Spin states, electronic structure and phonon properties of ZnxFe[Fe(CN)6] (x = 0 – 1) by hybrid density functional theory
Abstract
Hexacyanoferrates (HCF) or Prussian blue analogues (PBAs) have emerged as potent ion insertion materials for battery electrodes. They are also among the very few hosts in which reversible insertion of multivalent ions such as Zn 2+ into the framework is experimentally established. Zinc-containing ZnFe[Fe(CN) 6 ] members of the iron hexacyanoferrate series are particularly interesting for the anode-free zinc cells where cathode can supply the entire zinc inventory. Yet essentially nothing is fundamentally known about them. Here we report the symmetry, spin states, electronic structure and lattice dynamics of ZnFe[Fe(CN) 6 ], calculated within the all-electron linear combination of atomic orbitals (LCAO) approach using the hybrid B1WC exchange–correlation functional. We show by group-theoretical analysis that ordered occupation of a single interstitial 32 f site of the cubic Fm 3̄ m parent generates the observed rhombohedral R 3 m symmetry within the primitive cell, without recourse to a supercell, and that the resulting tetrahedral zinc coordination is consistent with the rhombohedral phases reported experimentally for Zn-containing hexacyanoferrates. By considering all site resolved spin state/configurations, we identify the low spin (LS) state on two Fe ions (i.e., Fe LS C +Fe LS N ) as the ground state in the rhombohedral ZnFe[Fe(CN) 6 ]. The first excited state is given by Fe LS C +Fe HS N and is separated by about 0.5 eV/f.u. from the ground state. We validated our calculation model by calculating the spin states/configurations in two reference materials, namely Fe[Fe(CN) 6 ] andKFe[Fe(CN) 6 ]. For KFe[Fe(CN) 6 ], the B1WC functional correctly reproduces the experimentally established configuration of LS state on the C-coordinated Fe and high spin (HS) state on the N-coordinated Fe. The dynamical stability of rhombohedral ZnFe[Fe(CN) 6 ] is confirmed by phonon calculations at the L, Γ, Z, and F points and by phonon dispersion curves along the L–Γ–Z path obtained using two supercell sizes. The calculated Raman spectrum for rhombohedral ZnFe[Fe(CN) 6 ] exhibits a pronounced gap of approx. 1400 cm −1 between the low and high frequency regions. The high frequency region of Raman spectrum is dominated by intense C–N stretching vibrations, whereas the low frequency region contains two well-resolved peaks due to bending vibration involving Fe N , N and C atoms and stretching motion of Fe N –N bond, respectively.
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BibTeX
@misc{gryaznov2026spin,
title = {{Spin states, electronic structure and phonon properties of ZnxFe[Fe(CN)6] (x = 0 – 1) by hybrid density functional theory}},
author = {Denis Gryaznov and Linas Vilčiauskas},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15010081/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010081/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Spin states, electronic structure and phonon properties of ZnxFe[Fe(CN)6] (x = 0 – 1) by hybrid density functional theory
AU - Denis Gryaznov
AU - Linas Vilčiauskas
PY - 2026
DA - 2026/10/08
PB - ChemRxiv
DO - 10.26434/chemrxiv.15010081/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010081/v1
AB - Hexacyanoferrates (HCF) or Prussian blue analogues (PBAs) have emerged as potent ion insertion materials for battery electrodes. They are also among the very few hosts in which reversible insertion of multivalent ions such as Zn 2+ into the framework is experimentally established. Zinc-containing ZnFe[Fe(CN) 6 ] members of the iron hexacyanoferrate series are particularly interesting for the anode-free zinc cells where cathode can supply the entire zinc inventory. Yet essentially nothing is fundamentally known about them. Here we report the symmetry, spin states, electronic structure and lattice dynamics of ZnFe[Fe(CN) 6 ], calculated within the all-electron linear combination of atomic orbitals (LCAO) approach using the hybrid B1WC exchange–correlation functional. We show by group-theoretical analysis that ordered occupation of a single interstitial 32 f site of the cubic Fm 3̄ m parent generates the observed rhombohedral R 3 m symmetry within the primitive cell, without recourse to a supercell, and that the resulting tetrahedral zinc coordination is consistent with the rhombohedral phases reported experimentally for Zn-containing hexacyanoferrates. By considering all site resolved spin state/configurations, we identify the low spin (LS) state on two Fe ions (i.e., Fe LS C +Fe LS N ) as the ground state in the rhombohedral ZnFe[Fe(CN) 6 ]. The first excited state is given by Fe LS C +Fe HS N and is separated by about 0.5 eV/f.u. from the ground state. We validated our calculation model by calculating the spin states/configurations in two reference materials, namely Fe[Fe(CN) 6 ] andKFe[Fe(CN) 6 ]. For KFe[Fe(CN) 6 ], the B1WC functional correctly reproduces the experimentally established configuration of LS state on the C-coordinated Fe and high spin (HS) state on the N-coordinated Fe. The dynamical stability of rhombohedral ZnFe[Fe(CN) 6 ] is confirmed by phonon calculations at the L, Γ, Z, and F points and by phonon dispersion curves along the L–Γ–Z path obtained using two supercell sizes. The calculated Raman spectrum for rhombohedral ZnFe[Fe(CN) 6 ] exhibits a pronounced gap of approx. 1400 cm −1 between the low and high frequency regions. The high frequency region of Raman spectrum is dominated by intense C–N stretching vibrations, whereas the low frequency region contains two well-resolved peaks due to bending vibration involving Fe N , N and C atoms and stretching motion of Fe N –N bond, respectively.
ER -