# Geometry of the pentachloridoindate(III) anion

According to Brown et al.,1 the crystal structure of $\ce{[NEt4]2[InCl5]}$ reveals that the pentachloridoindate(III) anion, $\ce{[InCl5]^2-}$, adopts a square pyramidal $C_\mathrm{4v}$ geometry (VSEPR theory would predict trigonal bipyramidal $D_\mathrm{3h}$):

According to Greenwood and Earnshaw,2

It will be noted that $\ce{[InCl5]^2-}$ is not isostructural with the isoelectronic species $\ce{[SnCl5]-}$ and $\ce{SbCl5}$, which have the more common $D_\mathrm{3h}$ symmetry. […] $\ce{[NEt4]2[TlCl5]}$ is isomorphous with $\ce{[NEt4]2[InCl5]}$ and presumably has a similar structure for the anion.

However, the structure of $\ce{[PPh4]2[InCl5].MeCN}$ was reported to have the usual trigonal bipyramidal structure for the anion,3 which throws a spanner in the works. I can't understand much of the paper as it's in German. Since it's a report of a crystal structure, though, I don't really expect it to say much about the chemistry of the compound.

Can the reported differences in molecular geometry here be rationalised?

References

1. Brown, D. S.; Einstein, F. W. B.; Tuck, D. G. Tetragonal-pyramidal indium(III) species. Crystal structure of tetraethylammonium pentachloroindate(III). Inorg. Chem. 1969, 8 (1), 14–18. DOI: 10.1021/ic50071a004.

2. Greenwood, N. N.; Earnshaw, A. Chemistry of the Elements, 2nd ed.; Butterworth–Heinemann: Oxford, U.K., 1997, p 238.

3. Bubeinheim, W.; Frenzen, G.; Müller, U. Die Chloroindate $\ce{[PPh4]2[In2Cl6]}$ und $\ce{[PPh4]2[InCl5].CH3CN}$. Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 1995, 51, 1120–1124. DOI: 10.1107/S0108270194011789.

• Do you have a CIF-file from [Brown1969]by any chance? In addition to [Bubenheim1995] I've just found three more recent crystal structures with nearly perfect trigonal bipyramidal $D_\mathrm{3h}$ geometry of $\ce{[InCl5]^{2-}}$ and it looks like the Brown's work is the only featuring square pyramid. I wonder whether it has something to do with the experimental data or refinement at that time -- $R$-factor of nearly 10% seems quite lousy for such a simple small-molecule structure. – andselisk Aug 7 '17 at 20:37
• @andselisk no cif, sorry. I guess that might be a possibility, although I don't know much about crystallography to begin with - so I'm happy to hear any thoughts on the matter. – orthocresol Aug 7 '17 at 20:42
• Well, having a look at the structure with checkcif.iucr.org is where I would start. As I said, $R$-factor might be a bit off due to the wrong initial symmetry and it might cause the wrong structure, especially if there is a proposed disorder (according to the paper). I cannot find the data in CCDC either, though the entry exists. Weird, maybe it's just me doing something wrong. – andselisk Aug 7 '17 at 20:47
• – andselisk Aug 7 '17 at 23:17

TL;DR Initially published crystal structure of $\ce{[NEt4]2[InCl5]}$ [1] according to the further investigations [3], is not valid. The $\ce{InCl5^2-}$ ion does not have $C_\mathrm{4v}$ symmetry, and VSEPR theory pretty much explains formation of numerous slightly distorted trigonal bipyramidal $\ce{InCl5^2-}$-containing complexes according to the most recent single-crystal structure experiments.

From the other side, the bond lengths and geometry index refer to the dominating character of square pyramidal environment, which is in this case can be dictated by the crystal packing, towards which $\ce{[InCl5]^2-}$ is more sensible than $\ce{[SnCl5]-}$ due to the noticeable size difference ($\ce{[InCl5]^2-}$ is bulkier). Either way, it looks like another crystallographic experiment (preferably at lower temperatures to decrease the size of thermal ellipsoids) is needed to determine the angles more precisely.

