Substituent effects on the [1-closo-CB₉H₁₀]⁻ anion geometry: experimental and DFT studies†

Anna Pietrzak *^a, Michael J. Carr ^b and Piotr Kaszyński *^cde
aFaculty of Chemistry, Łódź University of Technology, 90-924 Łódź, Poland. E-mail: anna.pietrzak.1@p.lodz.pl
^bSchool of Chemistry of the University of Leeds, Leeds, England UK LS2 9JT, UK
^cFaculty of Chemistry, University of Łódź, 91-403 Łódź, Poland
^dCentre of Molecular and Macromolecular Studies, Polish Academy of Sciences, 90-363 Łódź, Poland
^eDepartment of Chemistry, Middle Tennessee State University, Murfreesboro, TN 37130, USA

First published on 7th June 2023

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Introduction

Carbaborate anions¹ [closo-1-CB₁₁H₁₂]⁻ and [closo-1-CB₉H₁₀]⁻ (1a, Fig. 1) are of increasing importance as structural elements of functional materials,^2,3 such as ionic liquids,^4–6 ionic liquid crystals,^7–9 electrolytes^10–12 for energy storage, and polar liquid crystals^13–16 investigated for display applications. Many of these applications require substitution patterns in antipodal positions, 1 and 12 for the former anion, and 1 and 10 in 1a, to obtain structures with elongated molecular shapes. Therefore there is significant interest in synthetic and structural chemistry of both clusters with such substitution patterns. While substantial effort has been directed to the larger cluster, [closo-1-CB₁₁H₁₂]⁻, the smaller, 10-vertex anion 1a receives much less attention. This is evident from e.g., the number of single crystal structures deposited in Cambridge Structural Database (CSD). Thus, there is a total of 740 structures containing the {closo-1-CB₁₁} cluster and 301 with substitution at the antipodal positions. In contrast, there are only 88 reported structures with the {closo-1-CB₉} skeleton (62 with organic substituents and 26 with organometallic groups), out of which only 30 have substituents at the C(1), B(10) or both positions.

The disproportionally low number of {closo-1-CB₉} structures with apical substituents deposited in CSD is related to the fact that convenient access to the parent 10-vertex anion 1a was developed relatively late, about two decades ago.^17,18 Prior to 2000 structure of the parent 1a (ref. 19) and its 8 derivatives were reported, out of which only one, the C(1)–NMe₃ derivative 1b,²⁰ had an apical substituent.

The new three-step Brellochs' method,¹⁷ involving thermal rearrangement of the {closo-2-CB₉} intermediates, opened up a relatively efficient access to the parent anion [closo-1-CB₉H₁₀]⁻ (1a)¹¹ and its C(1) substituted derivatives (Fig. 2). Consequently, several compounds were obtained directly, such as 1c,^21,221d,²³1e,¹⁸1f,²⁴1g,²⁵1h,²⁴ or through simple chemical transformations (1i,²⁶1j,²⁷ and 1k (ref. 24)) and their structures were reported (Fig. 1). Other derivatives, such as 1l, 1m, 1n, and 1o were prepared²⁸ through chemical transformations of the COOH group in 1h, but their XRD structures were not reported. Soon after the discovery of the Brellochs' method, it was demonstrated²⁹ that thermal rearrangement of easily obtainable 7-halo {closo-2-CB₉} derivatives lead to a mixture of 1,6- and 1,10-disubstituted derivatives of the [closo-1-CB₉H₁₀]⁻ anion (Fig. 2), and the structure of the first 1,10-difunctionalized derivative 1p was reported.²⁹ This discovery was exploited in 2005 in the development of a practical access to a broad range of 1,10-difunctionalized derivatives of 1a, such as 1q,⁹ starting with the isomerically pure [closo-1-CB₉H₈–1-COOH-10–I]⁻.³⁰

Transformation of the iodo substituent led to the dinitrogen zwitterion 1r, which was converted to pyridinium 1s and sulfonium derivative 1t.³¹ Crystal structures of all three 1-carboxylic acid derivatives, 1r–1t, were reported.³¹

