Theoretical study of ternary silver fluorides AgMF₄ (M = Cu, Ni, Co) formation at pressures up to 20 GPa

Abstract

Only several compounds bearing the Ag(II) cation and other paramagnetic transition metal cations are known experimentally. Herein, we predict in silico stability and crystal structures of hypothetical ternary silver(II) fluorides with copper, nickel and cobalt in 1 : 1 stoichiometry at a pressure range from 0 GPa up to 20 GPa employing the evolutionary algorithm in combination with DFT calculations. The calculations show that AgCoF₄ could be synthesized already at ambient conditions but this compound would host diamagnetic Ag(I) and high-spin Co(III). Although none of the compounds bearing Ag(II) could be preferred over binary substrates at ambient conditions, at increased pressure ternary fluorides of Ag(II) featuring Cu(II) and Ni(II) could be synthesized, in the pressure windows of 7–14 and 8–15 GPa, respectively. All title compounds would be semiconducting and demonstrate magnetic ordering. Compounds featuring Ni(II) and particularly Co(II) should exhibit fundamental band gaps much reduced with respect to pristine AgF₂. The presence of Cu(II) and Ni(II) does not lead to electronic doping to AgF₂ layers, while Co(II) tends to reduce Ag(II) entirely to Ag(I).

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Introduction

Recent experimental and theoretical research on AgF₂ demonstrated that this material mimics very closely the key structural and electronic properties of the well-known lanthanum oxocuprate La₂CuO₄ (ref. 1) – the prototype precursor of high-temperature oxocuprate superconductors – that are believed to be a necessary prerequisite for the unique behaviour of the latter. They account for strong antiferromagnetic coupling via a superexchange mechanism in two-dimensional sheets² and substantial mixing of ligand and metal states in the top of the valence band. Superconductivity is reached in the oxocuprates via chemical doping and because of the striking similarities, not observed in any other known compound, it was suggested that superconductivity could be obtained also in the related silver(II) fluorides if proper chemical doping to AgF₂ that would lead to metallization could be realized.^1,3,4 It is therefore highly desirable to examine various possibilities to modify its electronic and magnetic properties via doping.

Doping in essence is equivalent to the insertion of surplus holes or electrons into the chemical system. However, in contrast to cuprates, the bulk AgF₂ has so far resisted all doping attempts. The hole doping of AgF₂ could be introduced by F adatoms, but theoretical studies show that doping to this 001-type system via the addition of F atoms does not lead to a stable metallic phase.⁵ Partial oxidation of Ag(II) is also difficult, due to the immensely strong oxidative character of Ag(III); compounds of Ag(III) are even more difficult to synthesize and manipulate than Ag(II) compounds.

Therefore, our attention turned to electron doping, which could be introduced in two general ways. The first one is provided by vacancies at anionic sites (AgF₂ → AgF_2−δ). Similarly, as with additional F⁻, the study shows that the vacancies lead to clustering and phase separation without the prospect of obtaining a metallic phase.⁵ The second possibility, that we focus on here, is to modify AgF₂ via substitution at the cationic site injecting the surplus electron. Early attempts to dope ternary silver fluorides (e.g. KAgF₃) in a manner analogous to cuprates, i.e. substituting partially M(I) cations with M(II), failed. Recent theoretical investigations suggest that electron doping to AgF₂ would not lead to a stable metallic phase due to a lattice polaronic effect and charge localization.⁶ Therefore the remaining way to achieve electron doping in AgF₂ is to try partial isostructural substitution of Ag(II). By this, we mean to replace square planar Ag(II) in AgF₂ with another redox-active metal cation, M(II), so that the layered structure is preserved but the electrons may partly flow from M(II) to Ag(II). This type of doping has not been yet achieved experimentally. Thus, in this study, we explored new ternary phases bearing Ag(II), especially isostructural to AgF₂, to learn to what extent could the electronic structure of AgF₂ sheets be altered by the presence of other metal cations.

The natural choice for the M element is a transition metal which also presents octahedral coordination featuring Jahn–Teller distortion like Ag(II). Accordingly, we considered diverse ternary fluoride stoichiometries which may host strongly coupled AgF₂ sheets. Among ternary fluorides Ag^IIM_xF_y, many transition metal systems have been successfully prepared so far,³ i.e. for M = Au(III), Au(V), Nb(V), Ta(V), Ti(IV), Zr(IV), Hf(IV), Ru(V), Rh(IV), Ir(V), Pd(IV), Pt(IV), Pt(V), Mn(IV) and Cr(IV) (AgMn^IVF₆ (ref. 7) and AgCr^IVF₆ (ref. 8) structures not known). None of these fluorides host [AgF₂] sheets or chains required for achieving strong antiferromagnetic coupling. Yet the great majority of these compounds contain closed-shell or low-spin cations which would not hold any magnetic interactions.

Late 3d-block transition metals, especially Cu, Ni and Co, seem to be promising candidates for electron doping due to their relative resistance towards oxidation in the fluoride environment while having partly filled d subshell. The redox potentials for the M^3+/M²⁺ redox pairs decrease in the Cu > Ni > Co sequence. Experimentally, CoF₃ and NiF₃ (actually Ni^IINi^IVF₄ (ref. 9)) are moderately stable in an inert atmosphere, and they constitute strong fluorinating agents. On the other hand, CuF₃ is quite unstable thermally and thermodynamically¹⁰ (even more than AgF₃ (ref. 11)), thus minimizing the possibility of the intrinsic redox reaction between Ag(II) and Cu(II). Remarkably, such appealing synthesis has not been achieved experimentally yet, so no fluorides having Ag(II) and M(II) (M = Cu, Ni, Co) in any ratio are known, despite many similarities between these cations. There are, however, some examples of compounds with Ag(I) and M(III) valences. Among fluoride systems, only the Ag(I)Co(III) fluoride with Ag₃CoF₆ formula has been already described,¹² suggesting that as yet unobserved Ag(II)Co(II) pair might be just beyond the border of intrinsic redox reaction. Silver fluorides with M = Cu or Ni are not known, thus the forms bearing Ag(II) and M(II) or Ag(I) and M(III) can not be excluded. Furthermore, there are known ternary oxide systems having Ag(I) and M(III) with AgMO₂ formula (M = Cu, Ni, Co).^13–17 Oxide and fluoride systems of silver tend to differ dramatically, thus the question about the nature of the late 3d ternary fluorides remains open.

