Polyanion Condensation in Inorganic and Hybrid Fluoridometallates (IV) of Octahedrally Coordinated Ti, Zr, Hf, V, Cr, W, Mn, Ge, Sn, and Pb

Abstract

In fluorides, the M⁴⁺ cations of M = Ti, V, Cr, Mn, Ge, Sn, and Pb favour the octahedral coordination of six F ligands. Some examples of M⁴⁺ with larger cations (M = Zr, Hf, W) in octahedral coordination are also known. If not enough F ligands are available to have isolated M^IVF₆ octahedra, they must share their F ligands. The crystal structures of such fluoride metalates (IV) show the variety of possible structural motifs of the zero-dimensional oligomeric anions [M₂F₁₁]³⁻ (M = Ti, Cr), [M₃F₁₅]³⁻ (M = Zr, Hf), [M₃F₁₆]⁴⁻ (M = Ge), [M₄F₁₈]²⁻ (M = Ti, W), [M₄F₁₉]³⁻ (M = Ti), [M₄F₂₀]⁴⁻ (M = Ti), [M₅F₂₃]³⁻ (M = Ti), [M₆F₂₇]³⁻ (M = Ti), [M₆F₂₈]⁴⁻ (M = Ti), [M₈F₃₆]⁴⁻ (M = Ti, Mn), [M₁₀F₄₅]⁵⁻ (M = Ti) to one-dimensional chains ([MF₅]⁻)_∞ (M = V, Ti, Cr, Ge, Sn, Pb), double chains ([M₂F₉]⁻)_∞ (M = Ti, Mn), columns ([M₃F₁₃]⁻)_∞ (M = Ti), ([M₄F₁₉]³⁻)_∞ (M = Ti), ([M₇F₃₀]²⁻)_∞ (M = Ti), ([M₉F₃₈]²⁻)_∞) (M = Ti), two-dimensional layers ([M₂F₉]⁻)_∞ (M = Cr), ([M₈F₃₃]⁻)_∞ (M = Ti), and three-dimensional ([M₆F₂₇]³⁻)_∞ (M = Ti) architectures. A discrete monomeric [M₂F₉]⁻ anion with two M^IVF₆ octahedra sharing a common face has not yet been experimentally demonstrated, while two examples containing discrete dimeric [M₂F₁₀]²⁻ anions (M = Ti) with two M^IVF₆ octahedra sharing an edge are still in question.

1. Introduction

In the structural chemistry of inorganic and hybrid (with organic cation and inorganic anion) fluorine compounds, the coordination number six with an octahedral coordination of the metal atom (M) of the anion by six fluorine ligands is preferred for almost all transition elements and for some main group elements [1,2]. Exceptions are metal cations of heavier elements, which prefer a higher coordination than six, and metal cations with the electron configurations d⁸ and d⁹, which often occur in square-planar coordination. In the fluorides, condensation of MF₆ octahedra is favoured over the apexes, in contrast to the higher halogen homologues, where associations over the edges or faces are more common [3].

When the number of F ligands per M^IV cation is less than six, the M^IVF₆ octahedra must share their F ligands instead of being isolated. The usual term for such shared F atoms is a bridging fluorine atom (F_b), i.e., the fluorine atom connects two metal centres of the anion. The term terminal fluorine atom (F_t) is used for the remaining fluorine atoms that are not involved in such bridging.

The crystal structures of fluoride metallates (IV) with linked M^IVF₆ octahedra show the variety of possible structural motifs, from oligomeric anions to chains and columns to layers and three-dimensional framework architectures of the anions. This paper summarizes known perfluoridometallate (IV) salts with different anions determined in the crystal structures of inorganic and hybrid fluoridometallates (IV) with M = Ti, Zr, Hf, V, Cr, W, Mn, Ge, Sn, and Pb. Only examples with octahedral coordination of the M(IV) centre are included.

Many new inorganic and hybrid fluoridometallate (IV) salts of octahedrally coordinated Ti, Zr, Hf, V, Cr, W, Mn, Ge, Sn, and Pb have been structurally characterized in the last two decades. They contain anions in different sizes and geometries. Some of them were prepared for the first time and have a unique geometry. The aim of this review was to collect all of these data in one place and provide researchers with useful information for further planning of the preparation of new inorganic and hybrid fluoridometallate (IV) salts with anions in the desired geometry.

2. Discrete Oligomeric Anions

2.1. [M₂F₉]⁻ Anion (M = Ti, Ge)

¹⁹F NMR spectroscopy was used to detect the existence of the dimeric [Ti₂F₉]⁻ anion in liquid SO₂ solution [4]. The [Ti₂F₉]⁻ anion has a face-linked bioctahedral structure (Figure 1). The “volume-based” thermodynamic approach suggests that cations larger than Cs⁺ favour the formation of solid perfluoridotitanium (IV) salts with discrete dimeric [Ti₂F₉]⁻ anions [5]. However, experiments have shown that an increase in the size of monocations does not favour the formation of [Ti₂F₉]⁻ over [Ti₄F₁₈]²⁻ salts (containing discrete anions). Crystal structure determination of the [Me₄N]⁺ and [Ph₄P]⁺ salts revealed that both compounds were [Ti₄F₁₈]²⁻ salts, i.e., [Me₄N]₂[Ti₄F₁₈] and [Ph₄P]₂[Ti₄F₁₈] were obtained instead of [Me₄N][Ti₂F₉] and [Ph₄P][Ti₂F₉] [6]. Although a theoretical ab initio study revealed that the dimeric [M₂F₉]⁻ anions (M = T, Ge) are predicted to be electronically and thermodynamically stable systems [7], all attempts to isolate salts with such anions in the solid state have failed so far.

2.2. [M₂F₁₀]²⁻ Anion (M = Ti)

The M^IVF₆ edge-sharing structure of the dimeric anion [Ti₂F₁₀]²⁻ was proposed on the basis of the ¹⁹F NMR data of the SO₂ solution of the di-n-propylammonium hexafluoridotitanate–TiF₄ system (Figure 2) [4]. Later, two crystal structures were described. However, both are doubtful. The first report describes a [Ti₂F₁₀]²⁻ salt of tetramethyltetrathiafulvalene (TMTTF), where the average charge of the single TMTTF cation was estimated to be +2/3, while the oxidation state of the titanium was assumed to be Ti⁴⁺ [8]. The second compound was originally formulated as a salt of the diprotonated piperazinium cation [C₄H₁₂N₂]₂[Ti₂F₁₀]·2H₂O [9]. In this case, the anion has a charge of −4, which corresponds to a Ti³⁺ compound. Later, the formula was corrected by removing a hydrogen atom, resulting in a monoprotonated piperazinium cation [C₄H₁₁N₂]₂[Ti₂F₁₀]·2H₂O [10]. In the figures shown, however, diprotonated cations remained [10]. The 3+ oxidation state is also indicated by the Jahn–Teller distortion of the octahedrally coordinated titanium atoms mentioned by the author. Therefore, the structure of the discrete dimeric [Ti₂F₁₀]²⁻ anion is still limited to the reported DFT-optimised theoretical structure [11], while reliable experimental evidence is still pending.

2.3. [M₂F₁₁]³⁻ Anion (M = Ti, Cr)

A summary of the crystal data of the salts consisting of [M₂F₁₁]³⁻ anions (M = Ti, Cr) is given in

Table 1. Crystal data of the salts consisting of [M₂F₁₁]³⁻ anions (M = Ti, Cr).

Compound	Space Group	a, b, c/Å	α, β, γ/°	V/Å3	Z	T/K *	Ref.
[C3H5N2]3[Ti2F11]	monoclinic	13.5371(2)	90	3563.0(1)	8	200	[12]
	C2/m	25.7451(4)	100.980(1)
		10.4139(2)	90
[C5H6N]2[H3O][Ti2F11]·H2O	triclinic	6.684(5)	84.733(5)	454.1	1	293	[13]
	P-1	8.215(5)	85.250(5)
		8.345(5)	86.692(5)
[N(CH3)4]4[Ti2F11][Ti2F9(H2O)2]	monoclinic	10.7241(4)	90	870.82(5)	2	150	[14]
	C2	13.7028(5)	90.169(4)
		5.9260(2)	90
K3Cr2F11·2HF	monoclinic	11.694(8)	90	1114.9(13)	4	200	[15]
	P21/n	7.541(4)	111.102(14)
		13.552(10)	90

* The crystal structures were determined at the indicated temperatures.

.

In discrete [M₂F₁₁]³⁻ anions (M = Ti, Cr), two MF₆ octahedra share a common vertex. The distortion of the geometry of the [M₂F₁₁] units is usually described by the bridging angle α (bending of F₅M–F_b–MF₅ around the bridging fluorine F_b) and the torsion angle ψ (torsion of two planar MF_4,eq groups from the eclipsed to the staggered conformation). There are three crystallographically unique Ti₂F₁₁ units in [ImH]₃[Ti₂F₁₁]. Each of them has a different conformation (Figure 3) [12]. In two of them, the equatorial TiF₄-planes of the TiF₆ octahedra of [Ti₂F₁₁]³⁻ are eclipsed and the Ti–F_b–Ti angle is 180°. In the third, the TiF₄-planes of two TiF₆ octahedra are in gauche conformation with a dihedral angle of 8.50(6)° and a slightly bent Ti–F_b–Ti angle (174.28(18)°) [12]. In both, [ImH]₃[Ti₂F₁₁] and [C₅H₆N]₂[H₃O][Ti₂F₁₁]·H₂O, the Ti–F_t bond lengths are comparable. They range from 1.768(3) to 1.908(2) Å for Ti–F_t bonds and from 1.9683(5) to 1.9805(6) Å for Ti–F_b bond lengths [12,13].