A more efficient and general method for the preparation of B(10) substituted derivatives of the [closo-1-CB₉H₁₀]⁻ anion was discovered in 2015 (Fig. 2).³² Unlike the Brellochs' procedure, the new method relies on substitution of the parent 1a and its C(1) derivatives with a phenyliodonium group, which undergoes a nucleophilic displacement or can be reduced to the iodo substituent. The proportion of the B(10) vs. B(6) substitution is about 1:1, the highest to date for an electrophilic substitution of 1a, but the two regioisomers are conveniently resolved by differential reactivity with nucleophiles (kinetic resolution).³³ This method was used to obtain zwitterionic derivative 1u, which was transformed to the B(10)–iodo derivative 1v.³⁴ Analogous transformations of the parent 1a led to B(10) derivatives 1w–1y.³³ Crystal structures of all five derivatives have been established and reported.^33,34 This demonstrates a significant potential for further development of 1,10-difunctional derivatives of 1a.

The growing number of derivatives brings up a question whether there is a pattern in response of the {closo-1-CB₉} skeleton geometry to the electronic nature of apical substituents. Such relationships were found in derivatives of the related dianion [closo-B₁₀H₁₀]²⁻, in which the B(1)⋯B(10) separation decreases with an increasing electron-withdrawing character of the substituent(s).^35–37 This leads to a question, whether this trend is specific to the [closo-B₁₀H₁₀]²⁻ dianion derivatives or more universal and applicable also to derivatives of the [closo-1-CB₉H₁₀]⁻ anion (1a).

Herein we report structural data for 5 derivatives of the [closo-1-CB₉H₁₀]⁻ anion substituted in the C(1) position (1l, 1m, 1n, and 1o, Fig. 1) or C(1) and B(10) positions (1q). Geometry of these compounds together with that of 19 similar structures, selected from the crystallographic database and containing simple substituents with known electronic characteristics (Fig. 1), are analyzed in detail. The experimental structural parameters of the entire set of 24 compounds are compared to those obtained from DFT calculations. Finally, substituent effects on the {closo-1-CB₉} cluster geometry are analyzed using Hammett constants.

Experimental

X-ray crystallography

Single-crystal X-ray diffraction measurements for 1l[PyrCH₂Cl], 1m[Et₄N]·[Et₄NBr], 1n, 1o and 1q were performed with a Bruker Nonius Kappa CCD diffractometer. The crystals were kept at 150(2) K during data collection, while measurements for 1o were conducted at 195(2) K. Data collections were performed using the Mo Kα radiation (λ = 0.71073 Å).^38,39 All structures were solved using direct methods by ShelXS-97 (ref. 40) and refined in the ShelXL-97.⁴¹ All non-hydrogen atoms were refined anisotropically. C–H and B–H hydrogens were generated geometrically using the HFIX command in ShelXL. Additional data collection and refinement information is listed in ESI.†

CCDC files 265347–265351 contain the ESI† crystallographic data for new structures.

Computational details

Quantum-mechanical calculations were carried out using Gaussian 09 suite of programs. Geometry optimizations were undertaken using the B3LYP^42,43 functional with Karlsruhe triple-ζ polarization Def2TZVP basis set^44,45 and tight convergence limits with appropriate symmetry constraints. All calculations were performed in PhCl dielectric medium (arbitrarily chosen) with the PCM model⁴⁶ requested with SCRF(SolventC₆H₅Cl) keyword, since it was demonstrated³⁵ that low dielectric medium is important for obtaining accurate geometry of zwitterions. The ground state nature of stationary points for the obtained equilibrium geometry was confirmed with vibrational frequency calculations.

Results and discussion

Molecular and crystal structure

Crystals suitable for structural analysis were grown by slow evaporation of solutions of compounds reported previously:^9,281l[PyrCH₂Cl] (yellow prisms from CH₂Cl₂–Et₂O), 1m[Et₄N]·[Et₄NBr] (yellow prisms from CH₃CN–Et₂O), 1n (colorless prisms from CH₂Cl₂–n-hexane), 1o (colorless needles from CH₂Cl₂–Et₂O), and 1q (yellow crystals from CH₂Cl₂–n-hexane). Their solid-state structures were determined by low temperature single crystal X-ray analysis, and the results are shown in Fig. 3–5. Full details of data collection, refinement and molecular geometry are provided in the ESI.†