The theoretical search for ternary systems bearing initially divalent cations has the aim of verification if it could possibly form a metallic phase with Ag(II). Since ternary oxides with Ag : M ratio of 1 : 1 are known, here we decided to study ternary fluorides with the same ratio. To understand whether ternary fluorides bearing Ag(II) in combination with another transition metal (TM) constitute a viable synthetic target, we have examined here AgMF₄ systems with Cu, Ni and Co using Density Functional Theory (DFT) methods in combination with evolutionary algorithms for crystal structures' prediction.

Preliminary results showed that such systems are very close in terms of energy to the sum of binary substrates but have lower volume, suggesting they could be obtained at elevated pressures. It is well-known that pressure may affect to a great extent both the crystal structures and stability of chemical compounds.¹⁹ High-pressure synthesis proved to be crucial in the synthesis of some transition metal compounds, e.g. copper oxyfluorides¹⁸ (and references therein), as well as for inducing metallization,^19,20 the latter being not possible in pure AgF₂.²¹ Thus, aside from variations of the chemical composition, we also study the impact of external pressure on crystal and electronic structure, and stability of AgMF₄ systems with respect to the mixture of binary fluorides, AgF₂ and MF₂ (M = Cu, Ni, Co). Since both stability and electronic properties may depend on pressure, we have investigated the effect of external pressure on the formation and properties of the title AgMF₄ compounds.

Computational methods

This theoretical study is based on periodic electronic-structure calculations for solids carried out with Vienna Ab initio Simulation Package 5.4.4 (VASP) software using projector-augmented wave method.^22–24 We used the potentials set recommended by VASP with a 520 eV plane-wave energy cut-off. Energy calculations utilized collinearly spin-polarized DFT method using generalized gradient approximation functional PBEsol (i.e. solid-revised Perdew, Burke and Ernzerhof correlation–exchange functional²⁵). The on-site electronic correlation was included with Hubbard and exchange repulsion terms (U and J) using Dudarev's approach.^26,27 Geometry optimizations were done with k-spacing of 2π × 0.024 Å⁻¹ (using the Monkhorst–Pack scheme) and conjugate-gradient algorithm for ionic relaxation with the criteria of 10⁻⁷ eV for electronic self-consistent-field convergence and 10⁻⁵ eV for ionic cycles convergence. In this approach effective U_eff = U − J, is considered, thus we used U_eff equal 4 eV (for Ag, Ni), 5 eV (Co) and 8 (Cu). These values were earlier used and validated in respective systems exhibiting +II oxidation state.^2,28–30

In our quest for the lowest-energy crystal structure of hypothetical compounds of AgCuF₄, AgNiF₄ and AgCoF₄, we have initially tested various substitutions within the known crystal structure of AgF₂. We have tested also various prototypical M^IM^IIIF₄ structures, which allow for electron transfer between metal sites; notably, we presumed that electron-hungry Ag(II) could undergo reduction, with the concomitant 1 − e⁻ oxidation of its neighbouring TM cations. The three scrutinized 3d elements, Cu, Ni and Co, differ in terms of redox properties, electron count, U-induced splitting of upper and lower Hubbard d-bands, and degree of tetragonal distortion of MF₆ octahedra. All above-mentioned cations also have significantly smaller cationic radii than Ag(II). AgMF₄ (M = Cu, Ni, Co) fluorides were modelled in the appropriate ABC₄ structure types selected from the Inorganic Crystal Structure Database (ICSD). Furthermore, in each case, we have searched for the global minimum structure using evolutionary algorithms (EA) as implemented in the XtalOpt software³³ for crystal structure prediction. The starting pool (i.e. 1^st generation) for each XtalOpt run constituted 30 initial random structures containing 2 or 4 formula units in the unit cell. After the pool of structures is optimized by VASP, XtalOpt selects the best possible candidates for the next generation, employs such operators as strain, exchange, ripple, and crossover on the selected candidates, which form the next generation of structures. Such structure generation and optimization continue until the energy convergence is reached. The XtalOpt runs were performed for the three title stoichiometries of AgMF₄, at 0 and 10 GPa considering unit cells containing 2 to 4 formula units. XtalOpt runs were done in combination with DFT calculations using VASP optimizer. A four-step optimization procedure of each structure was performed increasing accuracy at each step, using DFT for the first two and DFT+U (i.e. with Dudarev's approach) approach for the last two steps. These calculations were performed with reduced convergence criteria (5 × 10⁻⁷ eV and 5 × 10⁻⁵ eV for the electronic and ionic cycle, respectively) and k-point mesh (2π × 0.048 Å⁻¹). For each system, we have obtained about optimized 500 structures (more in ESI, see Fig. S1 and S2‡). The selected lowest-energy EA structures were reoptimized with higher precision as described above. The XtalOpt is a robust tool that has been utilized more than sixty times in solid-state chemistry or physics applications.³⁴

For selected systems, geometry optimization was additionally performed using the HSE06 hybrid functional³⁵ with a coarser k-spacing (2π × 0.048 Å⁻¹). For the chosen systems we calculated the electronic density of states (DOS) with tetrahedron method and Blöchl corrections, with both DFT+U and HSE06.

Dynamic stability was investigated in VASP by calculating Γ-point vibrational frequencies, using the density functional perturbation theory method and the DFT+U framework.

For visualization of crystal structures, VESTA³⁶ software was used. Band structure plots were made using PyProcar library³⁷ and AFLOW³⁸ program.

Results and discussion

The idea of pressure study originates from preliminary results, as numerous low-volume polymorphs have already been identified in the XtalOpt quest at ambient pressure (Fig. S1a, c and e‡). Consequently, we have studied the AgMF₄ phases in a range of hydrostatic pressure with the prospect of obtaining pressure-induced stability of AgMF₄ (M = Cu, Ni and Co) in respect to binary substrates AgF₂ and MF₂, and to evaluate the possibility of high-pressure metallization of the ternary silver(II) fluorides. The formation enthalpy of the lowest-energy polymorphs from the substrates was investigated in the 0–20 GPa pressure range. The pressure evolution for AgMF₄ systems with respect to the sum of those for the binary substrates in their most stable polymorphs is presented in Fig. 1. With our choice of U_eff we successfully confirmed the experimentally observed pressure-induced phase transitions of AgF₂,²¹ CuF₂,³¹ NiF₂ (ref. 32) and CoF₂ (ref. 28 and 32) up to 20 GPa (note in ESI, see also Table S1 and Fig. S3,‡ these phase transitions are marked in Fig. 1). The phase-transition sequences in the considered stoichiometries were calculated with the described DFT+U framework assuming hydrostatic conditions.