As a general advice, always pay attention to the $R_1$ and $R_2$ values of the crystal structure. A rule of thumb: a good structure refinement of small molecules should lead to $R_1 < 0.05$ and $R_2 < 0.12$.

Crystal structure of $\ce{[NEt4]2[InCl5]}$, determined in 1969 [1], has been subsequently criticized in several publications, mainly involving additional symmetry vibration analysis of Raman spectra for $\ce{MX5^2-}$ anions [2]. It's been established that $\ce{InCl5^2-}$ ion does not have $C_\mathrm{4v}$ symmetry (but retains $C_\mathrm{2v}$), and that the crystal may not be centrosymmetric.

The results are summarized in [3]:

Deconvolution of the single-crystal data was again performed with the aid of the low temperature data, revealing $11$ $\ce{InCl5^2-}$ bands between $300$ and $\pu{100 cm-1}$. Two overlapping A stretches are clearly evident at $292$ and $\pu{286 cm-1}$, but no B stretch is apparent. The two E symmetry stretches expected for the anion of a $C_2$ site, but not for a $C_4$ site, are evident at $281$ and $\pu{271 cm-1}$. [...] With the aid of low-temperature data, the four E modes predicted for $\ce{InCl5^2-}$ at $C_2$ sites are found at $144$, $136$, $122$, and $\pu{103 cm-1}$ in the single-crystal data. With this reinterpretation of the spectrum it is no longer necessary to assume arbitrarily the presence of a lattice mode in this region.

In summary, the vibrational data for the tetraethylammonium salts of $\ce{InCl5^2-}$ and $\ce{TlCl5^2-}$ indicate that these complexes reside on sites lacking full $C_4$ symmetry. The most straightforward conclusion from the vibrational data is that the $\ce{InCl5^2-}$ ions have local $C_2$ symmetry, which would be inconsistent with the previous structure determination [1]. [...]

The structure of $\ce{[(C2H5)4N]2[InCl5]}$, as previously reported, consisted of centrosymmetrically related $\ce{InCl5^2-}$ ions situated about the Wyckoff c positions of $C_4$ symmetry in space group $C_\mathrm{4h}-P4/n$. Coaxial with the $\ce{InCl5^2-}$ ions are disordered $\ce{(C2H5)4N+}$ ions also situated about the Wyckoff c positions. The N atoms of the two remaining $\ce{(C2H5)4N+}$ ions in the unit cell occupy the centrosymmetrically related Wyckoff b sites of $S_4$ symmetry, the cation as a whole again being disordered. There are two disturbing features of this solution and its subsequent refinement: the disorder of the $\ce{(C2H5)4N+}$ ions and the significant residual electron density in the region of the basal Cl atoms of the tetragonal-pyramidal anion.

It is demonstrated further that for the ordered model the most satisfying crystallographic interpretation coexists with $C_2$ rather than $C_4$ symmetry. A correlation of allowed point symmetries implies switching from $P4/n$ to $P\bar{4}$ space group, thus reducing $R$-factor ($R_1$) from $9.5\%$ to $6.7\%$.

During the refinement in $P\bar{4}$, small but significant changes occur in the basal plane of the $\ce{InCl5^2-}$ ion. The basal Cl atoms have moved by $\pu{-0.5 A}$ from their fourfold symmetric positions in $P4/n$, leading to variations in the bond distances and angles about the In atom (Figure 3) that are qualitatively sufficient to explain the vibrational results.