Crystal structures of 1n, 1o, and 1q are formed by single symmetry-independent molecules resulting in unit cells containing two molecules related by inversion (1n) or four molecules related by inversion and 2-fold rotoinversion axes (1o and 1q, Fig. 3). In contrast, asymmetric units of 1l[PyrCH₂Cl] and 1m[Et₄N]·[Et₄NBr] contain two symmetry-independent pairs of ions. In addition, the asymmetric unit of the latter crystal contains two disordered ion pairs [Et₄N]⁺ Br⁻, which results in a cocrystal of 1m[Et₄N] and [Et₄NBr]. Although both structures 1l[PyrCH₂Cl] and 1m[Et₄N]·[Et₄NBr] are characterized by Z′ = 2, the respective symmetry independent ions adopt similar conformations, and their overlay gives low root-mean-square deviation (RMSD) values (i.e., 0.007 for 1l[PyrCH₂Cl] and 0.097 for 1m[Et₄N]·[Et₄NBr]).

The two symmetry-independent anions 1l are differentiated by their type of assembly within the crystal and nonbonding interactions with accompanying cations. The crystal system of 1l[PyrCH₂Cl] is composed of chains formed by the anions linked through short contacts which are inside the van der Waals separation: −0.039 Å for Cl(1b)⋯B(10A) and −0.014 Å for B(7A)⋯H(9B). The chains are arranged parallel to the (010) planes separated by layers of 1-chloromethylpyridynium counterions (Fig. 4a). The crystal lattice stabilization is augmented by coulombic short contacts between the [closo-1-CB₉H₉–1-Cl]⁻ anions and 1-chloromethylpyridinium cations.

Similarly to 1l[PyrCH₂Cl], crystal structures of 1n and 1o can be defined as layers formed by individual molecules (Fig. 4b and c). Supramolecular layers in zwitterion 1n extend along the (110) plane. They are formed by S⋯B and C–H⋯B non-bonding interactions between the Me₂S⁺ substituent and a B atom of the neighboring {closo-1-CB₉} cage and strengthen by B–H⋯B close contacts between adjacent molecules. The inter-layer contacts are provided through C–H⋯B interactions between Me₂S⁺ fragment and the {closo-1-CB₉} cage.

In the crystal structure of zwitterion 1o, layers are parallel to the (110) plane and are stabilized by the N–H⋯B and C–H⋯B short contacts between the pyridine fragment and the {closo-1-CB₉} cage of the neighboring molecules, while contact between layers involves interactions of pyridine π-electron system and the {closo-1-CB₉} cage.

Molecules of 1q form chains extending along the [100] direction (Fig. 4d) through B⋯I interactions between neighboring molecules. Adjacent chains are linked through B–H⋯B contacts between the {closo-1-CB₉} cages.

As in the structure of 1q, supramolecular chains of 1m[Et₄N]·[Et₄NBr] extend in the [100] direction. However, these infinite substructures are formed by [closo-1-CB₉H₉–1-(NNC₆H₄–4-NH₂)]⁻ and Br⁻ anions linked through interactions between the NH₂ groups and Br⁻ ions (Fig. 5). Neighboring chains in 1m[Et₄N]·[Et₄NBr] are separated by the [Et₄N]⁺ counterions. Geometrical parameters of short contacts stabilizing the crystal systems are listed in the ESI.†

Cambridge structural database (CSD) search

For the purpose of a broader structural analysis, Cambridge Structural Database (CSD, version 5.43, November 2022) was searched to obtain a larger pool of experimental structural data using search criteria defined in Fig. 6.

The search yielded a total of 32 crystal structures containing the {closo-1-CB₉} skeleton with substituents at the C(1), B(10) or both apical positions and the parent 1a (for the complete list see the ESI†). In the entire set, there are 29 structures with unique substitution on the {closo-1-CB₉} cluster and the parent, out of which 19 structures were selected as suitable for further investigation.