Fig. 1 Calculated relative enthalpy of ternary silver fluorides AgMF₄ (a) M = Cu, (b) M = Ni, (c) M = Co, with respect to lowest-enthalpy polymorphic forms of binary fluorides at each given pressure point. All the lowest enthalpy Ag(II)–M(II) fluorides comprise M-half-substituted AgF₂ type structures. Vertical dashed lines indicate phase transitions calculated for the MF₂ substrates.

Additional insight into pressure-induced effects on the enthalpy of formation of the ternary fluorides comes from pV term analysis (ESI, Fig. S4‡). Both for low pressure (<3 GPa) and high-pressure range (>9 GPa) the pV factor works against the formation of the studied ternary fluoride phases. Consequently, the ternary fluoride phases benefit from the pV term with respect to the substrates in the range 3–9 GPa; at higher pressures, binary substrates experience volume-reducing phase transitions which reduces this advantage. The crucial is the phase transition of constituent AgF₂ at about 14 GPa into an unprecedented inorganic nanotube.²¹ This incredibly low-volume polymorph reduces the pV term of substrates and gradually destabilizes thermodynamically all proposed ternary fluorides at pressures approaching 20 GPa. These factors result in re-entrant instability of the ternary phases above certain characteristic pressure in each case.

The hypothetical mixed-cation AgMF₄ fluorides from Fig. 1 are below described in the order of M = Cu, Ni, Co, in terms of their structure and stability, and then of the pressure effects. Finally, we investigate their electronic properties at ambient and elevated pressures.

Copper

Ambient pressure. Due to the similar chemistry of Ag(II) and Cu(II), as well as similar crystal structures of binary fluorides, our primary candidate for the AgCuF₄ structure was the orthorhombic layered structure typical of AgF₂ (ref. 39) (Fig. 2a). Three types of substitutions at the metal site were considered, i.e. metal alternation in the directions perpendicular to the lattice vectors (cf. ESI, Fig. S5‡). Notably, these three diverse polymorphs were also found during EA search (see ESI, Fig. S1 and S2‡). We found that a monoclinic variant of the AgF₂ type structure with metal alternation in the original b direction is the lowest-energy structure of AgCuF₄ (marked here as low-pressure, LP, structure, Fig. 2b), as confirmed by evolutionary algorithm quest. This polymorph preserves the layered character of its binary constituents by separating Ag and Cu into distinct puckered [AgF_4/2] and [CuF_4/2] layers. Substantial axial elongation of both Ag(II) and Cu(II) octahedra is predicted (i.e. four shorter equatorial and two considerably longer axial Ag(Cu)–F distances (2 + 2) + 2 coordination), in agreement with the strong Jahn–Teller effect which is expected for d⁹ species in octahedral field. The rhombic distortion can be approximated to tetragonal distortion (4) + 2 in most cases. The ratio of axial to equatorial bond lengths R = d_ax/d_eq (dimensionless Jahn–Teller distortion parameter often used to describe such compounds⁴⁰) equals 1.24 for the Ag(II) site and 1.14 for the Cu(II) one. The tetragonal distortion for both cations is similar as in the parent phases where this ratio equals 1.23 and 1.15, for AgF₂ and CuF₂, respectively (all geometry parameters are summarised in Table 1).

Fig. 2 Crystal structures of (a) parent AgF₂, the lowest-energy predicted (b) AgCuF₄, and (c) AgNiF₄, and metastable (d) Ag^IICo^IIF₄ at ambient pressure (LP structure of each). The threshold for Ag–F bond drawing is 2.15 Å in all cases. All bond lengths provided in angstroms, and angles in degrees. Grey for silver atoms, green for fluorine, blue for copper, orange for nickel and magenta for cobalt.

Table 1 Key geometry parameters of structures of parent AgF₂ and ternary silver fluorides Ag^IIM^IIF₄ (M = Cu, Ni, Cu) at ambient and increased pressure. Also, octahedral distortion parameter R is provided. N.D. stands for ‘not determined’ which is due to strong rhombic distortion

System	Label	p (GPa)	Bond length (Å)			R	Bond length (Å)			R
			Ag–F1	Ag–F2	Ag–F3		M–F1	M–F2	M–F3
Ag^IIF2	LP	0	2.07	2.08	2.56	1.23	—	—	—	—
	HP1	10	2.06	2.06	2.37	1.15	—	—	—	—
Ag^IICu^IIF4	LP	0	2.05	2.07	2.60	1.26	1.92	1.92	2.19	1.14
	HP1	10	2.03	2.10	2.38	1.15	1.85	1.91	2.15	1.14
Ag^IINi^IIF4	LP	0	2.02	2.26	2.33	0.88	1.94	1.99	2.01	0.97
	HP1	10	2.02	2.11	2.43	1.18	1.93	1.94	1.95	0.99
Ag^IICoF4	LP	0	2.03	2.27	2.33	0.88	1.98	2.03	2.03	0.98
	HP1	10	2.01	2.18	2.33	N.D.	1.92	2.00	2.03	0.95

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Axial elongation suggests that in both cations d-hole occupies d_x²−y² orbital. Both constituent layers [AgF_4/2] and [CuF_4/2] of AgCuF₄ preserve intra-sheet antiferromagnetic ordering.

The geometry within the puckered layers is reminiscent of those found in binary fluorides; the [AgF_4/2] layers are more buckled than in pure AgF₂ (the Ag–F–Ag angle is 122° vs. 129° in bulk AgF₂), while [CuF_4/2] layers are flattened (the corresponding angle is 141° vs. 132° in bulk CuF₂). This feature stems from the difference in the ionic radii between Ag(II) and Cu(II). In order to form a segregated layer structure, the [AgF₂] sheets must buckle and the [CuF₂] sheets must simultaneously flatten; this accommodation is associated by bending of the crystallographic beta angle from 90° (for bulk AgF₂) to 105°. We notice that two other models with mixed [(Ag,Cu)F_4/2] layers (ESI, Fig. S5c and d‡), have energies higher by +6.4 and +7.3 kJ mol⁻¹, respectively, as compared to the LP structure. We also found a crystal structure containing Ag–F–Cu bridges and exhibiting genuine 3D connectivity (Fig. S5b‡), characterized by much lower volume. Importantly, the most stable LP polymorph is computed to be +6.7 kJ mol⁻¹ uphill in energy with respect to substrates:

AgF₂ + CuF₂ → AgCuF₄ (1)

Thus, if prepared, this ternary fluoride might be only metastable. However, its kinetic stability with respect to phase separation is indicated by our phonons calculations, yielding no imaginary frequencies for this polymorph (Appendix S4,‡ the same is true for all structures examined in this work).

