Linear Trimeric Hafnium Clusters in Hf 0 . 86 ( 1 ) I 3

The reduction of hafnium tetraiodide, HfI4, with aluminum at 600 °C or 850 °C in the presence of a NaI flux resulted in black single crystals of Hf0.86(1)I3. This composition corresponds well to the upper end of the non-stoichiometry range 0.89 ≤ x ≤ 1.00 previously reported for HfxI3. The crystal structure (a = 1250.3(2), c = 1999.6(3) pm, R-3m, Z = 18) is made up of hexagonal closest packed layers of iodide ions. One third of the octahedral holes would be filled as in TiI3 or ZrI3 if it were Hf1.00I3. In Hf0.86(1)I3, one out of six octahedral holes along [001] are, however, only occupied by 16%. In contrast to TiI3-I and ZrI3, one striking structural feature is in the formation of linear hafnium trimers with identical Hf―Hf distances of 318.3(2) pm rather than the formation of dimers. These may be associated with Hf―Hf bonding although only 2.64 electrons are available for one Hf5.16I18 column.


Introduction
The group four elements, titanium, zirconium and hafnium, are, in principle, capable of forming iodides in the +2, +3 and +4 oxidation states.The di-, tri-and tetraiodides of titanium [1][2][3][4][5] and zirconium [6][7][8][9][10] appear to be well characterized.At least, their crystal structures and the importance OPEN ACCESS of metal-metal bonding at sufficiently low temperatures are now well established.Of the hafnium iodides, only the crystal structure of HfI 4 has been determined [11].
Attention to the lower iodides of hafnium was given only rarely.Early work stated that hafnium triiodide, HfI 3 , should exist [12].Powder X-ray diffraction established that HfI 3 , as the trichlorides, bromides and iodides of titanium and zirconium, belongs structurally to an ever growing family of trihalides with hexagonally closest packed halide layers, between which one-third of the octahedral voids are occupied by metal atoms [13].
A number of important conclusions were drawn from a closer inspection of the phase equilibria in the Hf-HfI 4 system [14]: First, no lower iodide of hafnium than hafnium triiodide, HfI 3 , exists in equilibrium.Second, beyond HfI 3 there is a non-stoichiometric phase HfI 3+x with x ranging from 0.2 to almost 0.5.Third, powder X-ray diffraction data show that there must be a super-structure with respect to the unit cell as established previously [13].Fourth, the hexagonal sub-cell parameters are dependent upon the composition of HfI 3+x with a decreasing and c increasing with x.
New investigations into reduced hafnium iodide systems have brought about single crystals of HfI 3.50 , or better: Hf 0.86 I 3 .The crystals have a clearly resolved superstructure although with the statistical under-occupation of one out of six hafnium sites.

Experimental Section
Hafnium tetraiodide, HfI 4 , was prepared from hafnium metal powder (99.6%, 2-3.5% Zr, Alfa Aesar) and iodine (resublimed p.a., Acros Organics) in stoichiometric amounts.The crude product was sublimed in high vacuum prior to use and handled only under dry box conditions (argon atmosphere, MBraun, Garching).HfI 4 (for example 200 mg, 0.29 mmol), aluminum metal powder (99.99%,Chempur) and NaI (99.5%, Merck) were weighed in 1:4:1 molar quantities and filled in tantalum containers which were sealed by helium arc welding and jacketed in silica [15].The sample was heated to 850 °C (or 600 °C in another reaction) and held there for 16 days.Slow cooling to room temperature (5 °C/h) yielded shiny, black, rod-shaped crystals.Some crystals were selected under a microscope in a dry box and sealed in thin-walled glass capillaries.After their quality had been checked by Laue diffraction patterns, the best specimen was transferred to a single-crystal X-ray diffractometer (Stoe Image Plate Diffraction System, IPDS I) to collect a complete intensity data set at ambient temperature.
Crystal data for Hf 0. Goof = 0.900.For atomic coordinates and equivalent displacement factor coefficients see Table 1.