In [C₅H₆]₂[H₃O][Ti₂F₁₁]·2H₂O, the dimeric [Ti₂F₁₁]³⁻ anions are linear (Figure 4), nearly symmetric dimers (α = 180°; ψ is close to zero) [13].

The crystal structure of [N(CH₃)₄]₄[Ti₂F₁₁][Ti₂F₉(H₂O)₂] contains disordered [Ti₂F₁₁]³⁻ anions [14]. The DFT optimized structure of the [Ti₂F₁₁]³⁻ anion has been also published [11]. The corner-sharing structure of the dimeric [Ti₂F₁₁]³⁻ anion was also proposed based on the ¹⁹F NMR data of the SO₂ solution [4].

The crystal structure of K₃Cr₂F₁₁·2HF shows [Cr₂F₁₁]³⁻ anions strongly distorted from the ideal D_4h symmetry (Figure 5) [15]. The bridging angle is 141° and the dihedral angle is 43° [15]. Due to the large Cr–F_b–Cr bending angle, the fluorine atoms are in a staggered (gauche) conformation to minimize their repulsion. As expected, the Cr–F_t bonds are shorter (1.757 Å–1.817 Å) than the Cr–F_b bonds involved in the Cr–F_b–Cr bridge (1.916(3) Å, 1.924(5) Å) or the Cr–F bonds involved in hydrogen bonding (1.901(5) Å) [15].

2.4. [M₃F₁₃]⁻ Anion (M = Ti, Ge)

Theoretical ab initio calculations have shown that the global minimum structure of the [Ti₃F₁₃]⁻ anion corresponds to a C_3v-symmetry structure comprising an equilateral triangle of three TiF₆ octahedra that additionally share an F atom over the centre of the triangle (Figure 6) [7]. The entire structure can be considered as consisting of three octahedra sharing four F atoms. The oligomeric [Ti₃F₁₃]⁻ anion, the similar [Ge₃F₁₃]⁻ isomer, or another [M^IV₃F₁₃]⁻ anion (M = M⁴⁺) have not yet been observed experimentally.

2.5. [M₃F₁₅]³⁻ Anion (M = Zr, Hf)

A summary of the crystal data of the salt consisting of [M₃F₁₅]³⁻ anions (M = Zr) is given in

Table 2. Crystal data of the salt consisting of [M₃F₁₅]³⁻ anions (M = Zr).

Compound	Space Group	a, b, c/Å	α, β, γ/°	V/Å3	Z	T/K *	Ref.
[C27H37N2]3[Zr3F15]·4thf · 0.55(CH2Cl2)	triclinic	15.935(4)	81.698(16)	5401(3)	2	120	[16]
	P-1	17.240(4)	85.337(17)
		21.679(7)	66.454(13)

* The crystal structure was determined at the indicated temperature.

.

The crystal structure of [IDiPPH]₃[M₃F₁₅]·4thf·0.55(CH₂Cl₂) (M = Zr or Hf) (IDiPP = 1,3-(2,6-di-isopropylphenyl)imidazol-2-ylidene) consists of oligomeric trinuclear [M₃F₁₅]³⁻ (M = Zr, Hf) anions composed of three octahedral MF₆ units sharing two cis-vertices and forming a triangle (Figure 7) [16]. In the Zr salt, the Zr–F_t bond lengths (1.942(4)–1.988(4) Å) are shorter than the Zr–F_b bond lengths (2.124(4)–2.139(4) Å), and the Zr–F_b–Zr angles are in the range 155.6(2)–159.6(2)° [16]. The Hf system formed crystals of poor quality, so its complete crystal structure is not known.

2.6. [M₃F₁₆]⁴⁻ Anion (M = Ge)

A summary of the crystal data of the salts consisting of [M₃F₁₆]⁴⁻ anions (M = Ge) are given in

Table 3. Crystal data of the salts consisting of [M₃F₁₆]⁴⁻ anions (M = Ge).

Compound	Space Group	a, b, c/Å	α, β, γ /°	V/Å3	Z	T/K *	Ref.
[(CH2)2SOH][Ge3F16]	monoclinic	7.9406(11)	90	3094	2	123(2)	[17]
	P21/c	27.224(2)	90.00
		7.8817(11)	90
[C(NH2)2(NH3)2][Ge3F16]·HF	tetragonal	12.000(5)	90	1617.1(12)	4	143(2)	[18]
	P42bc	12.000(5)	90
		11.230(5)	90
[C(NH2)2(NH3)2][Ge3F16]·2HF	triclinic	7.3073(5)	86.360(7)	429.46(6)	1	143(2)	[18]
	P-1	7.4883(6)	80.768(6)
		8.2439(7)	74.743(6)

* The crystal structures were determined at the indicated temperatures.

.

Linear trimeric [Ge₃F₁₆]⁴⁻ anions were found in [(CH₂)₂SOH][Ge₃F₁₆] (Figure 8) [17], [C(NH₂)₂(NH₃)₂][Ge₃F₁₆]·HF (Figure 9) [18], and [C(NH₂)₂(NH₃)₂][Ge₃F₁₆]·2HF (Figure 10) [18]. The [Ge₃F₁₆]⁴⁻ anion consists of a chain of three slightly distorted GeF₆ octahedra connected by the bridging F atoms in a staggered conformation. The F_b atoms are in the trans position. In [(CH₂)₂SOH][Ge₃F₁₆], as expected, the Ge–F_t bonds are shorter (1.744(3) Å–1.788(2) Å) than the Ge–F_b bonds (1.914(2)–1.921(2) Å) involved in the Ge–F_b–Ge bridge [17]. The Ge–F_b–Ge angles are in the range (144.8–149.9 Å) [17]. The corresponding bond lengths and angles in [C(NH₂)₂(NH₃)₂][Ge₃F₁₆]·nHF (n = 1, 2) are comparable [18].

2.7. [M₄F₁₈]²⁻ Anion (M = Ti, W)

A summary of the crystal data of the salts consisting of [M₄F₁₈]²⁻ anions (M = Ti, W) is given in

Table 4. Crystal data of the salts consisting of [M₄F₁₈]²⁻ anions (M = Ti, W).

Compound	Space Group	a, b, c/Å	α, β, γ /°	V/Å3	Z	T/K *	Ref.
[TiF2([15]crown-5)][Ti4F18]⋅0.5MeCN	monoclinic	8.3335(9)	90	5560.4(11)	8	198	[5]
	P21/c	41.887(5)	103.927(2)
		16.412(2)	90
[N(CH3)4]2[Ti4F18]	orthorhombic	13.278(1)	90	2431.1(3)	4	200	[6]
	Pnma	10.4935(6)	90
		17.448(1)	90
[(C6H5)4P]2[Ti4F18]	triclinic	10.1172(1)	83.880(9)	2544.4(2)	2	200	[6]
	P-1	13.0011(3)	80.335(8)
		20.913(1)	69.988(6)
[o-C6H4(P(C6H5)2H)2][Ti4F18]	monoclinic	15.264(2)	90	3698.8(6)	4	120	[19]
	P21/n	14.925(2)	104.312(7)
		16.747(2)	90
[WCl2(cp)2][W4F18] (cp = η-C6H5)	orthorhombic	13.625(5)	90	3418(2)	8	296(1)	[20]
	Pnma	11.225(3)	90
		22.350(3)	90

* The crystal structures were determined at the indicated temperatures.

.

The crystal structure of [TiF₂([15]crown-5)][Ti₄F₁₈]⋅0.5MeCN was the first example of a tetrameric [Ti₄F₁₈]²⁻ anion (Figure 11) [5]. Later, it was also found in the salts [N(CH₃)₄]₂[Ti₄F₁₈] [6], [(C₆H₅)₄P]₂[Ti₄F₁₈] [6], [o-C₆H₄(P(C₆H₅)₂H)₂][Ti₄F₁₈] [19], o-C₆H₄(As(CH₃)₂H)₂][Ti₄F₁₈] [19], and [HⁱPrS(CH₂)₂SⁱPrH][Ti₄F₁₈] [19]. The latter two were only identified spectroscopically [19]. In the [Ti₄F₁₈]²⁻ anion, each TiF₆ octahedron shares three of its F_b atoms (in the fac position) with three other TiF₆ octahedra. Consequently, the Ti atoms of each TiF₆ octahedron are coordinated by three terminal and three bridging fluorine atoms. The tetramer exhibits an overall T_d symmetry. The DFT-optimized structure of the [Ti₄F₁₈]²⁻ anion has also been reported [11].

The [W₄F₁₈]²⁻ anion in [WCl₂(cp)₂][W₄F₁₈] (cp = η-C₆H₅) has the same geometry as the [Ti₄F₁₈]²⁻ anion (Figure 11) [20]. The W–Ft bond distances range from 1.66(1) to 1.89(1) Å, while the W–F_b bond lengths are on average longer, ranging from 1.88(1) to 2.174(5) Å [20].

2.8. [M₄F₁₉]³⁻ Anion (M = Ti)

A summary of the crystal data of the salt consisting of [M₄F₁₉]³⁻ anions (M = Ti) is given in

Table 5. Crystal-data of the salt consisting of [M₄F₁₉]³⁻ anions (M = Ti).

