Crystal-Field Theory Validity Through Local (and Bulk) Compressibilities in CoF₂ and KCoF₃

Abstract

Crystal field theory (CFT) predicts that crystal field acting on an transition-metal (TM) ion complex of cubic symmetry varies as R –5, where R is the TM-ligand distance. Yet simple and old-fashioned, CFT is used extensively since it provides excellent results in most TM ion-bearing systems, although no direct and thorough validation has been provided so far. Here we investigate the evolution of the electronic and crystal structures of two archetypal Co2+ compounds by optical absorption and X-ray diffraction under high pressure. Both the electronic excited states and crystal-field splitting, Δ = 10Dq, between 3d(e g + t 2g) orbitals of Co2+ as a function of volume, V, and Co–F bond length, R, in 6-fold octahedral (oct) and 8-fold hexahedral (cub) coordination in compressed CoF2 have been analyzed. We demonstrated that Δ scales with R in both coordinations as R –n , with n close to 5 in agreement with CFT predictions. The pressure-induced rutile to fluorite structural phase transition at 15 GPa in CoF2 is associated with an increase of R due to the 6 → 8 coordination change. The experimental Δ­(oct)/ Δ­(cub) = −1.10 for the same R-values is close to −9/8, in agreement with CFT. A similar R-dependence is observed in KCoF3 in which the CoF6 O h coordination is maintained in the 0–80 GPa pressure range.

Jahn–Teller and Non-Jahn–Teller Systems Involving CuF64– Units: Role of the Internal Electric Field in Ba2ZnF6:Cu2+ and Other Insulating Systems

“…Although the rough crystal-field theory, which treats the ligands as point charges, predicts a dependence of 10Dqint(R)  R -5 this agreement has to be viewed only as a fortuitous coincidence because that theory also leads to 10Dq values which are one order of magnitude smaller than experimental ones 17 . For this reason, although there are still papers claiming that an experimental dependence 10Dq  R -n (n ≈ 5) proves the validity of crystal-field theory 59 that assertion is simply meaningless.…”

The Jahn-Teller Distortion at High Pressure: The Case of Copper Difluoride

“…This compound is one of the simplest binary connections containing the Cu 2+ cation. It belongs to the family of metal difluorides, which have been extensively studied at high pressure [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. Due to the operation of the JT effect CuF 2 adopts at ambient conditions a rarely-encountered crystal structure found only in one other compound (CrF 2 ) [38].…”

Pressure dependence of the crystal-field spectrum of KNiF3 : Single and double excitations

“…The results will be compared with well-known correlations already established in ABF 3 : Mn 2+ [26,27]. Also, they allow us to compare the experimentally obtained n exponent for KNiF 3 with that obtained for KZnF 3 : Ni 2+ (n = 6) from DFT methods [13], which is different from that spectroscopically derived for Mn 2+ along the ABF 3 : Mn 2+ series (n = 4.7) [26,27] or that reported for Co 2+ in KCoF 3 (n = 5.1) through high-pressure measurements [21]. Precise measurements of n are deserving of adequate theoretical methods to explain the slight departure of n from the CF theory estimates of n = 5, due to bonding effects related to specificities of the transition-metal cation and the ligand (crystal structure) [13,28,29].…”

“…In spite of it, different values of the bulk modulus ranging from 60 to 115 GPa have been recently reported in KNiF 3 [9,10,17,18], showing important discrepancies with the experimental value derived from acoustic measurements of K 0 = 84 GPa [18,19]. It shows also important differences with bulk moduli obtained from the experimental V(P) data in isostructural KCoF 3 (K 0 = 117 GPa) [20,21], KMnF 3 (K 0 = 59 GPa) [22], or KZnF 3 (K 0 = 78 GPa) [23]. This dispersion of data points out that precise theoretical methods for determining structural properties in such simple systems are yet to be improved.…”

“…Interestingly, the exponent n is larger than the exponent n = 5 predicted by the CF theory [28], and its difference must be ascribed to changes of the actual molecular-orbital wave function with R (bonding), which modulates the dependence of 10Dq(R) yielding a potential law proportional to R -n with n = 6.6 in KNiF 3 . Previous works exploring the R dependence of 10Dq in the ABF 3 : Mn 2+ perovskite series [26] and in Co 2+ in the isostructural KCoF 3 (Pm 3m) [21] provide potential law dependencies with n exponents of 4.7 and 5.1, respectively. Though in all cases exponents are around 5, their departures from n = 5 unveil singularities which are related to the different nature of the lattice and the bonding between the transition-metal ion and the ligand.…”