{closo-1-CB₉} cage geometry – a comparison of experimental and DFT results

In order to facilitate comparison of experimental and DFT-optimized structures, and also data analysis, geometrical parameters of the {closo-1-CB₉} skeleton were defined as shown in Fig. 7. The B(10)–B, B(6)–B(7), B(2)–B(6), B(2)–B(3), and B–C(1) distances are averaged and designated as d_1B, d_2B, s, d_2C, and d_1C, respectively. The esd's associated with these parameters reflect the distribution of individual values in both experimental and theoretical structures. Such an analysis of average parameters allows for avoiding conformational differences between the solid-state and DFT-derived geometries. DFT structures were obtained by full geometry optimization at the B3LYP/Def2TZVP level of theory in PhCl dielectric medium. This weak, arbitrary selected dielectric medium was demonstrated to be important for accurate geometry modeling.³⁵ All values used in the analysis are listed in the ESI.†

A comparison of all experimental and DFT-derived geometrical parameters defined in Fig. 7 for derivatives 1 shows an excellent correlation with r² > 0.999 and with the slope equal unity, and essentially no systematic error (Fig. 8). This demonstrates that in general the DFT method reproduces the experimental structures accurately. Detailed analysis of each group of parameters shows, however, some significant deviation from this general trend related mainly to the quality of some experimental data. Thus, analysis of the heights of the tetragonal pyramids demonstrates that h_B for the B(10) pyramid (Fig. 7) is more accurately reproduced by DFT (conforming to the general fitting line with r² = 0.88) and has a nearly 3 times larger span of values than the height of the C(1) pyramid (h_C, r² = 0.75, Fig. 9). Parameter h_B for 1q (X = N₂⁺, Y = I) exhibits the largest deviation (0.023 Å vs. the average of absolute differences of 0.005 Å) from the value expected on the basis of the general correlation (Fig. 8). Removing this data point improves correlation for h_B to r² = 0.925. The observed large deviation for 1q is due, in part, to a relatively large error on individual bonds (std ∼ 0.010 Å) and, in part, to difficulties with accurate modelling of the iodine atom with this DFT method.

The B–B distance s (Fig. 7) between the equatorial planes is nearly constant in the entire series and for most compounds is clustered within 0.015 Å. The only exceptions are 1d (XC₆H₄F) and 1q, which differ from the DFT estimate by 0.032 and 0.015 Å, respectively, while the average value of the absolute differences in the series is about 0.006 Å and within a typical experimental error.⁴⁷ Inspection of the results indicates that the difference between the experimental and DFT values for the first derivative is related to large experimental errors, as evident from multiple B alerts in Checkcif validation procedure involving the Hirshfeld rigid bond test. In addition, molecules of 1d exist as cocrystals with its 2-carba isomer, [closo-2-CB₉H₉–2-C₆H₄F]⁻ in a 1:1 ratio from incomplete thermal rearrangement. In contrast, deviation for 1q data point is presumably due to inaccurate DFT geometry modeling.

The total length l of the {closo-1-CB₉} cluster is a sum of tetragonal pyramid heights h and the separation between the equatorial planes. A comparison of the experimental and DFT-calculated parameter l indicates good correlation with the exception of 1d (vide supra). Without this data point the correlation is satisfactory (r² = 0.86).⁴⁷

Other {closo-1-CB₉} cage dimensions include the length of the tetragonal pyramid edge d₁ and base d₂. The former parameter assumes values in two ranges: lower d_1C values are in a narrow range of 1.60–1.62 Å, while the d_1B values are between 1.65 and 1.71 Å (Fig. 10). These differences reflect the generally lower impact of the C(1) substituent on the cage geometry, when compared with the effect of the B(10) substitution.

All data points for the d_1C parameter appear close to the general fitting line, albeit due to a narrow range of the values the resulting correlation parameter is low (r² = 0.33). The largest differences from the expected values are observed for 1g (XC₆H₄CN, 0.07 Å) and again for 1d (0.011 Å), while the distribution of the individual measurements is 0.005 and 0.020 Å. Removing these data points from the correlation improves r² to 0.55 and gives the average absolute difference between experimental and DFT values of 0.003 Å.