Compound	Space Group	a, b, c/Å	α, β, γ/°	V/Å3	Z	T/K *	Ref.
[XeF5]3[Ti4F19]	monoclinic	12.0866(5)	90	2416.6(2)	4	200	[21]
	P21/c	9.5615(3)	96.301(2)
		21.0377(8)	90

* The crystal structure was determined at the indicated temperature.

.

The crystal structure of [XeF₅]₃[Ti₄F₁₉] is the only example containing discrete tetrameric [Ti₄F₁₉]³⁻ anions [21]. The [Ti₄F₁₉]³⁻ anion consists of four TiF₆ octahedra. Two of the TiF₆ octahedra, which share a fluorine atom, are additionally bridged by two TiF₆ octahedra (Figure 12).

2.9. [M₄F₂₀]⁴⁻ Anion (M = Ti)

A summary of the crystal data of the salts consisting of [M₄F₂₀]⁴⁻ anions (M = Ti) is given in

Table 6. Crystal data of the salts consisting of [M₄F₂₀]⁴⁻ anions (M = Ti).

Compound	Space Group	a, b, c/Å	α, β, γ/°	V/Å3	Z	T/K *	Ref.
α-[C3H5N2]4[Ti4F20]	triclinic	8.791(3)	118.808(8)	681.8(5)	1	200	[12]
	P-1	9.971(4)	92.366(3)
		10.126(4)	113.595(8)
β-[C3H5N2]4[Ti4F20]	monoclinic	13.2139(4)	90	1384.35(10)	2	298	[12]
	C2/m	15.2096(7)	129.690(1)
		8.9514(3)	90
[C(NH2)3]4[Ti4F20]	triclinic	8.6958(2)	118.467(3)	636.42(3)	1	200	[22]
	P-1	9.7433(2)	111.687(3)
		9.7533(3)	95.516(2)
[C(NH2)3]4(H3O)4[Ti4F20][TiF5]4	monoclinic	9.5935(4)	90	2171.0(2)	2	150	[22]
	P21/c	7.4536(4)	90.244(4)
		30.361(1)	90

* The crystal structures were determined at the indicated temperatures.

.

The [Ti₄F₂₀]⁴⁻ anion consists of four TiF₆ octahedra, which are connected to each other and form a slightly distorted planar square. Each octahedron shares two F atoms in the cis position. In all known examples (α- and β-[C₃H₅N₂]₄[Ti₄F₂₀] (Figure 13 and Figure 14), [C(NH₂)₃]₄[Ti₄F₂₀] (Figure 15), and [C(NH₂)₃]₄(H₃O)₄[Ti₄F₂₀][TiF₅]₄) (Figure 16), it has a similar geometry [12,22]. Each Ti atom is coordinated with two bridging and four terminal fluorine atoms. In β-[ImH]₄[Ti₄F₂₀], the Ti–F_t bond lengths range from 1.776(3) to 1.824(4) Å and are significantly shorter than the Ti–F_b bonds (1.956(2) Å; 1.978(2) Å) [12]. The Ti–F_t and Ti–F_b bond lengths in other [M₄F₂₀]⁴⁻ salts [22] are comparable to those in β-[ImH]₄[Ti₄F₂₀] [12]. Quantum chemical calculations at the B3LYP/SDDALL level of theory were used to determine the gas phase geometries and vibrational frequencies of the [Ti₄F₂₀]⁴⁻ anions, which was helpful in assigning the experimental vibrational frequencies of the anion [12].

2.10. [M₅F₂₃]³⁻ Anion (M = Ti)

A summary of the crystal data of the salt consisting of [M₅F₂₃]³⁻ anions (M = Ti) is given in

Table 7. Crystal data of the salt consisting of [M₅F₂₃]³⁻ anions (M = Ti).

Compound	Space Group	a, b, c/Å	α, β, γ /°	V/Å3	Z	T/K *	Ref.
[C3H5N2]3[Ti5F23]	orthorhombic	22.0259(4)	90	2784.29(9)	4	200	[12]
	Pna21	10.2622(2)	90
		12.3180(2)	90

* Crystal structure was determined at the given temperature.

.

The crystal structure of [ImH]₃[Ti₅F₂₃] (Im = imidazole) is the only example that contains a discrete pentameric [M₅F₂₃]³⁻ anion (Figure 17) [12]. It is built from five TiF₆ units, with four of the TiF₆ octahedra sharing two cis-vertices and forming a tetrameric ring as in [Ti₄F₂₀]⁴⁻, and the fifth TiF₆ unit sharing three fluorine vertices with three TiF₆ units of the tetrameric ring. The bond lengths of Ti–F_t and Ti–F_b are 1.757(3)–1.848(3) Å and 1.942(2)–2.014(2) Å, respectively [12]. Quantum chemical calculations at the B3LYP/SDDALL level of theory were used to determine the gas phase geometries and vibrational frequencies of the [Ti₅F₂₃]³⁻ anions, which were helpful in assigning the experimental vibrational frequencies [12].

2.11. [M₆F₂₇]³⁻ Anion (M = Ti)

A summary of the crystal data of the salts consisting of [M₆F₂₇]³⁻ anions (M = Ti) is given in

Table 8. Crystal data of the salts consisting of [M₆F₂₇]³⁻ anions (M = Ti).

Compound	Space Group	a, b, c/Å	α, β, γ /°	V/Å3	Z	T/K *	Ref.
C(NH2)3]3[Ti6F27]·SO2	monoclinic	18.0595(3)		6240.5(2)	8	150	[22]
	P21/c	12.6281(2)	99.744(2)
		27.7642(5)
[C3H5N2]2[H3O][Ti6F27]	tetragonal	22.1506(4)	90	5686.1(2)	8	150	[22]
	P42/nmc	22.1506(4)	90
		11.5890(3)	90

* The crystal structures were determined at the indicated temperatures.

.

In C(NH₂)₃]₃[Ti₆F₂₇]·SO₂, the [Ti₆F₂₇]³⁻ anion consists of six TiF₆ octahedra (Figure 18) [22]. Three TiF₆ octahedra form a trimeric ring by sharing cis-vertices. Two such rings are connected via the bridging fluorine atoms and form a trigonal-prismatic geometry. In this way, all titanium atoms are coordinated with three F_t and three F_b atoms, which are located in the fac positions. The bond lengths of Ti–F_t and Ti–F_b are 1.754(1)–1.788(1) and 1.943(1)–2.010(1) Å, respectively [22].

The [Ti₆F₂₇]³⁻ anion with the same geometry was also observed in the crystal structure of [C₃H₅N₂]₂[H₃O][Ti₆F₂₇] (Figure 18), where disordering of the imidazolium cations was observed and there were problems in determining additional cations providing the missing positive charge [22]. It was assumed that [H₃O]⁺ cations were most likely present.

2.12. [M₆F₂₈]⁴⁻ Anion (M = Ti)

In the study of the imidazole–TiF₄-HF system, single crystals of the compound [ImH]_8−n[X]_n[Ti₈F₃₆][Ti₆F₂₈] were grown [23]. Its crystal structure contains two different perfluoridotitanate (IV) anion–cubic [Ti₈F₃₆]⁴⁻ octamers and a hexameric [Ti₆F₂₈]⁴⁻ anion. Unfortunately, it was not possible to accurately determine all cations in the crystal structure, but the proposed models of the anions are well refined. The [Ti₆F₂₈]⁴⁻ anion has a very unusual geometry (Figure 19). In the centre are two TiF₆ octahedra that share a vertex. Attached to this pair is a TiF₆ unit that shares a fluorine atom with each of the octahedra. There is also a chain of three TiF₆ octahedra in which each octahedron at the end of the chain shares two vertices with two octahedra in the centre of the [Ti₆F₂₈]⁴⁻ anion.

2.13. [M₈F₃₆]⁴⁻ Anion (M = Ti, Mn)

A summary of the crystal data of the salts consisting of [M₈F₃₆]⁴⁻ anions (M = Ti, Mn) is given in

Table 9. Crystal data of the salts consisting of [M₈F₃₆]⁴⁻ anions (M = Ti, Mn).

Compound	Space Group	a, b, c/Å	α, β, γ/°	V/Å3	Z	T/K *	Ref.
K4Ti8F36·8HF	triclinic	10.2054(7)	79.808(14)	886.21(14)	1	200	[24]
	P-1	10.3448(1)	65.208(11)
		10.5896(2)	60.889(11)
Rb4Ti8F36·6HF	triclinic	10.199(2)	89.68(6)	908.2(7)	1	200	[24]
	P-1	10.4191(5)	66.41(5)
		10.5848(7)	64.17(4)
[H5O2]4[Ti8F36]	tetragonal	11.3935(5)	90	1613.7(2)	2	150	[22]
	I4/m	11.3935(5)	90
		12.4312(9)	90
[XeF5]4[Mn8F36]	monoclinic	9.34476(12)	90	1974.98(4)	2	150	[25]
	P21/c	17.9511(2)	99.5339(12)
		11.93831(15)	90

* The crystal structures were determined at the indicated temperatures.

.

