Article pubs.acs.org/JPCC
Controlling the Structure of Reactive Intermediates via Incipient Covalent Bonding with the Counterions: Coexistence of Two Distinct Forms of the C6F6 Cation Radical in a Single Crystal Marat R. Talipov, Qadir K. Timerghazin,* and Rajendra Rathore* Department of Chemistry, Marquette University, P.O. Box 1881, Milwaukee, Wisconsin 53201, United States S Supporting Information *
ABSTRACT: A number of highly reactive charged intermediates have been stabilized by crystallization with appropriate counterions and cocrystallization partners. Here, we computationally address a recent unexplained observation of the two Jahn−Teller forms of the otherwise unstable C6F6 cation radical in a single crystal with supposedly noncoordinating Sb2F11− counteranions. However, our density functional calculations and the natural bond orbital based analysis techniques clearly demonstrate that the specific charge-transfer interactions with close-contact fluorine atoms of the Sb2F11− counteranions are responsible for the selective stabilization of the bisallyl and quinoidal forms of the C6F6+• cation radical in different counteranion environments. Similar donor−acceptor interactions are also responsible for the much debated stabilization of the crystalline Et3Si+/toluene complex. This paradigm of charge-transfer control of the chemical nature of the crystallized molecules may hold potential for design of the next-generation materials.
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INTRODUCTION In solution-phase reactions, most of the reactive intermediates such as cations, anions, radicals, and radical-ions appear as fleeting, short-lived species only present in low concentrations. However, in certain cases a charged intermediate that is highly unstable in solution can be crystallized with a suitable counterion, which allows its structure determination by X-ray crystallography.1−3 However, the question whether these structures truly correspond to the same reactive species as observed in solution can be raised.4 For instance, nearly two decades ago, Lambert et al.5 reported an X-ray structure of an extremely reactive triethylsilyl (or triethylsilylium) cation and showed that it was packed in a close proximity to a cocrystallized toluene molecule (Figure 1),
with the Si···Car distance (2.18 Å) significantly shorter than the sum of the respective van der Waals radii (3.96 Å).6 In fact, Pauling,7 Olah,8 and others9,10 suggested that this structure actually corresponds to an altered, chemically different form which is stabilized by incipient covalent bonding with the electron-rich toluene molecule. In this context, we note a recent report of a successful isolation and X-ray crystallography of a highly reactive hexafluorobenzene cation radical (C6F6+•) with the Sb2F11− counteranion.11 Intriguingly, C6F6+• is present in two distinct bond-stretch forms, bisallyl (B) and quinoidal (Q), within the same crystal (Figure 2).11 These two forms of C6F6+•, which arise as a consequence of the Jahn−Teller effect,12−15 cannot be
Figure 2. Overlap of van der Waals surfaces of Sb2F11− with bisallyl (B) and quinoidal (Q) forms of C6F6+• in the reported X-ray structure.11 Received: September 5, 2013 Revised: October 10, 2013
Figure 1. Crystal structure of triethylsilyl cation showing the Si···Car close contact. © XXXX American Chemical Society
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no more than 0.0025, thus indicating that spin contamination was not an issue for the performed calculations. Tight cutoffs on forces and atomic displacement were used to determine convergence in the geometry optimization procedure. Partial optimization was performed using Z-matrices, and they can be found in the archive entries from the calculation files, which are included in a separate Supporting Information file. Electrostatic potential maps were plotted on the isodensity surface with isovalue of 0.001 au, with false-color representation ranging from 0.12 au (red) to 0.23 au (blue). Natural bond orbitals in Figures 9 and 10 of the main text were plotted at isovalues of 0.03 au. Natural energy decomposition analysis (NEDA)23 was performed at the M06-HF/6-31G(d) level of theory using NBO 622 and US GAMESS21 programs.