Geometry index $\tau_5$ for $\ce{[InCl5]}$ fragment can be used to determine formal coordination environment as follows:

$$\tau_5 = \frac{\beta - \alpha}{60^\circ},$$

where $\alpha$, $\beta$ - two greatest valence angles of the coordination center ($\angle \ce{Cl - In - Cl}$, $\alpha < \beta$).

\begin{align} \begin{cases} \tau_5 &= 0 \qquad &\text{square pyramidal geometry} \\ \tau_5 &= 1 \qquad &\text{trigonal bipyramidal geometry} \end{cases} \end{align}

For the original $\ce{[NEt4]2[InCl5]}$ structure refined in [3] I've taken angular values from their supplementary materials. It turned out that changing space group to $P\bar{4}$ still results in dominating character of square pyramidal geometry of $\ce{[InCl5]^2-}$, though one must remember that the rotation axis of highest order is $C_2$, not $C_4$:

$$\alpha = (150.6 \pm 5.0)^\circ, \beta = (154.1 \pm 6.0)^\circ, \bar{\tau_5} = \frac{154.1^\circ - 150.6^\circ}{60^\circ} = 0.06; \tau_5 \in [0.04; 0.24]$$

Paper [4] mentions that for isoelectronic $\ce{[SnCl5]-}$-contining structures with various cations only trigonal-bipyramidal geometries were reported, and suggests higher influence of crystal packing on $\ce{[InCl5]^2-}$ geometry. This can also be explained by higher flexibility of $\ce{MX5}$ fragment in $\ce{[PPh4]2[InCl5]}$ in comparison with $\ce{[PPh4][SnCl5]}$ [5] due to greater average bond length: $d(\ce{In - Cl}) = \pu{2.5 A}$, $d(\ce{Sn - Cl}) = \pu{2.3 A}$.

As for auxiliary experimental data, all crystal structures including $\ce{[InCl5]^2-}$ fragment determined in the past two decade completely support VSEPR theory that predicts trigonal bipyramidal $D_\mathrm{3h}$ symmetry (with one intermediate exception of $\tau_5 \approx 50\%$).

1. bis(Tetraphenylphosphonium) pentachloro-indate(III) [4], trigonal bipyramidal geometry: $$\alpha = 124.24^\circ, \beta = 174.74^\circ, \tau_5 = \frac{174.74^\circ - 124.24^\circ}{60^\circ} = 0.84$$

$\color{#EEEEEE}{\Large\bullet}~\ce{H}$; $\color{#909090}{\Large\bullet}~\ce{C}$; $\color{#FF8000}{\Large\bullet}~\ce{P}$; $\color{#1FF01F}{\Large\bullet}~\ce{Cl}$; $\color{#A67573}{\Large\bullet}~\ce{In}$.

1. bis(Diphenyldichlorophosphonium) pentachloro-indate(III) [6], trigonal bipyramidal geometry: $$\alpha = 120.93^\circ, \beta = 179.29^\circ, \tau_5 = \frac{179.29^\circ - 120.93^\circ}{60^\circ} = 0.97$$

$\color{#EEEEEE}{\Large\bullet}~\ce{H}$; $\color{#909090}{\Large\bullet}~\ce{C}$; $\color{#FF8000}{\Large\bullet}~\ce{P}$; $\color{#1FF01F}{\Large\bullet}~\ce{Cl}$; $\color{#A67573}{\Large\bullet}~\ce{In}$.

1. tetrakis($\mu_3$-Selenido)-tetrakis($\mu_2$-1,5-bis(diphenylphosphino)pentane)-deca-gold(I) pentachloro-indate(III) [7], intermediate geometry: $$\alpha = 138.45^\circ, \beta = 166.50^\circ, \tau_5 = \frac{166.50^\circ - 138.45^\circ}{60^\circ} = 0.47$$

$\color{#EEEEEE}{\Large\bullet}~\ce{H}$; $\color{#909090}{\Large\bullet}~\ce{C}$; $\color{#FF8000}{\Large\bullet}~\ce{P}$; $\color{#1FF01F}{\Large\bullet}~\ce{Cl}$; $\color{#FFA100}{\Large\bullet}~\ce{Se}$; $\color{#A67573}{\Large\bullet}~\ce{In}$; $\color{#FFD123}{\Large\bullet}~\ce{Au}$.