The [Ti₈F₃₆]⁴⁻ anion in K₄Ti₈F₃₆·8HF [24], Rb₄Ti₈F₃₆·6HF [24], and [H₅O₂]₄[Ti₈F₃₆] [22] resembles a cube species consisting of eight TiF₆ octahedra, with the eight titanium atoms located at the vertices of a cube (Figure 20). Each of the TiF₆ octahedra shares three fluorine atoms (in the fac position) with three neighbouring TiF₆ octahedra. In K₄Ti₈F₃₆·8HF, the Ti–F_t bond lengths are 1.755(2)–1.801(2) Å and Ti–F_b 1.9239(19)–2.0139(19) Å, while in Rb₄Ti₈F₃₆·6HF, the Ti–F_t bond distances are 1.754(6)–1.783(6) Å and Ti–F_b 1.939(7)–2.005(6) Å [24]. Both sets of distances are consistent with those previously observed in various fluoride–titanate (IV) compounds. The crystal structure of the compound [H₅O₂]₄[Ti₈F₃₆] consists of octameric [Ti₈F₃₆]⁴⁻ anions (Figure 20) and asymmetric [H₅O₂]⁺ cations. The former have a similar geometry (Ti–F_t bonds with lengths of 1.757(1), 1.780(1), 1.784(1) Å and five Ti–F_b bonds with lengths of 1.956(1), 2 × 1.964(1), and 2 × 1.9738(4) Å) [22] as in the crystal structures of K₄[Ti₈F₃₆]·8HF and Rb₄[Ti₈F₃₆]·6HF [24].

The geometry of the [Mn₈F₃₆]⁴⁻ anion (Figure 21) in [XeF₅]₄[Mn₈F₃₆] [25] is completely different from that of the [Ti₈F₃₆]⁴⁻ anion. In [XeF₅]₄[Mn₈F₃₆], each MnF₆ octahedron of [Mn₈F₃₆]⁴⁻ shares three fluorine atoms (in fac position) with three neighbouring MnF₆ octahedra, resulting in a ring-shaped [Mn₈F₃₆]⁴⁻ geometry. Each [Mn₈F₃₆]⁴⁻ anion forms secondary F···Xe contacts with six [XeF₅]⁺ cations. The Mn–F bond distances can be divided into three groups. The Mn–F(···Xe), where F is involved in secondary contacts with [XeF₅]⁺ cations, are longer (1.740(2)–1.765(2) Å) than Mn–F_t bonds (F_t = terminal fluorine atoms without further interactions; 1.710(2)–1.717(2) Å) but shorter than the Mn–F_b(–Mn) bond distances (F_b = fluorine atoms bridging two Mn atoms; 1.8498(19)–1.9529(19) Å) [25].

2.14. [M₁₀F₄₅]⁵⁻ Anion (M = Ti)

A summary of the crystal data of the salt consisting of [M₁₀F₄₅]⁵⁻ anions (M = Ti) is given in

Table 10. Crystal data of the salt consisting of [M₁₀F₄₅]⁵⁻ anions (M = Ti).

Compound	Space Group	a, b, c/Å	α, β, γ/°	V/Å3	Z	T/K *	Ref.
α-[XeF5]5[Ti10F45]	monoclinic	18.9017(6)	90	5436.4(3)	4	150	[26]
	Cc	16.6334(5)	94.004(3)
		17.3336(5)	90
β-[XeF5]5[Ti10F45]	orthorhombic	18.8980(4)	90	5489.7(2)	4	296	[26]
	Cmc21	16.7388(4)	90
		17.3542(4)	90

* The crystal structure was determined at the indicated temperature.

.

The crystal structure determination of [XeF₅]₅[Ti₁₀F₄₅] reveals the largest known discrete perfluometallate (IV) anion [Ti₁₀F₄₅]⁵⁻ (Figure 22) [26]. [XeF₅]₅[Ti₁₀F₄₅] crystallises in two crystal modifications at low (α-phase, 150 K) and ambient (β-phase, 296 K) temperatures. The crystal structure of β-[XeF₅]₅[Ti₁₀F₄₅] consists of [XeF₅]⁺ cations and discrete decameric [Ti₁₀F₄₅]⁵⁻ anions composed of ten TiF₆ octahedral units. Each of the ten TiF₆ octahedra shares three fac-vertices with neighbouring TiF₆ units, resulting in a double ring-like geometry of the [Ti₁₀F₄₅]⁵⁻ anion. The bond lengths of Ti–F_t and Ti–F_b are in the range of 1.728(7)–1.823(6) Å and 1.916(6)–2.006(6) Å, respectively [26]. The low-temperature phase α-[XeF₅]₅[Ti₁₀F₄₅] is monoclinic. The main difference between the α- and β-[XeF₅]₅[Ti₁₀F₄₅] phases is that the [XeF₅]⁺ cations in the α-phase are fully ordered, whereas one of the three crystallographically unique [XeF₅]⁺ cations in the β-phase is two-fold disordered.

3. Polymeric Chain-like ([MF₅]⁻)_∞ Anion (M = Ti, V, Cr, Mn, Ge, Sn, Pb)

Polymeric ([MF₅]⁻)_∞ anions consist of single chains of MF₆ octahedra connected via cis- or trans-vertices or both as in (XeF₅CrF₅)₄·XeF₄.

3.1. Trans-([MF₅]⁻)_∞ Anion (M = Ge, Cr)

A summary of the crystal data of the salts consisting of trans-([MF₅]⁻)_∞ anions (M = Ge, Cr) is given in

Table 11. Crystal data of the salts consisting of trans-([MF₅]⁻)_∞ anions (M = Ge, Cr).

Compound	Space Group	a, b, c/Å	α, β, γ/°	V/Å3	Z	T/K *	Ref.
XeF5GeF5	orthorhombic	7.119(2)	90	683.9(5)	4	293	[27]
	Pmnb	12.986(4)	90
		7.398(1)	90
XeF2·CrF4	monoclinic	7.666(2)	90	551.5	4	293(1)	[28]
	P21/n	7.268(5)	91.25(2)
		9.901(3)	90

* The crystal structures were determined at the indicated temperatures.

.

The crystal structure of XeF₅GeF₅ is a rare case in which M^IVF₆ octahedra share their F atoms in trans position to form infinite ([MF₅]⁻)_∞ chain-like anions (Figure 23) [27]. The coordination around each Ge atom is an elongated octahedron of fluorine atoms. The Ge–F_b–Ge angle is equal to 140.70(20)° [27]. Viewed along the GeF₅ chain, all F_t are in eclipsed positions. All Ge–F_t distances within the square plane are equal at 1.745(2) Å, and the Ge–F_b distance is 1.890(1) Å [27].

The Xe–F bond lengths in XeF₂·CrF₄ indicate that XeF₂ is at the beginning of its ionization pathway (XeF₂ → [XeF]⁺ + F⁻) [28]. Therefore, the formulation of the compound as the adduct XeF₂·CrF₄ is more suitable than the ionic formulation [XeF]⁺[CrF₅]⁻. The structure of XeF₂·CrF₄ consists of an infinite chain of CrF₆ octahedra sharing trans-vertices (Figure 24). For each CrF₆ octahedron, one F atom is provided by a XeF₂ molecule. The CrF₆ unit consists of three F_t (1.71(2)–1.75(2) Å) and three F_b (1.88(2)–2.00(2) Å) atoms [28]. The Cr–F_b–Cr angle is 147.3(8)° [28]. Viewed along the ([CrF₅]⁻)_∞ chain, all F_t are in eclipsed positions.

3.2. Cis-([MF₅]⁻)_∞ Anions (M = Ti, V, Cr, Mn, Ge, Sn, Pb)

There are many more examples of polymeric ([MF₅]⁻)_∞ anions (M = Ti, V, Cr, Mn, Ge, Sn, Pb) in which MF₆ octahedra share F atoms in the cis position, especially in the case of titanium. The different tilting of the MF₆ octahedra in the chains leads to small differences in their geometry. A summary of the crystal data of the salts consisting of cis-([MF₅]⁻)_∞ anions (M = Ti, V, Cr, Mn, Ge, Sn, Pb) is given in

Table 12. Crystal data of the salts consisting of cis-([MF₅]⁻)_∞ anions (M = Ti, V, Cr, Mn, Ge, Sn, Pb).