Results and Discussion
The idealized nickel arsenide, NiAs [21], and cadmium iodide, CdI 2 [22], types of structure are usually described as consisting of hexagonal closest packings of spheres of As and I, respectively, with all and half of the octahedral interstices filled with Ni and Cd atoms, respectively.Thus, the hexagonal unit cell with the parameters a 0 and c 0 contains two and one formula units, respectively.For CdI 2 , the lattice parameters are a = 424.45(1)and c = 686.42(3)pm [22].
In metal triiodides MI 3 , only one third of the octahedral interstices of a hexagonal closest packing of iodide ions need to be filled.This can be done in at least two ways: First, between every second iodide layer two thirds of the octahedral voids are occupied, the others are all empty; this is the arrangement of the BiI 3 type of structure [23] which has recently been refined for YI 3 [24]; a super-cell with a = a 0 √3 and c = 3c 0 with Z = 6 results.Second, between all layers one third of the octahedral voids are filled in such a way that columns of octahedra sharing common faces are formed; this is the arrangement of the TiI 3 type of structure [4,5] with a super-cell with a = a 0 √3 and c = c 0 for the hexagonal (P6 3 /mcm, No. 193, Z = 2) high-temperature and a = 3a 0 , b = c 0 and c = a 0 √3 for the orthorhombic (Pmmn, No. 59, Z = 4) modifications, respectively.
In the low-temperature modification of titanium triiodide, TiI 3 -I, Ti-Ti distances in such a column are 309.6(2)and 339.6(2) pm at 293 K, attesting for single-bonded Ti-Ti dimers; in high-temperature TiI 3 -I, Ti-Ti distances are all equal, 326 pm at 317 K, the transition temperature for TiI 3 -I to TiI 3 -II [4].For ZrI 3 , this phase transition has not been observed and can probably not be observed because decomposition occurs before the bond energy for the Zr-Zr bond has been acquired.However, ZrI 3 is isostructural with TiI 3 -I, with Zr-Zr bond distances of 317.2(2) pm [9].
For "HfI 3 ", a hexagonal super-structure of a = 3a 0 and c = 3c 0 with Z = 18 is observed, see Experimental Section and Table 1 for atomic parameters.Again, the structure is determined by a hexagonal closest packing of iodide anions, see Figure 1.The 54 iodide ions per unit cell produce 54 octahedral holes, of which 18 would be filled if it were HfI 3 .The single crystal that we refer to has the composition Hf 0.86(1) I 3 , or HfI 3.50 (1) , and marks the most oxidized end of the non-stoichiometry range.The previously reported sub-cell, a' = 723, c' = 667 pm (± 1 pm) [14], is in excellent agreement with the sub-cell lattice parameters calculated from the super-cell, a' = a/√3 = 721.9,c' = c/3 = 666.5 pm.There are four crystallographically independent hafnium sites in the super-cell of Hf 0.86(1) I 3 of which three sites, Hf2 (3b), Hf3 (6c), and Hf4 (6c) are fully occupied.Site Hf1 (3a) has an occupancy factor of k = 0.141( 14) accounting to 0.42 hafnium atoms occupying statistically three octahedral voids, which is associated with a large displacement factor, see Table 1 and Figure 1.No solid indications for a further ordered superstructure could be found; refinement with split positions is not indicated by SHELX and does not yield a better result.The center of gravity of the electron density for Hf1 is in the special position 3a.If the hafnium site (3a) were fully occupied, this iodide would have the composition Hf 18 I 54 = HfI 3 .
Within the non-stoichiometry range for Hf x I 3 with 0.86 ≤ x ≤ 1.00 [14], the empty voids are gradually filled, which is in accord with the decrease of the c lattice constant.More voids filled means more electrons available for metal-metal bonding interactions and thus shorter distances in the [001] direction.Complete non-occupation of the Hf1 site-which would correspond to the composition Hf 0.83 I 3 or HfI 3.6 -apparently destabilizes the structure electrostatically.Full occupation, i.e., HfI 3 , is obviously possible and it is-according to the phase diagram [14]-also the most reduced hafnium iodide, in equilibrium with the metal.The crystals that we have obtained are at the most oxidized end, Hf 0.86 I 3 or HfI 3.50 , because we have, with an ample excess of the reductant aluminum, at temperatures of 850 °C or 600 °C first reached the most reduced end, HfI 3 , and then, by slow cooling-hence in equilibrium-the composition gradually reaches the least reduced end of the non-stoichiometry range, Hf 0.86 I 3 .
