Spin crossover in theCsFeII[CrIII(CN)

Abstract

General rightsCopyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policyThe University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact openaccess@ed.ac.uk providing details, and we will remove access to the work immediately and investigate your claim. Solid-state lattice-dynamics calculations within the hybrid density-functional approach are applied to the study of the thermally induced Fe 2+ low spin͑LS; S =0͒ ↔ high spin͑HS; S =2͒ crossover ͑SCO͒ in the extended network of the CsFe͓Cr͑CN͒ 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 Ϸ 14% provides reliable values. The transition is shown to be dominated by the entropy difference, ⌬S, associated with the softening of low-frequency vibrational ͑vib͒ modes in the HS state, as has been suggested previously for a wide range of SCO materials, more than half of ⌬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 Fe 2+ 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, ⌫-point vibrational frequencies, and crystal-field energy models are discussed for all relevant spin states.

First principles calculation of a large variation in dielectric tensor through the spin crossover in the CsFe[Cr(CN)6] Prussian blue analogue

“…Individual bond lengths are very similar to those presented in the earlier study [54]. where eight triply-degenerate F 2 -symmetry optical modes contribute to…”

“…Examining optimized structures, it is found that, as in the previous DFT study [54], the present structural optimizations accurately reproduce the experimental increase in lattice constant Δa HS − LS = +0.38 Å (denoted Δa hereafter) through the LS→HS transition [8]. An average over functionals yields Δa = +0.418 Å and Δc HS − LS = +0.427 Å (denoted Δc hereafter) with respect to the tetragonal HS cell, and Δa aver = +0.421 Å assuming an axial average consistent with HS state orbital disorder.…”

“…Examining the computed results, first, the previous solid-state calculations [54] orbital degeneracy. This is in keeping with the understanding that JT distortions associated with t !"…”

“…The admixture of HF exchange in the functional is denoted as F 0 , with values F 0 =14 and 20% being used here, as supported by the results of a previous study [54]. All structures were fully geometry optimized (varying all cell parameters and atomic positions) prior to calculations of vibrational frequencies and dielectric tensors.…”

“…It has been the subject of previous theoretical studies [52,53], the most recent by one of the present authors, seeking to compute the free energies of the HS and LS states and T !/! by means of lattice dynamics calculations using hybrid density functionals [54]. 6 ] − sublattices, the facile displacements of the former ions within the structure, and the substantial volume expansion through the LS→HS transition.…”