Compound	Space Group	a, b, c/Å	α, β, γ /°	V/Å3	Z	T/K *	Ref.
H3OTiF5	monoclinic	14.528(5)	90	874.9	8	RT **	[29]
	C2/c	4.839(l)	115.59(5)
		13.798(5)	90
NH4TiF5	monoclinic	14.683(1)	90	1829.9(3)	4	293(2)	[30]
	P21/n	6.392(l)	110.538(2)
		20.82(2)	90
NaTiF5·HF	monoclinic	15.1768(9)	90	1004.2(1)	8	200	[31]
	C/2c	6.4171(3)	108.266(2)
		10.8580(7)	90
KTiF5	monoclinic	20.277(3)	90	1681.9(4)	16	157	[31]
	C/2c	6.1768(8)	110.960(9)
		14.380(2)	90
KTiF5·HF	monoclinic	13.671(2)	90	1020.9(2)	8	200	[31]
	C/2c	8.1382(6)	114.217(4)
		10.061(1)	90
RbTiF5·HF	monoclinic	13.823(6)	90	1072.1(8)	8	150	[31]
	C/2c	8.295(3)	114.35(2)
		10.264(5)	90
CsTiF5	orthorhombic	5.3986(2)	90	487.97(3)	4	150	[31]
	Pnam	14.0057(5)	90
		6.4536(3)	90
[C2H4(NH3)2](TiF5)2	monoclinic	5.7801(3)	90	489.06(5)	2	200	[32]
	P21/c	15.447(1)	92.433(5)
		5.4825(3)	90
[H3N(CH2)2NH2][VF5]	orthorhombic	10.5231(9)	90	609.70(9)	4	90(2)	[33]
	Pnma	5.7185(5)	90
		10.1319(8)	90
KCrF5	orthorhombic	5.425(2)	90	395.8(2)	-	200	[15]
	-	7.427(2)	90
		9.824(4)	90
RbCrF5	orthorhombic	5.5150(17)	90	429.7(8)	4	200	[15]
	Pmc21	7.653(14)	90
		10.181(5)	90
CsCrF5	orthorhombic	10.70(2)	90	476.5(14)	4	200	[15]
	Pnma	5.611(8)	90
		7.936(11)	90
O2GeF5·HF	monoclinic	9.8444(8)	90				[34]
	I2/a	8.0274(6)	110.774(10)	968.14(15)	8	150
		13.1030(12)	90
ClO2SnF5	monoclinic	7.3673(4)	90	507.354	4	100	[35]
	P21/n	5.1042(3)	93.026(2)
		13.5108(8)	90
ClOF2SnF5	monoclinic	15.828(3)	90	555.7(2)	4	100	[36]
	C2	5.0614(10)	111.25(3)
		7.4425(15)	90
ClOF2PbF5	monoclinic	16.1838(12)	90	583.29(7)	4	100	[36]
	C2	5.1546(4)	111.932(2)
		7.5376(5)	90
XeF5TiF5	orthorhombic	18.139(2)	90	2810.0(5)	16	150	[26]
	Pbca	8.5173(9)	90
		18.1876(16)	90
XeF5CrF5	orthorhombic	18.281(13)	90	2854(4)	16	268(2)	[37]
	Pbca	8.429(7)	90
		18.521(12)	90
XeF5MnF5	monoclinic	9.0265(5)	90	1348.4(2)	2	120	[25]
	P21/c	17.8898(9)	90.132(5)
		8.3506(5)	90
ClO2GeF5	orthorhombic	14.6480(15)	90	987.0(4)	8	168(10)	[27]
	C2221	7.5762(11)	90
		8.8941(15)	90

* The crystal structures were determined at the indicated temperatures.** Measured at room temperature. The exact temperature was not reported.

.

H₃OTiF₅ crystallizes in the monoclinic space group C2/c (Table 12) [29]. The Ti–F_b–Ti angle is 146.56° (Figure 25) [29].

NH₄TiF₅ crystallizes in the monoclinic space group P2₁/n (Table 12) [30]. The Ti–F_b–Ti angles are in the range 155.09–164.11° (Figure 26) [30].

NaTiF₅·HF crystallizes in the monoclinic space group C/2c (Table 12) [31]. The compound is composed of infinite single chains of ([TiF₅]⁻)_∞ anions (Figure 27), Na⁺ cations, and coordinated HF molecules. The Ti–F_t bond lengths range from 1.769(2) Å to 1.888(2) Å and are shorter than the Ti–F_b bond lengths, which are 1.965(1) Å and 2.009(1) Å, respectively [31]. The observed Ti–F_b–Ti angles are 180.0° and 154.5(2)° [31].

KTiF₅ crystallizes in the monoclinic space group C2/c (Table 12) [31]. The fluorine atoms are partially disordered (Figure 28).

The crystal structures of KTiF₅·HF and RbTiF₅·HF are isotypic [31]. They crystallize in the monoclinic space group C2/c (Table 12). The bond lengths between Ti and F_t atoms are in the range 1.795(3)–1.859(3) Å for K[TiF₅]·HF and 1.791(4)–1.862(4) Å for Rb[TiF₅]·HF [31]. The longest Ti–F bond lengths are between Ti atoms and F_b atoms bridging two octahedra (1.9605(7) Å and 1.9630(14) Å in KTiF₅·HF; 1.9639(12) Å and 1.968(2) Å in Rb[TiF₅]·HF) [31]. In contrast to the ([TiF₅]⁻)_∞ anions described in [H₃O][TiF₅], [NH₄][TiF₅], and Na[TiF₅]·HF, the chains in K[TiF₅]·HF and Rb[TiF₅]·HF have a significantly different conformation (Figure 29). Each TiF₆ octahedron is connected to two neighbouring TiF₆ units via bridging F atoms located in cis positions of the single octahedron, with the observed Ti–F_b–Ti angles being 180.0° (K, Rb salt), 148.5(2)° (K salt), and 147.2(3)° (Rb-salt) [31].

CsTiF₅ crystallizes in the orthorhombic space group Pnma (Table 12) [31]. Each of the terminal fluorine atoms is disordered over two crystallographic positions (Figure 30). The observed Ti–F_t bond lengths range from 1.687(11) Å to 1.904(6) Å, and the Ti–F_b bond lengths are 1.972(2) Å and 1.982(2) Å [31]. The Raman spectrum of Cs[TiF₅] recorded on a single crystal is identical to the previously reported Raman spectrum of “Cs₂[Ti₂F₁₀]”, which was claimed to consist of discrete [Ti₂F₁₀]²⁻ anions [31]. These results show that the previously reported Cs₂[Ti₂F₁₀] is, in fact, Cs[TiF₅].

[enH₂](TiF₅)₂ (en = ethane-1,2-diamine) crystallizes in the monoclinic space group P2₁/c (Table 12, Figure 31) [32]. The bond distances between Ti and F_t are between 1.780(1) and 1.850(2) Å, and the bond distances between Ti and F_b are between 2.023(1) and 2.028(1) Å [32]. All Ti–F_b–Ti angles in the crystal structure of [enH₂][TiF₅]₂ are equivalent and correspond to 138.31(7)° [32].

The crystal structure of [H₃N(CH₂)₂NH₂][VF₅] is a rare example of a structurally characterized V(IV) fluoride compound that does not consist only of [VF₆]²⁻ anions [33]. The anionic part is composed of polymeric infinite ([VF₅]⁻)_∞ chains (Figure 32). The chain consists of V(IV) octahedra that share cis-vertices to form a zig-zag profile. The V–F distances are 1.838(3) and 2.132(5) Å for the terminal and bridging fluorides, respectively [33]. The presence of V(IV) was confirmed by charge-balance considerations and b magnetic studies. The V–F_b–V angle is linear (180°) [33]. The F_t atoms of every second octahedron are in an eclipsed conformation (Figure 32).

The crystal structure of RbCrF₅ (KCrF₅ appears to be isotypic) crystallizes in the orthorhombic space group Pmc2₁ (Table 12) [15]. The Cr–F_t bond distances in the cis-([CrF₅]⁻)_∞ chain (Figure 33) are between 1.780(1) and 1.850(2) Å and Cr–F_b between 2.023(1)–2.028(1) Å [15]. The Cri–F_b–Cr angles are equal to 149.4(3)° [15]. Distorted [CrF₆] octahedra have four terminal fluorine atoms with Cr–F_t distances in the range of 1.743(8)–1.782(7) Å and two bridging fluorine atoms with Cr–F_b distances of 1.945(5) and 1.948(5) Å [15].

CsCrF₅ crystallizes in the orthorhombic space group Pnma (Table 12) [15]. The main feature of the CsCrF₅ structure is also a ([CrF₅]⁻)_∞ chain of distorted [CrF₆] octahedra connected by common cis-vertices (Figure 34). While the Cr–F_b–Cr angle in the Rb salt is bent, the corresponding angle in the Cs salt is linear (180°) [15]. The magnetic measurements show an antiferromagnetic interaction between the magnetic moments of Cr(IV) in ACrF₅ due to the coupling through Cr–F_b–Cr bridges [38]. In ACrF₅ (A = K, Rb), a weak ferromagnetic ground state was observed below T_c ~ 6 K, which can be explained as canted antiferromagnetism in correlation with the crystal structures of these two compounds.

In contrast to XeF₅GeF₅ with a trans-shared GeF₆ octahedra [27], the anion in the crystal structure of O₂GeF₅·HF (monoclinic space group I2/a, Table 12) consists of infinite ([GeF₅]⁻)_∞ chains of GeF₆ octahedra sharing cis-vertices (Figure 35) [34]. The HF molecules and O₂⁺ cations are located between the chains. The Ge–F_t bond lengths range from 1.729(2) Å to 1.7545(19) Å and are shorter than Ge–F_b (1.8817(3) Å and 1.8934(9) Å). There are alternating Ge–F_b–Ge angles of 180.0° and 140.04(13)° [34].

The crystal structure of ClO₂SnF₅ is a rare example of a structurally determined Sn salt with a polymeric pentafluoridostannate (IV) anion, ([SnF₅]⁻)_∞ (Figure 36) [35]. The previous reports on the structures of the [SnF₅]⁻ anions in the [NF₄]⁺, [N₂F₃]⁺, and [N₅]⁺ salts were based only on vibrational and/or ¹⁹F NMR spectroscopy in the solid state and in solution, respectively [39,40,41,42]. The ([SnF₅]⁻)_∞ anion is a linear zig-zag chain consisting of cis-bridged [SnF₆] polyhedra. The Sn–F bond length of ClO₂SnF₅ is in the range of 1.9047(13)–2.0627(13) Å [35]. The Sn–F_b–Sn angle is equal to 143.16° [35].