Columns of face-sharing octahedra run along the hexagonal c axis and, in accord with the space group symmetry R-3m, also parallel [⅓,⅔,1] and [⅔,⅓,1].The octahedral holes in the remaining six columns are empty.Thus, the columns of octahedra with holes occupied are isolated from each other such that the distribution of hafnium atoms is to be considered a one-dimensional problem. Figure 1 shows one column of the length of the c axis.Hf-I distances in the [HfI 6 ] octahedra are 285.5 pm on the average, if the Hf1-I distances are excluded.They are thereby slightly shorter than the respective mean distances Zr-I in ZrI 3 , 290.0 pm [9].Zr-Zr dimers are observed in ZrI 3 with an internuclear distance of 317.2(2) pm.This distance is associated with a Zr-Zr σ bond (each Zr 3+ has one 4d valence electron).In other words, the equidistant chain of Zr 3+ ions occupying the octahedral holes of face-sharing [I 6/2 ] columns distorts to alternating short (317.2(2)pm, bonding) and long separations (350.7(2)pm, not bonding).The transition to this Peierls distortion is actually observed for TiI 3 [4,5] and for a number of other halides as summarized in [25].An isolated [Zr 2 I 9 ] 3− dimer is also known from Cs 3 Zr 2 I 9 with a bonding distance of 312.9(4) pm.This compound is topologically very closely related to Cs 3 Y 2 I 9 .There are, however, no electrons available for bonding interactions as Y 3+ has the electronic configuration 4d 0 .Therefore, the "repulsive" Y-Y distance is 405.2(9)pm [26].
Trimeric clusters Hf3-Hf2-Hf3 occur in Hf 0.86(1) I 3 , Figure 1.In these clusters, the hafnium atoms are 318.3(2)pm apart, just as the zirconium atoms in the Zr-Zr dimers in ZrI 3 (above), and close to the Hf-Hf distances in octahedral hafnium clusters, for example 320.6 (av.) in Na 0.8 [{Hf 6 }Cl 15 ] [27].There appears to be a second dimer, Hf4-Hf1-Hf4, where the Hf-Hf distance is only 306.7(2) pm.This short distance, however, is obscured by the under-occupation of the Hf1 site producing a long Hf3-Hf4 distance of 374.8(3) pm.If the Hf1-Hf4 distance was equal to the Hf2-Hf3 distance, Hf3-Hf4 were 363.3 pm apart, a distance that agrees better with the non-bonding Zr-Zr separation of 350.7(2) pm in ZrI 3 .However, for the composition Hf 0.86(1) I 3 , equivalent to a Hf 5.16 I 18 repeat unit as shown in Fig. 1, there are only 2.64 electrons available for hafnium-hafnium bonding.If these were associated with two bonds in the Hf3-Hf2-Hf3 trimer, there were much fewer electrons than for a "normal" three-center-four-electron bond (two σ bonds).On the other hand, we have recently observed a linear [{Pr 3 } 16 ] 9− trimer in Ba 6 Pr 3 I 19 (three square antiprisms [PrI 8 ] share common faces).According to (Ba 2+ ) 6 (Pr 3+ ) 3 (e − ) 2 (I − ) 19 , there are two electrons available for Pr-Pr bonding.Theoretical calculations show that this situation is in accord with an "open" three-center-two-electron bond [28].The Pr-Pr distances are, however, with 356.4(2) pm much longer than the Hf-Hf distances in Hf 0.86(1) I 3 which may be attributed to some extent to the larger coordination number of Pr (eight) in Ba 6 Pr 3 I 19 .

Conclusions
Crystals of Hf 0.86(1) I 3 were obtained from HfI 4 by reduction with aluminum in the presence of a NaI flux.Their composition marks the most oxidized end of the non-stoichiometry range Hf x I 3 with 0.86 ≤ x ≤ 1.00.The crystal structure-a super-structure of the high-temperature TiI 3 type-is composed of hexagonally closest-packed layers of iodide ions between which 5.16 out of 6 voids in confacial octahedra along [001] are filled such that trimeric clusters occur with Hf-Hf distances of 318.3(2) pm.For bonding interactions within these trimers, 2.64 electrons are available.

Figure 1 .
Figure 1.Projection of the crystal structure of Hf 0.86(1) I 3 down [010] (left).Middle: One column of face-sharing octahedra as the repeat unit along [001] in Hf 0.86(1) I 3 (thermal ellipsoids are at a 90% probability level) and a cut-out of the trimer with relevant distances (in pm, right).