High pressures. In the case of AgCuF₄ system, the LP layered Ag^IICu^IIF₄ structure is predicted to transform to a high-pressure Ag^IICu^IIF₄ polymorph (Fig. 3b, denoted HP1) with three-dimensional connectivity. The phase transition to the HP1 structure takes place around 6 GPa. The HP1 form remains energetically favoured over the LP one up to the highest calculated pressure of 20 GPa (Fig. 1a). Moreover, HP1 would become stable with respect to the substrates in the pressure range of about 7–14 GPa with the minimum relative enthalpy (−1.9 kJ mol⁻¹, in eqn (1)) reached ca. 9 GPa.

Fig. 3 Crystal structures of (a) parent AgF₂, and the lowest-energy predicted (b) AgCuF₄, and (c) AgNiF₄, and metastable (d) Ag^IICo^IIF₄ at 10 GPa (HP1 structure of each). The threshold for Ag–F bond drawing is 2.15 Å in all cases. Another view of these structures is shown in ESI, Fig. S6.‡

The HP1 polymorph is also based on the AgF₂ type structure, but the fluorine bridges are now formed between the two chemically distinct metal cations (Ag–F–Cu) in contrary to the LP structure, where fluorine atoms bridge metal cations of the same type (Ag–F–Ag and Cu–F–Cu). One can think of the HP1 structure as the LP one with direct Jahn–Teller elongation taking place within the [AgF_4/2] and [CuF_4/2] layers (alternating along ) instead of in the direction perpendicular to the layers (along ). Consequently, the 2D connectivity within the [AgF_4/2] and [CuF_4/2] layers is broken and a 3D Ag–F–Cu one established with the cooperative Jahn–Teller mechanism. The HP1 form of AgCuF₄ has a ferrimagnetic character with a small uncompensated spin (ca. 0.02 μ_B) due to opposite spin on Ag(II) and Cu(II) cations with slightly different magnetic moments on each type of TM cation. Like in the LP polymorph, here the Cu and Ag octahedra are both axially elongated, see Table 1.

Nickel

Ambient pressure. Predictions of the crystal structure of AgNiF₄ – in contrast to those featuring Cu(II) – were influenced by the fact that Ni(II) reveals a known tendency to be oxidized to Ni(III) or even Ni(IV), though higher fluorides of nickel tend to release F₂.⁴¹ However, during our quest only very few such structures with intervalence charge transfer were found, having considerably higher enthalpy (i.e. at least +56.4 kJ mol⁻¹, Fig. S1c‡). Similarly, as in the case of Cu(II), the lowest-energy structure of AgNiF₄ is a monoclinic variant of the parent AgF₂ type structure, with a slightly larger beta angle of 107° compared to the LP AgCuF₄. However, in contrast to AgF₂ and LP AgCuF₄, the nickel compound is not layered. The Ag(II) cations are subject to inverse Jahn–Teller effect with axial compression of the AgF₆ octahedra taking place in the direction perpendicular to the [AgF_4/2] layers and with the R ratio equal to 0.88 (Fig. 2c and Table 1). The axial compression manifested by presence of quasi-dumbbell Ag(II) is known from the fluorine chemistry of Ag(II)⁴² and leads to d-hole sitting in d_z² orbital. On the other hand, the NiF₆ octahedra remain nearly undistorted with R ratio equal to 0.97 (compared to 0.98 calculated for rutile NiF₂), as typical for high-spin Ni(II). Consequently the Ag(II) cations act as connectors between octahedral [NiF_4/2F_2/1]²⁻ layers present within the bc plane. The axial Ag–F bonds involved in the formation of the Ag–F–Ni bridges are shorter than the equatorial Ag–F bonds within the [AgF_2/4] layers (Table 1). The cooperative Jahn–Teller effect results in LP AgNiF₄ structure with a three-dimensional Ag(II)Ni(II)F₄ network and antiferromagnetic coupling between Ag(II) and Ni(II) sites. This LP structure is the lowest energy among all structures found at 0 GPa, but it still has energy +8.6 kJ mol⁻¹ with respect to the binary substrates AgF₂ + NiF₂. However, it exhibits no imaginary phonon modes (Appendix S4‡) which points to its kinetic stability. Therefore, if synthesized, AgNiF₄ should be metastable at ambient pressure, similarly to AgCuF₄.

High pressures. In the AgNiF₄ system, similar high-pressure behaviour is predicted for AgCuF₄, and despite a different electron count on TM. Namely, the high pressures preserve the Ag(II) oxidation state and promote the increase of lattice connectivity by the cooperative Jahn–Teller mechanism. Under elevated pressures, the LP → HP1 transition is predicted to take place at 3 GPa (Fig. 1b). The axial compression in LP of Ag(II) is electronically stable only up to 6 GPa. Above this pressure, it vanishes, which is manifested in Fig. 1b by merging the LP curve with the HP1 from 7 GPa. The HP1 has negative enthalpy as compared to the binary fluorides from the pressure of 7 GPa up to ∼15 GPa (Fig. 1b). The maximum stabilization of AgNiF₄ relative to binary substrates reaches −3.9 kJ mol⁻¹ at 10 GPa. AgNiF₄ HP1 form remains the only high-pressure AgNiF₄ structure predicted by us up to 20 GPa. Due to small structural differences between both proposed AgNiF₄ structures, it may be expected that if HP1 structure was synthesized under high pressure it would decompress to its LP form without large internal strain.⁴³

In contrast to AgCuF₄, however, the HP1 Ag^IINi^IIF₄ structure emerges from the LP one while changing axial compression of Ag(II) cations to an elongation, taking place perpendicular to the [AgF_4/2] layers and resulting in a hole in d_x²−y² orbital. Consequently, two-dimensional connectivity within the [AgF_4/2] is established (Fig. 3c) in contrary to the situation in the LP form, where the Jahn–Teller distortion is responsible for no connectivity with the silver layers (Fig. 2c). Thus, the LP and HP1 Ag^IINi^IIF₄ structures differ topologically mainly by 2D Ag–F–Ag connectivity in the latter compared to no such connectivity in the former. The HP1 polymorph may be thought of as build from separate antiferromagnetic layers of [AgF_4/2] and [NiF_4/2] parallel to bc plane.