The crystal structures of ClOF₂SnF₅ and ClOF₂PbF₅ are isotypic (Table 12) [36]. The polymeric ([SnF₅]⁻)_n anion has a similar chain-like geometry (Sn–F: 1.901(6)–2.061(5) Å and Sn–Fb–Sn = 143.31°) as in ClO₂SnF₅. Apart from the known [PbF₆]²⁻ anion, the polymeric ([PbF₅]⁻)_∞ anion (Figure 37) is the only known example of a fluoridoplumbate (IV) anion. The Pb–F bond lengths are in the range of 1.979(3)–2.156(3) Å and the Pb–F_b–Pb angle is 140.74° [36].

The crystal structure of XeF₅CrF₅ [37] (XeF₅TiF₅ appears to be isotypic [26]) crystallizes in the orthorhombic space Pbca (Table 12; Figure 38). The ([CrF₅]⁻)_∞ chain also consists of CrF₆ octahedra that share cis-vertices to form a zig-zag profile. However, the chain geometry differs from the polymeric ([MF₅]⁻)_∞ chain structures of [H₃N(CH₂)₂NH₂][VF₅] [33], RbCrF₅ [15], CsCrF₅ [15], O₂GeF₅·HF [34], ClO₂SnF₅ [35], and ClOF₂MF₅ (M = Sn, Pb) [36]. The Cr–F bond lengths range from 1.675(11) Å to 1.971(10) Å) [37]. The Cr–F_b–Cr bridges are kinked with angles of 144.8(5) and 147.4(6)° [37].

XeF₅TiF₅ crystallizes in the orthorhombic space group Pbca (Table 12) [26] and is most likely isotypic with XeF₅CrF₅ [37].

Single crystals of red [XeF₅][MnF₅] were grown in the form of very thin and fragile plates [25], which resulted in poor quality of the collected X-ray data. An attempt to improve the crystal structure of [XeF₅][MnF₅] by synchrotron X-ray powder diffraction (SXRD) resulted I a monoclinic unit cell (Table 12) [25]. According to the SXRD analysis, the crystal structure of [XeF₅][MnF₅] (Figure 39) is slightly different from [XeF₅][CrF₅] and [XeF₅][TiF₅] (Table 12). XeF₅MnF₅ is paramagnetic in the temperature range of 296–200 K, with a Curie constant of C = 1.87 emu K mol–1 (μ_eff = 3.87 μB) and a Curie–Weiss temperature of θ = −9.3 K. Below 100 K, there is weak antiferromagnetic coupling between the Mn^IV ions, with a coupling constant of J = −1.3 cm⁻¹ [25].

The crystal structure determination of [C(NH₂)₃]₄(H₃O)₄[Ti₄F₂₀][TiF₅]₄ provided the first example of a perfluoridotitanate (IV) compound with two different perfluoridotitanate (IV) anions in the same salt [22]. The latter appears as a crenelated chain (Figure 40), which is also observed in XeF₅MF₅ (M = Ti [26], Cr [37], Mn [25]). The Ti–F bond lengths are typical for poly[perfluoridotitanate (IV)] compounds and range from 1.763(1) to 1.877(1) A and from 1.964(1) to 2.004(1) A for the Ti–F_t and Ti–F_b bonds, respectively [22]. The Ti–F_b–Ti angles are 148.48(7) and 157.07(7)° [22].

The crystal structure of ClO₂GeF₅ consists of infinite ([GeF₅]⁻)_∞ chains (Figure 41) [27]. However, their geometry differs from the geometry of the ([GeF₅]⁻)_∞ chains in O₂GeF₅·HF [34], where the GeF₆ octahedra also share common cis-vertices. The chains in the former salt are crenelated and not linear as in the case of O₂GeF₅·HF. The Ge–F_t bond lengths range from 1.73 Å to 1.78 Å and are shorter than the Ge–F_b bond lengths of 1.887(1) Å [27]. The Ge–F_b–Ge angles are 148.1° and 143.4° [27].

3.3. Cis- and Trans-([MF₅]⁻)_n Anions (M = Cr)

A summary of the crystal data of the salt consisting of cis- and trans-([MF₅]⁻)_n anions (M = Cr) is given in

Table 13. Crystal data of the salt consisting of cis- and trans-([MF₅]⁻)_n anions (M = Cr).

Compound	Space Group	a, b, c/Å	α, β, γ/°	V/Å3	Z	T/K *	Ref.
(XeF5CrF5)4·XeF4	orthorhombic	11.988(6)	90	3144.8	4	293(1)	[28]
	Pbca	15.862(2)	90
		16.538(2)	90

* The crystal structure was determined at the indicated temperature.

.

The crystal structure of (XeF₅CrF₅)₄·XeF₄ consists of infinite chains of distorted CrF₆ octahedra sharing alternating trans- and cis-vertices (Figure 42) and is the only example of its kind [28]. Cr–F_t bond lengths range from 1.701(8) Å to 1.895(7) Å and Cr–F_b from 1.8890(6) Å to 1.961(7) Å [28]. The Cr–F_b–Cr angles are 136.6(4) and 142.3(4)° [28].

4. Polymeric Double Chain-like ([M₂F₉]⁻)_∞ Anions (M = Ti, Mn, Sn)

A summary of the crystal data of the salts consisting of double chain-like ([M₂F₉]⁻)_∞ anions (M = Ti, Mn, Sn) is given in

Table 14. Crystal data of the salts consisting of double chain-like ([M₂F₉]⁻)_∞ anions (M = Ti, Mn, Sn).

Compound	Space Group	a, b, c/Å	α, β, γ/°	V/Å3	Z	T/K *	Ref.
α-O2Sn2F9	orthorhombic	4.0473(3)	90	371.63(4)	2	200	[34]
	Immm	8.0199(4)	90
		11.4491(8)	90
α-[H3O][Ti2F9]	orthorhombic	8.988(4)	90	722.6(5)	4	100	[6]
	Pnma	5.451(2)	90
		14.748(6)	90
β-[H3O][Ti2F9]	monoclinic	5.3178(2)	90				[22]
	P21/c	16.0786(8)	91.440(3)	756.10(6)	4	150
		8.8459(3)	90
NaTi2F9·HF	orthorhombic	5.3084(3)	90	740.98(7)	4	200	[31]
	Pnma	10.0736(6)	90
		13.8566(8)	90
RbTi2F9	monoclinic	15.0380(7)	90	1480.5(1)	8	157	[31]
	P21/c	5.3244(3)	93.788(5)
		18.531(1)	90
CsTi2F9	monoclinic	1136.3(3)	90	798.2(4)	4	200	[6]
	C2/c	1471.1(3)	116.41(2)
		533.18(14)	90
α-[C3H5N2][Ti2F9]	monoclinic	5.3914(3)	90	997.78(11)	4	200	[12]
	P21/a	15.4836(10)	90.977(4)
		11.9543(8)	90
β-[C3H5N2][Ti2F9]	orthorhombic	5.3978(2)	90	1004.63(8)	4	298	[12]
	Pnma	12.2169(6)	90
		15.2345(7)	90
[C(NH2)3][Ti2F9]	orthorhombic	5.4001(2)	90	952.87(9)	4	200	[22]
	Pnma	11.9123(5)	90
		14.813(1)	90
[ClO2][Ti2F9]	monoclinic	11.084(2)	90	801.4(2)	4	100	[35]
	C2/c	14.603(2)	111.73(1)
		5.330(1)	90
O2Mn2F9	monoclinic	17.55	90	1306.8	8	123	[43]
	C2/c	8.37	102.3
		9.10	90

* The crystal structures were determined at the indicated temperatures. The exact temperature was not reported.

.

The polymeric ([Sn₂F₉]⁻)_∞ anion in α-O₂Sn₂F₉ consists of two parallel, infinite chains composed of SnF₆ octahedra, with each SnF₆ octahedron of one chain connected to a SnF₆ octahedron of the second chain through a common fluorine vertex (Figure 43) [34]. The Sn–F_b–Sn angles within each chain are equal to 170.7(2)°, and the angles at which the Sn atoms belong to two neighbouring chains are linear (Sn–F_b–Sn = 180°) [34]. The three Sn–F_b bonds between tin and the bridging fluorine atoms are longer (2.0303(3) Å–2.0374(4) Å) than the three Sn–F_t bonds between tin and the terminal fluorine atoms (1.898(2) Å–1.909(4) Å) [34]. The negative charge of the ([Sn₂F₉]⁻)_∞ anions is compensated by partially disordered O₂⁺ cations located between the chains.

α-[H₃O][Ti₂F₉] crystallizes at 100 K in the orthorhombic space group Pnma (Table 14) [6]. In contrast to the ([Sn₂F₉]⁻)_∞ anion in α-O₂Sn₂F₉ [34], the individual chains in the double chain ([Ti₂F₉]⁻)_∞ anion are not linear (Figure 44). The Ti–F_b–Ti angles within the individual single zig-zag chains are kinked with an angle of 166.4(2)°, and the Ti–F_b–Ti angles, where the Ti atoms belong to two neighbouring chains, are 143.7(2)° [6].

β-[H₃O][Ti₂F₉] crystallizes at 150 K in the monoclinic space group P2₁/c (Table 14) [22]. In contrast to the eclipsed structure of the double-chain ([Ti₂F₉]⁻)_∞ anion in the orthorhombic modification α-[H₃O][Ti₂F₉] (Figure 44) [6], the double-chain ([Ti₂F₉]⁻)_∞ anion in the β-phase exhibits a gauche conformation of the TiF₆ octahedra belonging to two parallel single chains (Figure 45).