1. tetrakis($\mu_2$-chloro)-chloro-tetrakis(triphenylphosphine-P)-di-copper(I)-indium(III) tetrahydrofuran solvate [8], trigonal bipyramidal geometry (though authors refer to it as to "quasi square-pyramidal" coordination based on a single slightly shorter $\ce{In - Cl}$ bond distance $(d(\ce{In-Cl_\mathrm{ap}}) = \pu{2.36 A})$, shortest $d(\ce{In-Cl_\mathrm{eq}}) = \pu{2.42 A})$: $$\alpha = 123.90^\circ, \beta = 172.89^\circ, \tau_5 = \frac{172.89^\circ - 123.90^\circ}{60^\circ} = 0.82$$

$\color{#EEEEEE}{\Large\bullet}~\ce{H}$; $\color{#909090}{\Large\bullet}~\ce{C}$; $\color{#FF8000}{\Large\bullet}~\ce{P}$; $\color{#1FF01F}{\Large\bullet}~\ce{Cl}$; $\color{#C88033}{\Large\bullet}~\ce{Cu}$; $\color{#A67573}{\Large\bullet}~\ce{In}$.

### Bibliography

1. Brown, D. S.; Einstein, F. W. B.; Tuck, D. G. Inorganic Chemistry 1969, 8 (1), 14–18. DOI 10.1021/ic50071a004.
2. Adams, D. M.; Smardzewski, R. R. Journal of the Chemical Society A: Inorganic, Physical, Theoretical 1971, 714. DOI 10.1039/j19710000714.
3. Joy, G.; Gaughan, A. P.; Wharf, I.; Shriver, D. F.; Dougherty, J. P. Inorganic Chemistry 1975, 14 (8), 1795–1801. DOI 10.1021/ic50150a011.
4. Bubenheim, W.; Frenzen, G.; Müller, U. Acta Crystallographica Section C 1995, 51 (6), 1120–1124. DOI 10.1107/S0108270194011789.
5. Müller, U.; Siekmann, J. F. Acta Cryst C 1996, 52 (2), 330–333. DOI 10.1107/S0108270195011073.
6. Taraba, J.; Zak, Z. Inorganic Chemistry 2003, 42 (11), 3591–3594. DOI 10.1021/ic034091n.
7. Olkowska-Oetzel, J.; Sevillano, P.; Eichhöfer, A.; Fenske, D. European Journal of Inorganic Chemistry, 2004 (5), 1100–1106. DOI 10.1002/ejic.200300774.
8. Zhang, X.-Z.; Song, Y.-W.; HuiWu, F.; Zhang, Q.-F. Zeitschrift für Naturforschung B 2007, 62 (6). DOI 10.1515/znb-2007-0605.
• Certainly not the answer I expected - but excellent nonetheless. Thank you! – orthocresol Aug 8 '17 at 6:52
• @orthocresol I don't know what was wrong with me last night, but I calculated $\tau_5$ for your complex wrongly (improper $\alpha$ from SI), my sincere apologies. It actually supports square pyramidal geometry even for the structure refined for the second time, though due to lowered symmetry one cannot attribute $C_\mathrm{4v}$. I edited the answer correspondingly adding a few more details. Probably you might want to unmark it as accepted (or even downvote), as new experimental data or QC-calculations could be more significant that the idea of crystal packing effect proposed here. – andselisk Aug 8 '17 at 16:54
• No problem. Well, generally, if new information comes in, the accepted answer can always be changed, so IMO it's not much of a big deal. Downvoting would be cruel, no? ;) – orthocresol Aug 8 '17 at 16:57
• @orthocresol Well, it still was my fault and the faults should be punished/ignored, not rewarded. But thank you for the nice attitude! – andselisk Aug 8 '17 at 17:05