrational frequencies, and crystal-field energy models are discussed for all relevant spin states.