The crystal structure of NaTi₂F₉·HF also consists of zig-zag ([Ti₂F₉]⁻)_∞ double chains (Figure 46) [31]. The Ti–F_b bond lengths are in the range 1.963(2)–1.974(1) Å and the Ti–F_t bond lengths are in the range 1.768(2)–1.787(2) Å [31]. The Ti–F_b–Ti angles within individual single chains correspond to 158.7(1)° [31]. The Ti–F_b–Ti angles in which the Ti atoms belong to the two neighbouring single chains of the dimer are equal to 141.4(1)° [31]. The closest TiF₆ octahedra belonging to two individual single chains are in an eclipsed conformation to each other. The Na[Ti₂F₉]·HF compound contains HF molecules. There are hydrogen bond interactions between the HF molecules and the polymeric ([Ti₂F₉]⁻)_∞ anion.

The single-crystal structure of Rb[Ti₂F₉] consists of an infinite ([Ti₂F₉]⁻)_∞ anion in two different conformations (Figure 47) [31]. One ([Ti₂F₉]⁻)_∞ anion has a gauche conformation of the TiF₆ octahedral pairs belonging to the two single chains of the double chain, as in the anions in the crystal structures of β-H₃OTi₂F₉ (Figure 45), while the second anion has an eclipsed conformation of these TiF₆ octahedral pairs, similar to the anion in the crystal structures of α-[H₃O][Ti₂F₉] (Figure 44).

CsTi₂F₉ crystallizes in the monoclinic space group C2/c (Table 14, Figure 48) [6], where the Ti–F_b–Ti angles within the individual zig-zag chains are kinked with an angle of 156.3(4)°. The Ti–F_b–Ti angles where Ti atoms belong to two neighbouring chains are 149.3(6)° [6].

α-[ImH][Ti₂F₉] crystallizes at 200 K in the monoclinic space group P2₁/a (Table 14), while β-[ImH][Ti₂F₉] is orthorhombic at 298 K (Table 14) [12]. The geometry of the ([Ti₂F₉]⁻)_∞ anions in both structures (Figure 49 and Figure 50) show the same behaviour as in α- and β-[H₃O][Ti₂F₉] (Figure 44 and Figure 45). In α-[ImH][Ti₂F₉], the double-chain ([Ti₂F₉]⁻)_∞ anion exhibits an eclipsed conformation of TiF₆ octahedra belonging to two parallel single chains (Figure 49), while this conformation in β-[ImH][Ti₂F₉] is gauche (Figure 50). The Ti–F_b–Ti angles within the single zig-zag chains of the dimers are crystallographically equivalent in β-[ImH][Ti₂F₉] [152.1(1)°], while these angles are comparable in α-[ImH][Ti₂F₉] [149.54(8)° and 151.21(9)°] [12]. The Ti–F_b–Ti angles in [ImH][Ti₂F₉], where the titanium atoms belong to two neighbouring chains, are the same, within ±3σ for the α-phase [162.27(8)°] and the β-phase [163.1(2)°] [12].

The geometry of the ([Ti₂F₉]⁻)_∞ anion in [gvH][Ti₂F₉] (gv = guanidine) [22] is isostructural with the previous examples. It consists of TiF₆ octahedra that share vertices at the fac position and form dimeric zig-zag chains (Figure 51). Each titanium atom is coordinated with three bridging and three terminal fluorine atoms, with Ti–F bonds ranging from 1.771(1) to 1.777(1) Å and from 1.9713(4) to 1.980(1) Å for Ti–F_t and Ti–F_b, respectively [22]. The Ti–F_b–Ti angles within each chain of dimers are equal to 155.01(7)° [22]. The Ti–F_b–Ti angles where the titanium atoms belong to two neighbouring single chains of the dimer are equal to 163.5(1)° [22].

[ClO₂][Ti₂F₉] crystallizes in the monoclinic space group C2/c (Table 14, Figure 52) [35]. Each Ti atom is surrounded by six F atoms in the form of a distorted octahedron with Ti–F bond lengths of 1.776(2) to 1.980(2) Å [35].

O₂Mn₂F₉ crystallizes at 148 K in the orthorhombic space group C2/c (Table 14) [43]. The crystal structure consists of ([Mn₂F₉]⁻)_∞ anions with a unique geometry (Figure 53). The ([Mn₂F₉]⁻)_∞ chains are crenelated and not linear as in other examples of ([M₂F₉]⁻)_∞ (M = Sn, Ti) salts. It can be imagined to be composed of two single ([MnF₅]⁻)_∞ chains (as observed in [XeF₅][MnF₅] (Figure 39)), which additionally share some vertices to form a double ([Mn₂F₉]⁻)_∞ chain.

5. Polymeric Column-like ([M₃F₁₃]⁻)_∞, ([M₄F₁₉]³⁻)_∞, ([M₇F₃₀]²⁻)_∞ and ([M₉F₃₈]²⁻)_n Anions (M = Ti)

A summary of the crystal data of the salts consisting of polymeric column-like ([M₃F₁₃]⁻)_∞, ([M₄F₁₉]³⁻)_∞, ([M₇F₃₀]²⁻)_∞, and ([M₉F₃₈]²⁻)_n anions (M = Ti) is given in

Table 15. Crystal data of the salts consisting of polymeric column-like ([M₃F₁₃]⁻)_∞, ([M₄F₁₉]³⁻)_∞, ([M₇F₃₀]²⁻)_∞, and ([M₉F₃₈]²⁻)_n anions (M = Ti).

Compound	Space Group	a, b, c/Å	α, β, γ /°	V/Å3	Z	T/K *	Ref.
[XeF5][Ti3F13]	triclinic	9.7699(6)	89.601(5)	1327.82(14)	4	150	[26]
	P-1	11.0276(6)	69.992(5)
		13.4581(7)	77.717(5)
Cs3[Ti4F19]	orthorhombic	5.3999(4)	90	1771.7(2)	4	150	[31]
	Cmcm	15.2661(12)	90
		21.4921(15)	90
(O2)2[Ti7F30]	trigonal	10.19(2)	90	584.7	1	153	[44]
	P-3	10.19(2)	90
		6.50(0)	120
[XeF]2[Ti9F38]	monoclinic	17.5967(8)	90	3072.9(2)	4	150	[45]
	Cc	15.3862(6)	108.2795(16)
		11.9529(6)	90

* The crystal structures were determined at the indicated temperatures.

.

In [XeF₅][Ti₃F₁₃], the anionic part consists of tetrameric Ti₄F₂₀ and octameric Ti₈F₃₆ units that share vertices and are alternatively connected to form ([Ti₃F₁₃]⁻)_∞ columns (Figure 54) [26]. The negative charge of the anions is balanced by [XeF₅]⁺ countercations interacting via secondary Xe···F bonds. The Ti–F_t bond lengths range from 1.728(5) to 1.813(5) Ǻ and are significantly shorter than the Ti–F_b bonds (1.942(4)–2.049(5) Å) [26].

The polymeric ([Ti₄F₁₉]³⁻)_∞ anion in Cs₃[Ti₄F₁₉] consists of two zig-zag chains composed of TiF₆ units (Figure 55) [31]. In contrast to the polymeric ([Ti₂F₉]⁻)_∞ anion, the polymeric ([Ti₄F₁₉]³⁻)_∞ anion lacks a second link between the TiF₆ unit of one chain and the TiF₆ unit of the second chain. The length distribution of the Ti–F_t and Ti–F_b bonds is in the range of 1.768(3)–1.833(4) Å and 1.958(3)–2.006(3) Å, respectively [31]. The Ti–F_b–Ti angles within the zig-zag single chain are 155.7(2)°, and the Ti–F_b–Ti angles between two single chains are 151.6(3)° [31].

Both the crystal structure of Cs₃[Ti₄F₁₉] [31] and that of [XeF₅]₃[Ti₄F₁₉] [21] contain the anion, which can be expressed by the general formula [Ti₄F₁₉]³⁻. However, the [Ti₄F₁₉]³⁻ in [XeF₅]₃[Ti₄F₁₉] is an oligomeric species, whereas the [Ti₄F₁₉]³⁻ in Cs₃[Ti₄F₁₉] is polymeric. Although many fluoridotmetallate (IV) anions are known, this is a rare case where two different geometries have been structurally determined for the same general formula of the anion.

The crystal structure of (O₂)₂ [Ti₇F₃₀] consists of column-like ([Ti₇F₃₀]²⁻)_∞ anions (Figure 56) [44]. The structure of the ([Ti₇F₃₀]²⁻)_∞ anion is comprised of cubic units of eight TiF₆ octahedra, with two TiF₆ units in opposite corners of the cube sharing vertices with neighbouring cubes. In this way, the Ti atoms common to the neighbouring cubes are coordinated by six bridging fluorine atoms, while the other Ti atoms are coordinated by three F_b and three F_t atoms. The negative charge of the anions is compensated by O₂⁺ cations located between the ([Ti₇F₃₀]²⁻)_∞ columns.

The crystal structure of [XeF]₂[Ti₉F₃₈] consists of column-like ([Ti₉F₃₈]²⁻)_∞ anions (Figure 57) [45]. Trimeric rings of TiF₆ octahedra are linked to form trigonal prismatic Ti₉F₃₉ units, which are additionally connected by single fluorine bridges and form column-like ([Ti₉F₃₈]²⁻)_∞ anions.