detected in solution, which implies that their observation in the crystal structure became possible because of the presence of presumably11 noncoordinating counteranions. Unfortunately, no further explanation was forthcoming despite the fact that the reported X-ray structures showed that the fluorine atoms of the counteranions penetrated the molecular surface of C6F6+•, with the F···C distances (2.7−2.8 Å) that are significantly shorter than the sum of their van der Waals radii (3.3 Å, Figure 2). We believe that this highly surprising observation provides an excellent example of the control of electronic structure of reactive species by specific intermolecular interactions in crystals. Indeed, a cursory examination of the X-ray structure in Figure 2 indicates that juxtaposition of the Sb2 F11 − counteranions around the two bond-stretch isomers is significantly different. Moreover, akin to the [Et3Si+···toluene] complex in Figure 1, the close contact between Sb2F11− anions and C6F6+•, with the F···C distances 2.7−2.8 Å, suggests that in this crystal structure the counteranions must play a significant role in stabilizing the highly reactive C6F6+• cation radical either in B or Q form. Upon crystal formation, the long-range Coulombic forces bring the ions together, while short-range intermolecular interactions direct their assembly. Generally, it is expected that Coulombic forces cannot bring the molecules closer than their van der Waals surfaces because beyond that point they are counterbalanced by strong exchange-repulsion forces.16,17 Thus, in the cases of mutual penetration of the van der Waals surfaces, the exchange repulsion has to be compensated by charge-transfer interactions/incipient chemical bonding.18 These charge-transfer interactions in crystals can modulate the electronic structure of the interacting partners and, by extension, their chemical nature as well as the bulk material properties.19,20 Accordingly, we now question the possible significance of the specific charge-transfer/bonding interactions in the stabilization of the two distinct forms of C6F6+• in the crystal with Sb2F11−.11 To this end, we present a detailed computational investigation of the nature of the intermolecular interactions between these species using the density functional theory (DFT) and the Natural Bond Orbital (NBO)18,22−24 family of bonding analysis methods.25 The findings herein will demonstrate the crucial importance of the specific charge-transfer/bonding interactions in selective stabilization of the two Jahn−Teller states of the C6F6+• cation radical.
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RESULTS AND DISCUSSION The two symmetry-unique forms of free C6F6+•bisallyl (B) and quinoidal (Q)originate from Jahn−Teller distortion of a highly symmetric D6h structure that corresponds to the conical intersection between diabatic bisallyl and quinoidal electronic states (see Figure 3). These B and Q forms can be easily
Figure 3. Cross-section of the potential energy surface of C6F6+• (A) and C6F6+• interconversion between bisallyl and quinoidal forms (B). Fluorine atoms omitted for clarity. Relative energies (in kcal/mol) and bond lengths were calculated at the ωB97X-D/6-31+G(d) level.
distinguished by changes in the C−C bond lengths (see Figure 3A). The calculations suggest that Q corresponds to local minima, while B corresponds to first-order saddle points connecting two equivalent Q structures (Figure 3).11,38 However, the corresponding barrier height is only 0.2 kcal/ mol at the ωB97X-D/6-31+G(d) level of theory,27,28 well below the zero-point vibrational energy level which should lead to a dynamic averaging of Q and B structures. Therefore, observation of both Q and B forms within a single crystallographic cell must arise due to their preferential stabilization by the different arrangement of counteranions. To test this conjecture, we next evaluate the impact of the Sb2F11− counteranions on the C6F6+• potential energy surface (PES). The crystal environment models used in DFT calculations were based on the reported X-ray coordinates and included Sb2F11− counteranions in short contact with C6F6+•;11 only the internal coordinates of C6F6+• were allowed to relax during geometry optimization. The two counterion arrangements extracted from the X-ray structure around B and Q forms will be hereafter referred to as Xb and Xq. Within Xb, the two Sb2F11− anions are located on each side of the aromatic ring, with the proximal fluorine atoms oriented on the top and bottom of the opposite C−C bonds (Figure 4, top). In Xq, there are four Sb2F11− anions on each side, with proximal
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THEORETICAL METHODS Electronic structure calculations were performed with the Gaussian 09 package, revision C01.26 For density functional theory (DFT) calculations, we used the range-separated ωB97X-D functional27 with 6-31+G(d) basis set by Pople and co-workers.28 For Sb, the LANL2DZ basis set with the effective core potential was used.29−31 Besides, we used hybrid functionals B3LYP,32,33 M06-2X,34 and M06-HF35 with 631G(d)28 basis set (LANL2DZ for Sb) to ensure that the reported results are not biased by a choice of particular DFT method. In all DFT calculations, ultrafine Lebedev’s grid was used with 99 radial shells per atom and 590 angular points in each shell. For all calculations involving the cation-radical form of hexafluorobenzene, a stability test of the wave function36,37 was performed to ensure the absence of solutions with lower energy. The values of the ⟨S2⟩ operator after spin annihilation were confirmed to deviate from the expectation value of 0.75 by B
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fluorine atoms located in an alternating manner above and below each C−C bond (Figure 4, bottom).
have different distributions of the positive charge (blue regions in Figure 5), they can be stabilized or destabilized by specific
Figure 5. Electrostatic potential maps of bisallyl (B) and quinoidal (Q) forms of isolated C6F6+•, calculated at the ωB97X-D/6-31+G(d) level. Concentrations of positive charge correspond to blue areas.
juxtaposition of negatively charged counterions. We tested this hypothesis by substituting the counteranion atoms by point charges obtained with natural population analysis18 (Figure 6).