Cobalt

Ambient pressure. Interestingly, in the case of AgCoF₄, the difference between standard reduction potentials for the Co^3+/2+ and Ag^2+/1+ redox pairs is considerable (1.82 V vs. 1.98 V,⁴⁴ respectively), so a reaction:

AgF₂ + CoF₂ → AgF + CoF₃ (2)

could be expected. Calculations show that this reaction between binary fluorides would not be favoured though, on both DFT+U level of theory (+25.8 kJ mol⁻¹) or hybrid density functional HSE06 (+12.2 kJ mol⁻¹, see HSE06 results for all the binary and ternary compounds in ESI, Table S2‡). Having learned that, we tried to stabilize the Ag^IICo^IIF₄ solution. This Ag^IICo^IIF₄ LP polymorph (Fig. 2d) is isostructural with the lowest-energy Ag^IINi^IIF₄ LP structure. It exhibits the same inverse Jahn–Teller distortion pattern as the one described above in Ag^IINi^IIF₄ structure, i.e. substantial axial compression of Ag(II) sites and much smaller distortion at Co(II) sites, indicating that their half-filled orbitals are directed towards each other. This, together with a sufficiently large Ag–F–Co angle results in an antiferromagnetic ground state which, however, is at +5.7 kJ mol⁻¹ above binary divalent substrates.

Importantly, it appears that the lowest-energy mixed-cation structure obtained in the cobalt system corresponds to the Ag^ICo^IIIF₄ formulation, for which we also found the lowest-energy Ag^ICo^IIIF₄ polymorph. Structure quests using evolutionary algorithms resulted in many similar layered Ag^ICo^IIIF₄ structures, including KFeF₄-HT polymorph (Z = 4, for others, see ESI, Fig. S1 and S2‡). Further modifications helped us finding the lowest-energy Ag^ICo^IIIF₄ LP polymorph in the KFeF₄-LT⁴⁵ type structure (Z = 8, Fig. 4a). DFT+U calculations yield the energy of this structure to be −4.2 kJ mol⁻¹ (or −24.8 kJ mol⁻¹ at HSE06 level) with respect to the binary divalent metal fluorides. It also turns out that the energy for the Lewis acid–Lewis base reaction:

AgF + CoF₃ → Ag^ICo^IIIF₄ (3)

is negative, about −34.8 kJ mol⁻¹ at DFT+U level (−37.4 kJ mol⁻¹ at HSE06 level, Table S2‡), and it compensates for the unfavourable energy of the redox reaction (eqn (2)). Even for the models derived from parent AgF₂ type structure suitable to host Ag(II), the spontaneous electron-transfer reaction takes place; it manifests itself by the disappearance of the spin on Ag site and change of magnetic moment on the Co site. The reaction described by eqn (3) has a close analogue for other stoichiometry; the known cryolite type Ag₃CoF₆ contains no Ag(II), and its formula may be written as Ag^I₃Co^IIIF₆.

Fig. 4 Structure of Ag^ICo^IIIF₄ at (a) ambient and (b) elevated pressure (10 GPa), with selected geometric parameters of Ag(I) coordination polyhedra and [CoF_4/2F_2/1] sheets. The threshold for Ag–F bond drawing is 2.7 Å in Ag^ICo^IIIF₄ structures.

The KFeF₄-LT type structure comprises the puckered antiferromagnetic anionic sheets of [CoF_4/2F_2/1]⁻ stoichiometry which features high-spin Co(III) cations, and diamagnetic Ag(I) counterions. While in parent CoF₃ the octahedra are almost perfectly symmetric (with all bond lengths of 1.89 Å, the F–Co–F angles are distorted ±1.5° from 90°), in Ag^ICo^IIIF₄ the CoF₆ octahedra are markedly compressed with axial bond length 1.82 Å resulting in R ratio equal 0.94 (equatorial bonds are highlighted on Fig. 4a). Considering the coordination sphere of Ag(I), pristine AgF crystalizes in rock-salt structure with regular octahedra having 2.426 Å Ag–F bond lengths. In the case of AgCoF₄, however, two types of Ag(I) can be distinguished, each with coordination number, CN = 7 within 2.65 Å radius, and both in the form of a bicapped tetragonal pyramid.

High pressures. Comparing to Ni and Cu systems, richer polymorphism is predicted under elevated pressures in the AgCoF₄ system. The Ag^IICo^IIF₄ solution gains stability at elevated pressures, forming the HP1 polymorph, which resembles the HP1 polymorph of AgCuF₄ described above (Fig. 3d). Ag(II) sites in Ag^IICo^IIF₄ HP1 are far more axially compressed, suggesting a d-hole occupation mainly of d_z² orbital oriented towards Co(II) sites. The Ag–F–Co bridges with 131° angle form chains leading to an antiferromagnetic ground state. The HP1 is favoured over LP polymorph above 5 GPa, but it would not be stabilized under high pressure like Ni and Cu systems. The relative enthalpy of Ag^IICo^IIF₄ HP1 with respect to the parent divalent fluorides reaches a local minimum at about 9–10 GPa with +3.2 kJ mol⁻¹ (Fig. 1c, green series).

Likewise, at ambient pressure conditions, the intrinsic redox reaction in AgCoF₄ system is favoured at elevated pressures. Here the lowest-energy mixed valence LP Ag^ICo^IIIF₄ is predicted to undergo two subsequent high-pressure transitions at about 1 GPa (HP1) and 15 GPa (HP2), respectively while maintaining the metal oxidation states (Fig. 1c, magenta series). Both, HP1 and HP2 forms represent KMnF₄ type structures similarly as the LP one but with reduced symmetry according to the sequence Pmna (LP) → P2₁/m (HP1) → C2/c (HP2). Apparently, it turns out that Ag^ICo^IIIF₄ stability would increase under high pressure about threefold with respect to substrates at 10 GPa, up to −12.6 kJ mol⁻¹.

