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Solid-state lattice-dynamics calculations within the hybrid density-functional approach are applied to the study of the thermally induced ${\text{Fe}}^{2+}$ $\text{low}\text{ }\text{spin}(\text{LS};S=0)\ensuremath{\leftrightarrow}\text{high}\text{ }\text{spin}(\text{HS};S=2)$ crossover (SCO) in the extended network of the $\text{CsFe}[\text{Cr}{(\text{CN})}_{6}]$ 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 ${F}_{0}\ensuremath{\approx}14\mathrm{%}$ provides reliable values. The transition is shown to be dominated by the entropy difference, $\ensuremath{\Delta}S$, 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 $\ensuremath{\Delta}{S}_{\text{vib}}$ deriving from modes with wave numbers of $250\text{ }{\text{cm}}^{\ensuremath{-}1}$ 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 ${\text{Fe}}^{2+}$ HS $({e}_{\text{g}}^{2}{t}_{2\text{g}}^{4})$ configurations is also detailed, evidence for the existence of an associated dynamic Jahn-Teller distortion being presented. Optimized structures, bulk moduli, $\ensuremath{\Gamma}$-point vibrational frequencies, and crystal-field energy models are discussed for all relevant spin states.

physical review b

Spin crossover in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mtext>CsFe</mml:mtext></mml:mrow><mml:mrow><mml:mtext>II</mml:mtext></mml:mrow></mml:msup><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mtext>Cr</mml:mtext></mml:mrow><mml:mrow><mml:mtext>III</mml:mtext></mml:mrow></mml:msup><mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>CN</mml:mtext></mml:mrow><mml:mo>)</mml:mo></mml:mrow></…

Spin crossover in theCsFeII[CrIII(CN)