Figure 4. Model crystal environments Xb and Xq and corresponding schematic potential energy surfaces of C6F6+•. Relative energies were calculated at the ωB97X-D/6-31+G(d) level. Also see Figures S2−S6 in the Supporting Information.
In both cases, ωB97X-D/6-31+G(d)39 optimizations of the C6F6+• moiety reproduced the experimental C−C bond lengths within 0.01 Å, yielding the geometries corresponding to B form or Q forms, respectively. However, only one of the three equivalent B or Q structures of the free C6F6+• (Figure 3B and Figure S1, Supporting Information) remains as stationary points on the PES, either a local minimum or maximum, depending on the environment. In the Xb environment, the B form is significantly stabilized relative to the Q form, ΔE(B−Q) = 5.2 kcal/mol, while in the Xq environment Q is slightly stabilized over B, ΔE(B−Q) = −1.2 kcal/mol.40 Calculated geometric and energetic parameters of coordinated C6F6+• only weakly depend on the density functional and the basis set used. For instance, ΔE(B−Q) values calculated at the M06-HF/6-31G(d) level of theory35 are 6.4 and −1.3 kcal/mol for Xb and Xq, respectively.25 Thus, these truncated counteranion environments are sufficient to reproduce the selective stabilization of B and Q forms of C6F6+• in the crystal and will serve as a basis for further investigation of the origins of this unusual effect. It has been suggested41 that preferential stabilization of the B and Q forms stems from simple Coulombic interactions between C6F6+• and the counteranions. Indeed, as B and Q
Figure 6. Three models of the crystal environment: counterions are treated explicitly (left); counterions are represented by point charges placed at the positions of short-contact fluorine atoms (center); and counterions are represented by point charges (right), applied to Xb and Xq. Values of ΔE(B−Q) were calculated at the ωB97X-D/631+G(d) level.
In a minimal model, the point charges were placed only at the proximal fluorine atom positions, while in a more extended model all counteranion atoms were represented by point charges. The minimal point-charge model seems to provide a correct picture of the C6F6+• structure modulation by the crystal environment (Figure 6). In Xb, the B form is stabilized by the negative charges of the four short-contact fluorine atoms interacting with the zones of positive charge concentration in C6F6+• (Figure 5). On the other hand, the six short-contact fluorine atoms in Xq are arranged slightly asymmetrically around C6F6+•, with two fluorine atoms ∼0.1 Å farther away from the ring (Figure 4B). As a result, two opposite C−C C
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and exchange repulsion should also play an important role in this effect. The relative importance of attractive electrostatic, polarization, dispersion, and charge-transfer interactions, exchange repulsion, and other contributions into the overall interaction energy can be quantified computationally using a variety of interaction energy decomposition analysis schemes.42 Here, we applied natural energy decomposition analysis23 (NEDA) that represents the interaction energy of molecular complexes as a combination of the three components: electrical (EL), charge transfer (CT), and residual core repulsion (CR). Conveniently, the NEDA results include a basis set superposition error (BSSE) correction,23 which mitigates the relatively small basis sets size used here. Typically for assemblies of charged species, the EL component, which encompasses electrostatic and polarization effects, has the largest contribution to the interaction energy between C6F6+• and the counteranions. At the M06-HF/631G(d) level, EEL ≃ −180 and −280 kcal/mol for the Xb and Xq models, respectively (Table 1). The CR component is
bonds experience a somewhat weaker effect of the negative charges, thereby leading to a small stabilization of Q over B. Single-point calculations of the ΔE(B−Q) values for the minimal Xb and Xq models yielded 6.1 and −2.2 kcal/mol, respectively, in good agreement with the explicit-counterion calculations, 5.2 and −1.2 kcal/mol (Figure 6). However, this qualitative and semiquantitative agreement proved to be superficial upon closer examination. The inadequacy of the point-charge approach becomes evident if one considers the distance dependence of the counteranion effect on C6F6+• or a more realistic extended point-charge model. Indeed, single-point DFT calculations of the Xb and Xq models with the explicit counterions gradually moving away from the aromatic ring (Figure 7) show that the