The first Ag^ICo^IIIF₄ high-pressure polymorph HP1 was found at 10 GPa using EA has a distorted monoclinic KMnF₄ type structure (Fig. 4b). This polymorph of Ag^ICo^IIIF₄ resembles the LP polymorph having antiferromagnetic puckered sheets of [CoF_4/2F_2/1]⁻ stoichiometry with high-spin Co(III) cations and diamagnetic Ag(I) in between. Volume decrease of Ag^ICo^IIIF₄ with respect to binary fluorides is mainly due to enhancement of [CoF_4/2F_2/1]⁻ layers buckling and increase of Ag(I) coordination number. Antiferromagnetic sheets are built from CoF₆ octahedra exhibiting axial bond compression with R ratio equal 0.92 (axial bonds are 1.78 Å, equatorial 1.92–1.93 Å, cf. Fig. 4b). The equatorial Co–F bonds form a layer parallel to the bc plane. The Ag(I) cation is found at 10 GPa in two distinct crystallographic sites which differ in their coordination number. Here, CN is either 9 or 10, with bond lengths varying from 2.31 up to 2.77 Å. For comparison, at the same pressure, parent AgF is found in the CsCl type structure with cubic coordination sphere (8 ligands) and Ag–F bond length of 2.47 Å. The second high pressure polymorph of Ag^ICo^IIIF₄ Ag^ICo^IIIF₄ also crystallizes in KMnF₄ type structure (C2/c). It features higher CN for Ag(I) sites and more buckled [CoF_4/2F_2/1]⁻ layers.

Electronic properties

The main motivation behind studying novel ternary Ag(II) fluorides is to achieve appreciable changes in electronic structure that would result in facile metallization within the [AgF₂] layers either at ambient or elevated pressures. To evaluate this possibility, we first discuss the electronic density of states (DOS) computed for AgF₂ and the studied ternary AgMF₄ fluorides at DFT+U level and zero pressure. Subsequently, we discuss the impact of pressure on their bandgaps.

Ambient pressure. The total and orbital-projected electronic DOS plots at ambient pressure are shown in Fig. 5. The DOS of the parent AgF₂ (Fig. 5a) shows a narrow band gap (1.33 eV) with a strong mixture of Ag 4d and F 2p orbitals around the Fermi level, with the Ag states dominate the lower-energy valence DOS and F states dominate the higher-energy valence DOS.^1,30 The gap opens between valence bands of predominantly F character and conduction bands of predominantly Ag character. The lowest-energy conduction band (centred around 1.5 eV) and the lowest-energy valence band (∼−6.5 eV) represent the upper and lower Hubbard band (UHB and LHB; marked with red arrows in Fig. 5) of dominant Ag d_x²−y² character, respectively. The large separation of these bands on the energy scale and their position relative to F states define AgF₂ as a charge-transfer (CT) insulator according to the Zaanen–Sawatzky–Allen classification scheme.⁴⁶

Fig. 5 Orbital projected electronic density of states (pDOS) calculated on DFT+U level for (a) parent AgF₂, (b) Ag^IICu^IIF₄, (c) Ag^IINi^IIF₄, and (d) Ag^IICo^IIF₄ compounds at 0 GPa. Red arrows indicate lower and upper Hubbard (LHB and UHB) bands of Ag²⁺. Dashed lines indicate total DOS, Ag states are drawn in grey, F in green, Cu in blue, Ni in orange and Co in magenta. Fermi level is set to zero. Spin-up and spin-down states were summed up.

Analysis of the LP Ag^IICu^IIF₄ electronic DOS (Fig. 5b) shows that the formation of this compound does not lead to significant electronic changes within the [AgF_4/2] layers with respect to pristine AgF₂. The main difference is the presence of Cu 3d states. The Cu valence states show similar distribution as the valence Ag states, while the LHB (∼7.5 eV) and UHB (∼4 eV) of Cu display even larger separation than the Ag ones, which reflects the larger U at Cu(II) sites. Consequently, the nature of the bandgap of AgCuF₄ is defined by the bandgap of the [AgF_4/2] sublayer. It is only slightly broader than in the parent AgF₂ (1.46 eV vs. 1.33 eV). Evidently, both the [AgF_4/2] and [CuF_4/2] layers in AgCuF₄ are well electronically separated, preserving the nature of their respective substrates, i.e. insulating character associated with a ligand to metal CT gap.

More significant changes vs. AgF₂ are observed in the DOS for AgNiF₄ (Fig. 5c). Here, the additional Ni 3d states predominate the valence DOS at the highest energies below the Fermi level and on average above the F 2p valence states. This contrasts AgF₂ and AgCuF₄ DOS, where the metal states are on average shifted to lower energies relative to F 2p valence states. Due to the appearance of the Ni states at higher energies the position of the Ni LHB is positioned just below the Fermi level, while the conduction band preserves the character of the Ag UHB band level. This means that the CT character of the bandgap has changed. Now the charge transfer is realized between the valence states of dominant Ni and conduction states of dominant Ag character. The appearance of Ni 3d states above the F 2p states of valence DOS results in a noticeably narrower band gap (1.09 eV) than in parent AgF₂ (1.33 e).

In the case of Ag^IICo^IIF₄, the Co 3d (Fig. 5d) valence states are shifted to even higher energies relative to the F 2p valence resulting in an even narrower bandgap of 0.90 eV. The Co LHB positioned just below the Fermi level has almost the entire Co character, meaning that charge transfer over the bandgap is now from Co(II) states to the UHB of Ag(II), and indicate the proximity of intrinsic redox reaction character.

Noticeably, the band gaps of Ag^IINi^IIF₄ and Ag^IICo^IIF₄ have an intervalence CT character, with Ni(II)/Co(II) serving as an electron donor, and Ag(II) as an acceptor, the intervalence CT being more pronounced in Ag^IICo^IIF₄. The picture of Ag^ICo^IIIF₄ is reversed relative to both Ag^IICo^IIF₄ and Ag^IINi^IIF₄, here the top of the valence band mainly consists of filled 4d states of Ag(I) while the bottom of the conduction band corresponds to the UHB of Co(III) (Fig. S7a‡). Due to the intrinsic redox reaction discussed above band gap increases up to 2.02 eV, it is thus larger than that of AgF₂, and of the Ag^IIM^IIF₄ analogues.

Clearly, the electronic structure of AgMF₄ compounds in the series M = Cu, Ni, Co, changes together with the redox properties of M(II) cations. The gradual change of M bands contribution to the valence band is apparent on band structure plots, Fig. S8,‡ as well as in DOS (Fig. 5). For AgCuF₄, with Cu(III) in fluoride environment is experimentally accessible with the greatest difficulty, AgCuF₄ preserves Ag(II) and Cu(II) oxidation states and a ligand to metal CT insulator character. For AgNiF₄, where Ni(III) forms easier, electronic DOS reveals moderate ease of intervalence CT between Ni(II) donor and Ag(II) acceptor, with the corresponding valence and conduction bands separated by a mere ∼1.1 eV. Finally, for Ag^ICo^IIIF₄, where Co(III) is most accessible, a genuine redox reaction is seen which leads to “inverse” intervalence CT character, where Ag(I) serves as an electron donor, while Co(III) as an acceptor. Note that our hybrid DFT (HSE06) calculations yielded qualitatively similar results for the ambient pressure AgMF₄ structures (Fig. S9‡).