Similar analysis of the d_1B parameter demonstrates that the largest differences of about 0.01 Å are observed for 1j (XCONHPr-i), 1d and 1q, which are comparable with the std of the individual values constituting the averages. Removing these data points from the correlation increases r² value from 0.60 to 0.75. Inspection of structural data retrieved from Crystallographic Information File (CIF) for 1j shows a relatively large R value of ∼8% accompanied by elongated ellipsoids and a low precision of determining individual bonds of about 0.006 Å. This certainly contributes to the observed differences in the correlation.

The distances between equatorial boron atoms fall into a range essentially the same for both equatorial belts. As previously observed, values d_2C and d_2B for 1d are far from the expected correlation with the largest deviations up to 0.050 Å for the former parameter (Fig. 11). Much smaller, nevertheless significant deviations are observed for 1j (0.013 Å) and for 1q (0.007 Å), while the average of absolute differences for the two parameters is 0.003 Å. Issues related to these three structures are described above.

Finally, analysis of exocyclic bonds at the apical positions of the [closo-1-CB₉H₁₀]⁻ anion demonstrates a very good agreement between the experimental and DFT-derived distances d_CX and d_BY (Fig. 12). The largest differences are observed for the B–I bonds in derivatives 1p (0.031 Å), 1r (0.0315 Å), 1v (0.035 Å), which are significantly larger than the experimental error of 0.006, 0.003 and 0.002 Å, respectively. At the same time, the mean difference between the remaining experimental and DFT exo-cage distances are 0.012 Å. This discrepancy indicates a systematic deficiency with accurate treatment of the iodine atom at this level of theory. Also the B–N bond in 1q is calculated shorter, by 0.032 Å, than suggested by experiment, although this value has an associate large experimental error of ±0.020 Å.

The comparison of geometrical parameters indicates a generally high level of accuracy of the B3LYP/Def2TZVP method in reproducing experimental structures. It revealed, however, significant problems with the experimental structure of 1d (XC₆H₄F) and, to a lesser extent, with 1q (XN₂⁺, YI) and 1j (XCONHPr-i) consistent with poor structural data. On the other hand, this DFT method lacks high accuracy in dealing with the iodine atom.

The availability of the experimental and theoretical models in series 1 permits a brief comment on the conformational orientation of substituents attached to positions C(1) and B(10). Inspection of series 1 indicates five general types of architectures of substituents: four are shown in Fig. 13 (A–D) and the fifth type has the axial symmetry, such as N₂, I, Cl. Analysis of the DFT-optimized structures demonstrates strong preference for the staggered orientation of the apical substituents. In class D, the two Me groups in the NMe₃ substituent adopt a staggered conformation, while the third group eclipses the C(1)–B(2) bond, due to steric requirements of the C₃–symmetric substituent.

The orientation of substituents at the C(1) position in classes A, B and D is described by the torsion angle θ_X defined by X_β–X_α–C(1)–B(2) atoms, in which case θ_X = 0 corresponds to an ideal eclipsed conformation. Atoms α and β are successive atoms of the substituent. For the azo group in A′ and substituents in B′ the angle θ_X is defined as X_β–X_α–C(1)–B(6). The sulfonium substituent in class C assumes an ideal staggered conformation when the difference of two torsion angles measured for two substituents on the connecting atom (sulfur) θ_X–θ_X′ = 0. Similarly, orientation of substituents at the B(10) position is defined by the analogous torsion angle θ_Y, e.g. for class A′ and B′, θ_Y is defined by Y_β–Y_α–B(10)–B(5) atoms. Full details are listed in the ESI.†

Results of DFT calculations indicate that most substituents adopt either an ideal eclipsed (A, B and D) or staggered (A′, B′ and C) orientation with respect to the {closo-1-CB₉} skeleton. The only exceptions are the C(1)–CH₂CH₂Ar (1v and 1u) and NHC(NH₂)Me (1y) groups, which are about 10.5°, 12.1°, and 9.4°, respectively, away from the ideal eclipsed orientation. Also the C(1)–CONHPr-i group in 1j is 12.1° away from the ideal staggered orientation. Interestingly, in contrast to 1-pyridinium in 1s and 1x, DFT predicts an eclipsed orientation for 2-pyridinium substituent in 1o (class B), presumably due to electrostatic interactions between hydrogens atoms of significant protic and hydridic characters, ⁺N–H⋯H–B⁻.