Table 1. Three-Component Decomposition of B and Q Forms of C6F6+• with Counterions in Xb and Xq Environments (kcal/mol) and the [Et3Si+···C6H5CH3] Complex at the M06-HF/6-31G(d) Level44 Xb environment B Q ΔE(B−Q) Xq environment B Q ΔE(B−Q) Et3Si+···C6H5CH3
EL
CT
CR
TOT
−177.3 −177.5 −0.2
−32.9 −28.3 4.6
51.8 53.8 2.0
−158.4 −152.0 6.4
−279.5 −278.7 0.8 −81.2
−40.3 −41.2 −0.9 −138.7
63.2 62.4 −0.8 171.6
−256.6 −257.5 −0.9a −48.3
A slight deviation from the ΔE(B−Q) = −1.3 kcal/mol, calculated from the SCF energies at the M06-HF/6-31G(d) level, is due to the fact that NEDA results are corrected for the basis set superposition error. a
Figure 7. Effect of counteranion displacement (explicit and minimal point charge model) on the relative energies of bisallyl (B) and quinoidal (Q) structures of C6F6+• in the crystal environments Xb and Xq, calculated at the ωB97X-D/6-31+G(d) level.
significantly smaller, +50 to +60 kcal/mol, and the CT component is the smallest, −30 to −40 kcal/mol. However, inspection of the EL, CT, and CR components into the total interaction energy clearly demonstrates that it is the CT component that is necessary to bring the counterions and C6F6+• to distances closer than the sum of van der Waals radii. Indeed, the dependence of the interaction energy components on the counteranion−C6F6+• distance shown in Figure 8 is obtained in a way similar to as in Figure 7, showing that if the CT component is removed the minimum on the interaction energy curve is observed at the van der Waals contact between C6F6+• and Sb2F11− (3.1 Å).43 The CT interactions are necessary to overcome the exchange repulsion and allow the interaction partners to penetrate each other’s van der Waals surfaces, which, in turn, further strengthens the electrostatic interactions.18 The CT component also has the largest contribution to the differential stabilization of B and Q by the counteranions. In the case of the bisallyl crystallographic environment Xb, there are very small differences in the EL term, ΔEEL(B−Q) = −0.2 kcal/mol, while the differences in the CT and CR terms, ΔECT(B−Q) = 4.6 kcal/mol and ΔECR(B−Q) = 2.0 kcal/mol,
counteranion effect on ΔE(B−Q) is the most prominent when the counteranions penetrate the van der Waals surface of C6F6+•. This short-range nature of the C6F6+• electronic structure modulation by counteranions is not correctly reproduced by the minimal point-charge model that predicts much slower decrease of ΔE(B−Q) with the distance (Figure 7). Moreover, if the point-charge model is extended to represent all counteranion atoms beyond the short-contact fluorine atoms, the agreement with the full-model calculations and experimental observations breaks down even at short distances (Figure 6). So much so, the calculations of the extended point-charge models of the Xb and Xq environments incorrectly predict the stabilization of the Q and B forms, respectively. Thus, the specific stabilization of the two forms of the C6F6+• cation radical in the crystal environment cannot be simply rationalized by the effect of the electrostatic interactions alone. Because the penetration of the van der Waals surface by counteranions is required for efficient modulation of the C6F6+• structure, the short-range charge-transfer/incipient bonding D
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Figure 8. Effect of counteranion displacement on the NEDA components applied to bisallyl C6F6+• in the Xb environment at the M06-HF/631G(d) level. (A) Individual decomposition terms. (B) Total interaction energy (TOT) and total interaction energy excluding the CT component (CR+EL). (C) Contribution of EL, CT, and CR terms into the B vs Q differential stabilization ΔE(B−Q) in the Xb environment. Also see Figures S7 and S8 in the Supporting Information for the Xq environment.