Increased pressures. Fig. 6 shows the evolution of the bandgap with pressure in all modelled AgMF₄ systems. The band gap of Ag^IICu^IIF₄ remains almost constant about 1.5 eV up to 20 GPa, while experiencing only a slight increase upon the LP → HP1 phase transition at ∼6 GPa. Interestingly in Ag^IINi^IIF₄ the LP → HP1 transition at ∼3 GPa is accompanied by severe reduction of the band gap by a factor of two from ∼1.1 to ∼0.6 eV. After the transition, however, the band gap remains almost unchanged up to 20 GPa, excluding the prospect of its metallization. These features suggest the intervalence CT character of AgNiF₄ and a certain propensity towards redox process yielding higher oxidation states of Ni, with a concomitant reduction of Ag(II) to Ag(I). On the other hand, band gap of Ag^IICo^IIF₄ decreases monotonically throughout the entire pressure range, but its reduction is nevertheless small, and the band gap equals ∼0.7 eV at 20 GPa, so the pressure does not provide an opportunity for its metallization below 20 GPa either. The picture of Ag^ICo^IIIF₄ is the opposite, its bandgap is increased with every phase transition after which it only slowly monotonically decreases. Consequently, the bandgap at 20 GPa is even slightly higher (2.1 eV) than the 0 GPa value of 2.0 eV.

Fig. 6 Electronic band gaps dependency on pressure elevation for the lowest-enthalpy structures of (a) AgCuF₄, (b) AgNiF₄ and (c) AgCoF₄ (shown together with AgF₂). Dotted lines connect values calculated for structures separated by phase transitions. Detailed data is provided in Table S3.‡

Conclusions

The silver(II) fluoride system is theoretically predicted to resist forming ternary fluorides with Cu, and Ni fluorides at ambient pressure conditions. The isostructural substitution is largely unfavoured at ambient pressure due to excessive differences in Ag(II) and M(II) bond lengths and in the extent of their tetragonal distortion. The energies of formation of Ag^IICu^IIF₄ and Ag^IINi^IIF₄ are positive but these compounds have real phonon frequencies, hence could be metastable if prepared. Both Ag^IICu^IIF₄ and Ag^IINi^IIF₄ are predicted to be semiconductors with a predominant charge-transfer character. There is a clear trend in electronic band gaps and character of the states at the top of the valence band as one moves from Cu, via Ni to Co. The AgCuF₄ system has a comparable band gap with that of pristine AgF₂ at ambient pressure (1.46 eV vs. 1.33 eV), while AgNiF₄ system features a narrower band gap (1.09 eV).

The cobalt(II) system displays many similarities to both nickel and copper structures while having an even smaller band gap (0.90 eV). However, Ag^IICo^IIF₄ configuration is predicted to be energetically unstable due to the potent oxidizing properties of Ag(II). The cobalt–silver fluoride system is thus quite different from the other two due to the intrinsic redox process resulting in a preference for as yet unknown Ag^ICo^IIIF₄. The ambient-pressure KFeF₄ type structure of this species is computed to be a ca. 2.02 eV band gap semiconductor, stable with respect to binaries and featuring antiferromagnetic sheets of [CoF_4/2F_2/1] stoichiometry.

Application of hydrostatic pressure in silico shows that there is a pressure range where the formation of ternary silver fluorides AgMF₄ is favoured over binaries. The calculated range of stability is about 7–15 GPa for AgCuF₄, 8–15 GPa for AgNiF₄, and 0–22 GPa for Ag^ICo^IIIF₄, meaning that in these conditions each system has a negative enthalpy of formation with respect to substrates. The nickel system appears to be interesting in terms of electronic structure because at 10 GPa it should form the separate layers polymorph with a narrow band gap of about 0.62 eV, less than half of that for AgF₂. Regretfully, none of the system studied would be metallic or would feature electronically doped AgF₂ sheets. The Co system is overdoped in that sense that Ag(II) becomes entirely reduced to Ag(I). Thus, doping to AgF₂ remains a daunting target for the future studies.

Importantly, our study shows that in ternary fluorides of Ag and M (M = Ni, Cu), the Ag^IM^IIIF₄ formulation is not stable with respect to Ag^IIM^IIF₄, unlike in the known ternary oxides of these metals, AgMO₂. Thus, Cu(II) and Ni(II) are expected to resist oxidizing power of Ag(II) both at ambient and elevated pressures while in the fluoride environment. Compounds with a formula Ag^IIM^IIF₄ might hold strong antiferromagnetic interactions due to the presence of strong spin-polarizer Ag(II) and second magnetic cation of 3d series. Scrutiny of the strength of magnetic interactions in these systems, especially a detailed description of superexchange coupling between Ag(II) and M(II) spins, will be performed in a forthcoming study.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by Polish National Science Center (NCN) within Beethoven project (2016/23/G/ST5/04320). The research was carried out using supercomputers of Interdisciplinary Centre for Mathematical and Computational Modelling (ICM), University of Warsaw, under grant number GA76-19. Dr Derzsi acknowledges the ERDF, R&I Operational Program (ITMS2014+: 313011W085), Scientific Grant Agency of the Slovak Republic grant (VG 1/0223/19) and the Slovak Research and Development Agency grant (APVV-18-0168).