Analysis of experimental structures revealed that phenyl (1c, 1p), 4-substituted phenyl (1d–1g, 1i), 1-pyridinium (1s, 1x) and carboxyl (1r–1t) substituents (class B′) generally conform to the staggered orientation relative to the {closo-1-CB₉} cage predicted by the DFT methods. The largest difference is observed for 1-pyridinium derivative 1x, which deviates from the ideal orientation by 28.4°, and for the COOH group in 1s and 1t with an average deviation of about 14°. The CONHPr-i group in this class of substituents (1j) deviates by 25° from the orientation predicted by the DFT method (θ_X = 12.1°), and assumes a nearly eclipsed orientation.

The azo and IPh substituents in 1m and 1u (class A′) and also dimethylsulfonium substituent in 1n (class C) little deviate from the ideal staggered orientation, by 4.8°, 14.6°, and 8.3°, respectively. In contrast, cyclic dialkylsulfonium group connected to the B(10) position in 1t assumes orientation significantly is away from the ideal staggered: 30.3° off in molecule 1 and 65° in the second independent molecule. The NMe₃ in 1b (class D) assumed an ideal eclipsed orientation, while 2-pyridinium in 1o (class B) is away from DFT predicted position by 27°.

Finally, the CH₂CH₂Ar substituent in group A (1u and 1v) is about 11° off the DFT-predicted pseudo eclipsed orientation (θ_X ≈ 10.5°), while the amidinium group in 1y is closer to the staggered orientation (θ_Y = 32.9°) than to the predicted pseudo eclipsed form (θ_Y = 9.4°). The most significant discrepancy in the entire series is observed for the CH₂OH substituent in 1k, for which the experimentally observed ideal staggered form in all four independent molecules in the solid is a rotational transition state in the DFT model, while the conformational ground state is the eclipsed form.

Substituent effect on the {closo-1-CB9} cage geometry

Analysis of structural data in series 1 indicates that the geometry of the {closo-1-CB₉} cage responses to the electronic nature of the apical substituents. The most convenient way to perform a quantitative analysis of such effects is by using Hammett substituent parameters σ_p, which are well established for about half of the substituents in series 1.⁴⁸ The σ_p parameters for 4-X–C₆H₄– substituents, where X = CN, COOH and N₂⁺, were estimated from a correlation of the available⁴⁸σ_p parameters for X and 4-XC₆H₄–, in which X = OMe, Me, Et, F, Cl, Br, I, NO₂.⁴⁷ Interestingly, the slope in this correlation is 0.32(2), which reflects the ability of two benzene rings (biphenyl) to transmit electronic effects. Hammett parameters σ_p for the PhI⁺– (1.50), 1-C₅H₅N⁺– (0.82), and MeC(NH₂)NH⁺– (0.48) groups were estimated previously with the accuracy of ±0.1 using a correlation of ¹H NMR chemical shifts of the C(1)–H proton in derivatives [closo-1-CB₉H₉–10-X]⁻ and known σ_p values.^33,47 A substituent parameter for the 2-C₅H₅N⁺ group in 1o remains unavailable. The analysis also excludes 1d, which shows significant problems with conforming to structural trends established for the entire series.

Available data allow for a separate analysis of the substituent effect at the C(1) (12 derivatives 1b–1n) or at both apical positions (10 derivatives 1p–1y) on the {closo-1-CB₉} cage geometry. Analysis of the first group of derivatives demonstrates essentially no effect on the heights of the square pyramids, h_C and h_B. Both values are constant within the experimental error in the series (average 0.941(9) Å and 1.092(6) Å, respectively), despite a significant range of σ_p values (0–0.90) of the C(1) substituents (Fig. 14). Other distances defined in Fig. 7, d and s, are nearly constant in the series of C(1) substituted derivatives.⁴⁷ The largest, although still marginal impact of the C(1) substituent is observed for the d_2C parameter (the B(2)–B(3) distance), which increases at a rate of 0.020(6) Å/σ_p.