account for most of the overall ΔE(B−Q) = 6.4 kcal/mol (Table 1). For the Xq environment, the three components of ΔE(B−Q) have a similar magnitude (∼0.8 kcal/mol), with the EL component favoring the B form and CT and CR components favoring the observed Q form (Table 1). The short-range nature of CT and CR interactions that control ΔE(B−Q) at the distances of the van der Waals contact and shorter (Figure 8C) accounts for the rapidly fading effect of the counterions on ΔE(B−Q) values observed in Figure 7. Natural bond orbital (NBO) analysis shows that the CT component arises from a multitude of individual donor− acceptor interactions between the lone pairs of the shortcontact fluorine atoms of the counterions and the empty p-type orbitals of the aromatic ring carbon atoms that represent the delocalized hole due to one missing β-electron (Figure 9).45 In
counterion atoms in the extended point-charge model, as discussed above (Figure 6). Therefore, in the crystal environment the structure of C6F6+• is controlled by the interplay of short-range CT and CR interactions arising due to orbital overlap between the aromatic π-system and the counteranions at the distances smaller than the van der Waals contact. The fluidity of the C6F6+• electronic structure, determined by the two Jahn−Teller states, and the resulting shallowness of the PES make this control exceptionally efficient. Interestingly, for the triethylsilyl cation−toluene complex in Figure 1, the interaction energy is dominated by the CT component due to the incipient Si−C bond (Figure 10A).
Figure 10. (A) Distance dependence of the NEDA components on the interaction energy in the [Et3Si+···C6H5CH3] complex at the M06HF/6-31G(d) level. (B) Natural bond orbital representation (0.03 au isovalue) of the donor−acceptor interactions between the π-orbitals of toluene and the empty p-orbital of the cationic silicon atom.
Figure 9. Natural bond orbital representation (0.03 au isovalue) of the donor−acceptor interactions between the short-contact fluorine atoms of Sb2F11− anions with a delocalized β-electron hole of C6F6+• in the Xb and Xq environments, calculated at the ωB97X-D/6-31+G(d) level.
Indeed, NBO analysis shows a strong interaction (∼152 kcal/ mol) of the toluene π-system with an empty p-orbital of the silicon atom (Figure 10B), reminiscent of the classical Wheland intermediate.7−10
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CONCLUSION We have clearly demonstrated that mutual penetration of the van der Waals surfaces of molecular components in a crystal necessitates contribution from strong charge-transfer interactions/incipient bonding required to overcome short-range exchange repulsion forces. These CT interactions can arise either from a single nascent covalent bond, such as in the case of the Et3Si+ cation cocrystallized with toluene, or from many disperse and not immediately obviousyet crucially importantdonor−acceptor interactions, such as in the case of
the B form, the higher localization of the β-electron hole at the two opposing C−C bonds favors electron density donation from the counterions and also leads to smaller exchange repulsion. In the Xq model, two of the six short-contact fluorine atoms are slightly more distant and thus have weaker CT and CR interactions with the two opposing C−C bonds which drives more π-electron density to these bonds and thus stabilizes the Q form. Large enough negative point charges in place of the short-contact fluorine atoms would have a similar effect that, however, becomes negated by the charges of other E
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crystalline [C6F6+•···Sb2F11−]. These intimate interactions in turn impinge on the electronic structure and thus the chemical properties of the interacting partners. As such, the specific charge-transfer interactions with close-contact fluorine atoms of the Sb2F11− counteranions selectively stabilize the bisallyl and quinoidal forms of the highly reactive C6F6+• cation radical. One can envision that similar charge-transfer control of the chemical nature of the crystallized molecules can be exploited in designing materials with novel properties.19,20,46
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ASSOCIATED CONTENT
S Supporting Information *
Geometric parameters of the bisallyl (B) and quinoidal (Q) forms of C6F6+• in different crystal environments; Potential energy surfaces of C6F6+• in the gas phase and in different crystal environments, calculated at the ωB97X-D/6-31+G(d) level; Results from other DFT methods; Effect of the counteranion displacement on the NEDA components applied to B and Q in different environments; Effect of the counteranion displacement on the contribution of NEDA terms into ΔE(B−Q) applied to B and Q in different environments; Distance dependence of the NEDA components on the interaction energy in the [Et3Si+···C6H5CH3] complex at the M06-HF/6-31G(d) level; and Archive entries from the calculation files. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank the National Science Foundation (Chemistry NSF) for financial support and Prof. Eric D. Glendening (Indiana State University) for helpful discussions. The calculations were performed on the high-performance computing cluster Père at Marquette University funded by NSF awards OCI-0923037 and CBET-0521602.
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REFERENCES
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The Journal of Physical Chemistry C
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dx.doi.org/10.1021/jp408912g | J. Phys. Chem. C XXXX, XXX, XXX−XXX