Notes and references

1. J. Gawraczyński, D. Kurzydłowski, R. A. Ewings, S. Bandaru, W. Gadomski, Z. Mazej, G. Ruani, I. Bergenti, T. Jaroń, A. Ozarowski, S. Hill, P. J. Leszczyński, K. Tokár, M. Derzsi, P. Barone, K. Wohlfeld, J. Lorenzana and W. Grochala, Proc. Natl. Acad. Sci. U. S. A., 2019, 116, 1495–1500.
2. D. Kurzydłowski, M. Derzsi, P. Barone, A. Grzelak, V. Struzhkin, J. Lorenzana and W. Grochala, Chem. Commun., 2018, 54, 10252–10255.
3. W. Grochala and R. Hoffmann, Angew. Chem., Int. Ed., 2001, 40, 2742–2781.
4. W. Grochala and Z. Mazej, Philos. Trans. R. Soc., A, 2015, 373, 20140179.
5. A. Grzelak, M. Derzsi and W. Grochala, Inorg. Chem., 2021, 60, 1561–1570.
6. S. Bandaru, M. Derzsi, A. Grzelak, J. Lorenzana and W. Grochala, Phys. Rev. Mater., 2021, 5, 064801.
7. R. Hoppe and G. Siebert, Z. Anorg. Allg. Chem., 1970, 376, 261–267.
8. G. Stebert and R. Hoppe, Naturwissenschaften, 1971, 58, 95–96.
9. C. Shen, L. C. Chacón, N. Rosov, S. H. Elder, J. C. Allman and N. Bartlett, C. R. Acad. Sci., Ser. IIc: Chim., 1999, 2, 557–563.
10. N. Bartlett, G. Lucier, C. Shen, W. J. Casteel, L. Chacon, J. Munzenberg and B. Žemva, J. Fluorine Chem., 1995, 71, 163–164.
11. B. Žemva, K. Lutar, A. Jesih, W. J. Casteel, A. P. Wilkinson, D. E. Cox, R. B. Von Dreele, H. Borrmann and N. Bartlett, J. Am. Chem. Soc., 1991, 113, 4192–4198.
12. J. Grannec, A. Yacoubi, A. Tressaud and L. Rabardel, Solid State Commun., 1988, 68, 363–367.
13. J. Curda, W. Klein, H. Liu and M. Jansen, J. Alloys Compd., 2002, 338, 99–103.
14. Y. J. Shin, J. P. Doumerc, P. Dordor, C. Delmas, M. Pouchard and P. Hagenmuller, J. Solid State Chem., 1993, 107, 303–313.
15. T. Sörgel and M. Jansen, Z. Anorg. Allg. Chem., 2005, 631, 2970–2972.
16. W. Stählin and H.-R. Oswald, Z. Anorg. Allg. Chem., 1969, 367, 206–208.
17. H. Muguerra, C. Colin, M. Anne, M.-H. Julien and P. Strobel, J. Solid State Chem., 2008, 181, 2883–2888.
18. M. AI-Mamouri, P. P. Edwards, C. Greaves and M. Slaski, Nature, 1994, 369, 382–384.
19. W. Grochala, R. Hoffmann, J. Feng and N. W. Ashcroft, Angew. Chem., Int. Ed., 2007, 46, 3620–3642.
20. Y. Liu-Xiang, Z. Jing-Geng, Y. Yong, L. Feng-Ying, Y. Ri-Cheng and J. Chang-Qing, Chin. Phys. Lett., 2006, 23, 426–427.
21. A. Grzelak, J. Gawraczyński, T. Jaroń, D. Kurzydłowski, A. Budzianowski, Z. Mazej, P. J. Leszczyński, V. B. Prakapenka, M. Derzsi, V. V. Struzhkin and W. Grochala, Inorg. Chem., 2017, 56, 14651–14661.
22. G. Kresse and J. Hafner, J. Phys.: Condens. Matter, 1994, 6, 8245–8257.
23. G. Kresse and J. Furthmüller, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169–11186.
24. G. Kresse and D. Joubert, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 59, 1758–1775.
25. J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou and K. Burke, Phys. Rev. Lett., 2008, 100, 136406.
26. A. I. Liechtenstein, V. I. Anisimov and J. Zaanen, Phys. Rev. B: Condens. Matter Mater. Phys., 1995, 52, R5467–R5470.
27. S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys and A. P. Sutton, Phys. Rev. B: Condens. Matter Mater. Phys., 1998, 57, 1505–1509.
28. J. A. Barreda-Argüeso, S. López-Moreno, M. N. Sanz-Ortiz, F. Aguado, R. Valiente, J. González, F. Rodríguez, A. H. Romero, A. Muñoz, L. Nataf and F. Baudelet, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 88, 214108.
29. M. Cococcioni and S. de Gironcoli, Phys. Rev. B: Condens. Matter Mater. Phys., 2005, 71, 035105.
30. C. Miller and A. S. Botana, Phys. Rev. B, 2020, 101, 195116.
31. D. Kurzydłowski, Crystals, 2018, 8, 140.
32. L. C. Ming, M. H. Manghnani, T. Matsui and J. C. Jamieson, Phys. Earth Planet. Inter., 1980, 23, 276–285.
33. D. C. Lonie and E. Zurek, Comput. Phys. Commun., 2011, 182, 372–387.
34. XtalOpt – Publications, http://xtalopt.github.io/pub.html, accessed October 2, 2020.
35. A. V. Krukau, O. A. Vydrov, A. F. Izmaylov and G. E. Scuseria, J. Chem. Phys., 2006, 125, 224106.
36. K. Momma and F. Izumi, J. Appl. Crystallogr., 2011, 44, 1272–1276.
37. U. Herath, P. Tavadze, X. He, E. Bousquet, S. Singh, F. Muñoz and A. H. Romero, Comput. Phys. Commun., 2020, 251, 107080.
38. W. Setyawan and S. Curtarolo, Comput. Mater. Sci., 2010, 49, 299–312.
39. P. Fischer, D. Schwarzenbach and H. M. Rietveld, J. Phys. Chem. Solids, 1971, 32, 543–550.
40. W. Massa and D. Babel, Chem. Rev., 1988, 88, 275–296.
41. B. Žemva, K. Lutar, L. Chacon, M. Fele-Beuermann, J. Allman, C. Shen and N. Bartlett, J. Am. Chem. Soc., 1995, 117, 10025–10034.
42. W. Grochala, Phys. Status Solidi B, 2006, 243, R81–R83.
43. In fact, during standard geometry optimization process a smooth transition between both HP1 and LP polymorphs occurred (i.e. optimization of HP1 polymorph at 0 GPa gave LP structure and also optimization of LP polymorph at 10 GPa led to HP1 structure).
44. A. J. Bard, R. Parsons, J. Jordan and International Union of Pure and Applied Chemistry, Standard potentials in aqueous solution, M. Dekker, New York, 1985.
45. J. Lapasset, P. Sciau, J. Moret and N. Gros, Acta Crystallogr., Sect. B: Struct. Sci., 1986, 42, 258–262.
46. J. Zaanen, G. A. Sawatzky and J. W. Allen, Phys. Rev. Lett., 1985, 55, 418–421.

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Footnotes

† This work is dedicated to Prof. Gary Schrobilgen at his 75th birthday.

‡ Electronic supplementary information (ESI) available: Study of difluorides compression, detailed results of EA runs, electronic structure details at HP, crystal structures and vibration frequencies. See DOI: 10.1039/d1ra04970d

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