A similar analysis for the second group of derivatives, those containing substituent at the B(10) position showed a much stronger substituent effect on {closo-1-CB₉} cage geometry. Since in most derivatives 1p–1y both apical positions are substituted, for the purpose of the analysis a sum of two Hammett constants was used. This approach was successful in analysis of [closo-B₁₀H₁₀]²⁻ dianion derivatives.³⁷ Results demonstrate that the heights of the two square pyramids response to the apical substituents; both parameters decrease as the electron withdrawing character of the substituents increases. This response is over twice greater for the B(10) pyramid (h_B) than for the C(1) pyramid (h_C, Fig. 15). Consequently, the overall length of the {closo-1-CB₉} cage, l, decreases at a rate −0.044 Å/∑σ_p with increasing electron demand of the substituents, despite the fact that the distance between the equatorial planes is essentially unaffected (Fig. 16).

The apical substituents also visibly affect distances d_C and d_B, particularly the equatorial B–B bond lengths (d_2C and d_2B), which expand with increasing value of the σ_p parameter at a rate of about 0.012 Å/∑σ_p (Fig. 17). Out of the two d₁ parameters, only d_1B (the B(10)–B distances) is affected by the apical substitution and it decreases (slope −0.009(5) Å/∑σ_p), while d_1C is constant within the experimental error (avrg 1.608(6) Å).

Analysis for the entire set of derivatives 1 revealed similar dependence of key structural parameters, h, d and s on the sum of the Hammett constants, as observed for the series 1p–1y.

Conclusions

Recent advances in the chemistry of the [closo-1-CB₉H₁₀]⁻ anion (1a) opened up a facile access to the parent anion itself and to its B(10) derivatives, which resulted in an increasing number of experimental structures. Analysis of a set of 24 structures demonstrates that the experimental geometrical parameters of the {closo-1-CB₉} cage are well reproduced by the B3LYP/Def2TZVP method in PhCl dielectric medium, giving an excellent overall correlation. The most common outliers in the analysis are 1d and 1q. The problem with fitting the former is related to poor experimental data, while deviations for 1q data points are possibly due to inaccurate DFT modeling of the iodine atom. Detailed analysis demonstrated good correlations for parameters h_B, h_C, and l, moderate quality for parameters d_1C, d_2C, d_2B, and d_1B, while the lowest agreement between theoretical and experimental values were observed for parameter s. On the other hand, the experimental exocyclic bonds (d_CX and d_BY) were well reproduced with the DFT method.

Structural analysis of series 1 revealed that substitution of the C(1) position with groups characterized by the Hammett σ_p parameter in a rage of 0.0–0.90 (derivatives 1b–1n) has a negligible effect on the {closo-1-CB₉} cage geometry. In contrast, the B(10) substituents in series 1p–1y affect the cage geometry, and the effect is generally stronger for the square pyramid containing the B(10) atom than on the C(1) pyramid. Thus, the heights of the pyramids and consequently the overall length of the {closo-1-CB₉} cage contracts with increasing electron-withdrawing character of the substituents. This is consistent with trends found in derivatives of the [closo-B₁₀H₁₀]²⁻ dianion.^35–37 At the same time, bases of both square pyramids expand (cage widening), while the edge marginally contracts only for the B(10) pyramid.

Overall, the presented analysis suggests that the B3LYP/Def2TZVP method well reproduces experimental structures, while the uncovered trends in substituent effects can effectively be used as guides in structural analysis of [closo-1-CB₉H₁₀]⁻ anion derivatives.

Author contributions

Conceptualization, data analysis, visualization, writing, and editing – P. Kaszyński and A. Pietrzak; XRD measurements – M. J. Carr.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This project was supported by the National Science Foundation (DMR-1611250). Single crystal X-ray measurements were supported with the UK EPSRC for instrumental grants M83360 and R61949. A. P. thanks the Faculty of Chemistry, Lódź University of Technology for Young Scientists' Fund (grant W-3D/FMN/1G/2022). M. J. C. thanks Andy Franken and John D. Kennedy for help with acquiring the XRD data.

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Footnote

† Electronic supplementary information (ESI) available: XRD data collection and refinement, details of CSD search, experimental and DFT structural data, additional correlation plots, and DFT computational results. CCDC 265347–265351. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d3ce00357d

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