6. Polymeric Layered ([M₈F₃₃]⁻)_∞ and ([M₂F₉]⁻)_∞ Anions (M = Ti, Cr)

A summary of the crystal data of the salts consisting of layered ([M₈F₃₃]⁻)_∞ and ([M₂F₉]⁻)_∞ anions (M = Ti, Cr) is given in

Table 16. Crystal data of the salts consisting of layered ([M₈F₃₃]⁻)_∞ and ([M₂F₉]⁻)_∞ anions (M = Ti, Cr).

Compound	Space Group	a, b, c/Å	α, β, γ /°	V/Å3	Z	T/K *	Ref.
CsTi8F33	trigonal	8.622(5)	90	1224.5	2	RT **	[46]
	P31c	8.622(5)	90
		19.02(1)	120
[Xe2F3][Ti8F33]	monoclinic	17.6347(5)	90	2929.1(1)	4	150	[45]
	P2/a	8.4106(2)	97.140(1)
		19.9028(5)	90
XeF2·2CrF4	triclinic	8.551(3)	76.02(2)	789.7(4)	4	293(2)	[37]
	P-1	9.221(3)	81.36(2)
		10.438(3)	88.08(3)

* Crystal structures were determined at the indicated temperatures. ** Measured at room temperature. The exact temperature was not reported.

.

The infinite two-dimensional (2-D) arrangement of poly[perfluoridometallate (IV)] anions is observed in the case of the ([Ti₈F₃₃]⁻)_∞ anion characterized in CsTi₈F₃₃ [46] and [Xe₂F₃][Ti₈F₃₃] [45]. In both cases, the ([Ti₈F₃₃]⁻)_∞ anion represents a layered structure with different structural motifs.

In CsTi₈F₃₃, two Ti atoms are coordinated by three bridging and three terminal fluorine atoms, while the other two are coordinated by four bridging and two terminal fluorine atoms, ultimately leading to a 2-D framework (Figure 58) [46].

Like CsTi₈F₃₃ [46], [Xe₂F₃][Ti₈F₃₃] [45] also exhibits a layered structure. However, the 2-D polymeric ([Ti₈F₃₃]⁻)_∞ anion in [Xe₂F₃][Ti₈F₃₃] has a different geometry (Figure 59) than in CsTi₈F₃₃. A basic structural motif resembles an oligomeric cubic [Ti₈F₃₆]⁴⁻ anion (Figure 20), which consists of eight TiF₆ octahedra. These octameric units are connected by six common fluoride vertices and form a layered anion. The [Xe₂F₃]⁺ cations are located in a semi-closed channel. CsTi₈F₃₃ and [Xe₂F₃][Ti₈F₃₃] are the other examples containing the anion, which can be expressed by the same general formula [Ti₈F₃₃]⁻, but have a different geometry.

Similar to XeF₂·CrF₄ [28], the determined Xe–F bond lengths in XeF₂·2CrF₄ indicate that XeF₂ is at the beginning of its ionization pathway (XeF₂ → [XeF]⁺+F⁻). Therefore, the formulation of the compound as the adduct XeF₂·2CrF₄ is more suitable than the ionic formulation [XeF⁺][Cr₂F₉] [37]. The basic structural unit is formed by four independent Cr atoms, each of which is octahedrally coordinated by six F atoms. To complete the octahedral coordination, two additional fluorine ligands are provided by two different XeF₂ molecules. The distorted CrF₆ octahedra are connected by common F atoms and form a layered structure (Figure 60).

7. Polymeric ([M₆F₂₇]³⁻)_∞ Anion in the Form of Three-Dimensional Framework (M = Ti)

A summary of the crystal data of the salt consisting of polymeric ([M₆F₂₇]³⁻)_∞ anion (M = Ti) in the form of a three-dimensional framework is given in

Table 17. Crystal data of the salt consisting of polymeric ([M₆F₂₇]³⁻)_∞ anion (M = Ti) in the form of a three-dimensional framework.

Compound	Space Group	a, b, c/Å	α, β, γ/°	V/Å3	Z	T/K *	Ref.
[H3O]3[Ti6F27]	cubic	17.2014(9)	90	5089.7(8)	8	150	[31]
	Pn-3n	17.2014(9)	90
		17.2014(9)	90

* The crystal structure was determined at the indicated temperature.

.

Slow decomposition in attempts to grow single crystals of K₄[Ti₈F₃₆]·8HF and Rb₄[Ti₈F₃₆]·6HF [24] led to the growth of cube-shaped crystals of ([Ti₆F₂₇]³⁻)_∞ salts. Later, the same type of anion ([Ti₆F₂₇]³⁻)_∞ was found in [H₃O]₃[Ti₆F₂₇] [31]. Unfortunately, in all three cases, there is a problem with charge balance, i.e., a deficit of cations. For K and Rb salts, there is a possibility that some [H₃O]⁺ was present, leading to mixed-cation A⁺/[H₃O]⁺ salts.

The ([Ti₆F₂₇]³⁻)_∞ anion is a three-dimensional framework consisting of TiF₆ octahedra (Figure 61). Its structure can be described as composed of non-planar tetrameric Ti₄F₂₀ units consisting of four octahedra, each sharing two cis-vertices. Each Ti₄F₂₀ unit is connected to four other Ti₄F₂₀ units so that each TiF₆ octahedron of a tetrameric ring is connected to another tetrameric unit. There are two types of channels in the crystal structure of the ([Ti₆F₂₇]³⁻)_∞ anion. The channels are occupied by cations and probably also by molecules of the solvent.

8. Conclusions

On the basis of this review is possible to draw some conclusions and determine the further direction of this work:

Among the fluoridometallates (IV), the largest number of different anions is known for Ti. This is not so surprising in view of the numerous studies that have been carried out in recent years [5,6,7,11,12,14,15,16,19,22,23,24,26,32]. The use of some other asymmetrical organic cations could still lead to new anions with hitherto unknown geometry. The examples of Zr and Hf salts are limited to a single case for each element [16]. Since both elements prefer a higher coordination than six, it is not very likely that many new examples will be prepared.

[H₃N(CH₂)₂NH₂][VF₅] is a unique example of a structurally characterized V(IV) fluoride compound that does not contain only an isolated [VF₆]²⁻ anion [33]. Therefore, the chemistry of hybrid compounds with V(IV) is still an unexplored area. In fluorides, vanadium occurs in different oxidation states, ranging from +2 to +5. This could be an obstacle on the way to synthesizing inorganic or hybrid V(IV) fluorides. V(IV)could be reduced, oxidized, or disproportionated, resulting in V(III) and V(V) salts instead of the desired V(IV) salts. There are only a few examples of Nb(IV) fluorides (all are [NbF₆]²⁻ salts [47,48]), while TaF₄ and Ta(IV) fluorides are not known at all. Therefore, these two elements are not good candidates for the preparation of new Nb(IV) and Ta(IV) fluoride polyanions.

The chemistry of Cr(IV) polyanions is limited to salts with inorganic cations such as alkali metals and noble gas fluoride cations [15,28,37]. Due to the oxidizing power of Cr(IV), it is not very likely that many new hybrid polyfluoridechromates (IV) could be prepared. It is interesting to note that the [W₄F₁₈]²⁻ salt [WCl₂(cp)₂][W₄F₁₈] (cp = η-C₆H₅)] is an example of a W(IV) fluoride salt [20], while [WF₆]²⁻ salts are not known. The Mo(IV) fluoride salts are rare and are limited to [MoF₆]²⁻ salts [49]. Therefore, these three elements are also not very promising candidates for the preparation of new M(IV) fluoride polyanions (M = Cr, Mo, W).

For similar reasons as for Cr(IV), Mn(IV) is not a good choice for the preparation of new M(IV) (M = Mn) fluoride polyanions.

The M(IV) fluorides (M = Re, Ru, Os, Rh, Ir, Pd, Pt) are limited to [MF₆]²⁻ salts, and no association of MF₆ octahedra has been observed so far.

In the case of M(IV) (M = Si, Ge, Sn, Pb), there are a number of reports in which selected anions have been observed in solution or suggested by vibrational spectroscopy in the solid state, but the determination of their crystal structures in the solid state is still pending:

(1)

Multinuclear NMR spectroscopy (¹⁹F, ¹¹⁹Sn) of N₅SnF₅ in aHF solution showed that the [SnF₅]⁻ anion exists as both a dimeric oligomer [Sn₂F₁₀]²⁻ and an oligomeric cyclic tetramer [Sn₄F₂₀]⁴⁻ [39].

(2)

The vibrational spectra of solid NF₄SnF₅ and NF₄GeF₅ are very similar to those of tetrameric NbF₅ and TaF₅, indicating the possible presence of [M₄F₂₀]²⁻ tetramers in NF₄SnF₅ and NF₄GeF₅ [40].

(3)

The nature of N₂FSn₂F₉ is still open. The anion [Sn₂F₉]⁻ most likely does not have a monomeric structure, but is probably present as an oligomer or polymer [41].

(4)

The geometries of the anions in the salts N₂F₃SnF₅, NF₄Ti₂F₉, NF₄Ti₃F₁₃, and NF₄Ti₆F₂₅ are unknown [42,50].

Therefore, these elements (especially Sn and Pb) are the most promising for the synthesis of hybrid salts with new fluoridometallate (IV) polyanions.

Although examples of [MF₆]² salts are known for M = Ce [51], U [51], and Tc [51], it is not very likely that new fluoride polyanions will be synthesized in their case.

We can therefore assume that various oligomeric and polymeric anions still need to be prepared and structurally characterized.