Markus
Rohdenburg
a,
Zheng
Yang
b,
Pei
Su
c,
Eduard
Bernhardt
d,
Qinqin
Yuan
b,
Edoardo
Apra
e,
Simon
Grabowsky
f,
Julia
Laskin
c,
Carsten
Jenne
d,
Xue-Bin
Wang
*b and
Jonas
Warneke
*gh
aInstitut für Angewandte und Physikalische Chemie, Universität Bremen, Fachbereich 2-Biologie/Chemie, 28359 Bremen, Germany
bPhysical Sciences Division, Pacific Northwest National Laboratory, Richland, WA 99352, USA. E-mail: xuebin.wang@pnnl.gov
cDepartment of Chemistry, Purdue University, West Lafayette, IN 47907, USA
dAnorganische Chemie, Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, 42119 Wuppertal, Germany
eEnvironmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, WA 99352, USA
fDepartement für Chemie und Biochemie, Universität Bern, 3012 Bern, Switzerland
gWilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Universität Leipzig, 04103 Leipzig, Germany. E-mail: jonas.warneke@uni-leipzig.de
hLeibniz Institute of Surface Engineering (IOM), Permoserstraße 15, 04318 Leipzig, Germany
First published on 22nd July 2020
Electronic structure, collision-induced dissociation (CID) and bond properties of closo-[B6X6]2− (X = Cl–I) are investigated in direct comparison with their closo-[B12X12]2− analogues. Photoelectron spectroscopy (PES) and theoretical investigations reveal that [B6X6]2− dianions are electronically significantly less stable than the corresponding [B12X12]2− species. Although [B6Cl6]2− is slightly electronically unstable, [B6Br6]2− and [B6I6]2− are intrinsically stable dianions. Consistent with the trend in the electron detachment energy, loss of an electron (e− loss) is observed in CID of [B6X6]2− (X = Cl, Br) but not for [B6I6]2−. Halogenide loss (X− loss) is common for [B6X6]2− (X = Br, I) and [B12X12]2− (X = Cl, Br, I). Meanwhile, X˙ loss is only observed for [B12X12]2− (X = Br, I) species. The calculated reaction enthalpies of the three competing dissociation pathways (e−, X− and X˙ loss) indicated a strong influence of kinetic factors on the observed fragmentation patterns. The repulsive Coulomb barrier (RCB) determines the transition state for the e− and X− losses. A significantly lower RCB for X− loss than for e− loss was found in both experimental and theoretical investigations and can be rationalized by the recently introduced concept of electrophilic anions. The positive reaction enthalpies for X− losses are significantly lower for [B6X6]2− than for [B12X12]2−, while enthalpies for X˙ losses are higher. These observations are consistent with a difference in bond character of the B–X bonds in [B6X6]2− and [B12X12]2−. A complementary bonding analysis using QTAIM, NPA and ELI-D based methods suggests that B–X bonds in [B12X12]2− have a stronger covalent character than in [B6X6]2−, in which X has a stronger halide character.
In this study, we explore the gas-phase ion properties of hexaborate dianions (closo-[B6X6]2−). These ions may be regarded as “half-weight” analogues of the well-explored and understood [B12X12]2− dianions. Both [B6X6]2− and [B12X12]2− are fully symmetric (all B and X atoms are chemically equivalent), see Fig. 1. We investigate how electronic structure, stability, dissociation pathways, and bond properties change when the number of atoms in this dianion is reduced by half. We employ a combination of photoelectron spectroscopy (PES), collision induced dissociation (CID), electronic structure calculations, and complementary bonding analyses to obtain a detailed understanding of the properties of isolated [B6X6]2− anions.
The theoretical Vertical Detachment Energies (VDEs) were calculated as energy differences between the singly charged anion and the corresponding dianion, both at the dianion's optimized geometry. The theoretical Adiabatic Detachment Energies (ADE) were determined by computing the energy difference between the singly charged anion at its own optimized geometry and the dianion at the dianion's optimized geometry. Zero-Point Energy (ZPE) corrections were computed using the harmonic approximation.
Dissociation enthalpies for ionic or radical loss of a substituent X from [B6X6]2− and [B12X12]2− were calculated by subtracting the 0 K molecular enthalpy (i.e., zero-point vibrational energy corrected electronic energy) of the dissociation products from that of the intact parent ion which was additionally BSSE-corrected using the counterpoise method.51,52 In some cases, additional calculations were performed on a MP2, SCS-MP253 and SOS-MP254 level to confirm that trends derived from DFT results are reproduced independent of the calculational method.
The electrostatic potential (ESP) was evaluated from the PBE0-GD3BJ/aug-cc-pVTZ wavefunctions using either the cubegen utility of the Gaussian software package43,44 to generate three-dimensional cube files or the Multiwfn software package, version 3.755 for evaluation along a certain direction. The electric field was derived from ESP cube files by differentiating the data points numerically employing difference quotients. The procedure is described in more detail in ref. 5 and 56. The electric field is a vector quantity. Herein, we evaluated the magnitude of the field with respect to a fixed position, which was chosen to be the center of the boron scaffolds of the investigated species.
We performed a complementary bonding analysis57 of the B–X bonds of the [B6X6]2− anions in direct comparison to their [B12X12]2− analogues based on the PBE0-GD3BJ/aug-cc-pVTZ wavefunctions. Quantum Theory of Atoms in Molecules (QTAIM)58 analyses and subsequent evaluation of electron-density-related properties (e.g. Laplacian of the electron density, total energy density H(r)) at the QTAIM bond critical points as well as calculation of AIM charges were performed with the Multiwfn software package version 3.7.55 The electron localizability indicator (ELI-D)59 was calculated using DGrid version 5.1.60 Grid files of electron density and ELI-D were calculated with a step size of 0.1 Bohr. The ELI-D was topologically analyzed yielding electron-pair basins. These ELI-D basins were cropped at an electron-density iso-contour of 0.001 a.u. Integration of the electron density was performed within the resulting basins to obtain the electron population of the ELI-D basins N(ELI). The Raub-Jansen Index RJI61 was as well calculated using DGrid version 5.160 by determining the contribution to the electron density in the intersection region of atomic QTAIM basins and ELI-D bond basins yielding a measure for bond polarity.61
![]() | ||
Fig. 2 Photoelectron spectra of (a) closo-[B6Cl6]2−, (b) closo-[B6Br6]2− and (c) closo-[B6I6]2−. Calculated orbital energy levels (HF/aug-cc-pVTZ) are shown as black lines below the spectra. The calculated HOMO is shifted in energy to the measured VDE, indicated by a dashed blue line. The ADE is indicated by a dotted green line. Distinct spectral bands are denoted with the labels A–D and T. On the left side of the spectra, molecular structures are shown, and the B–X and B–B bond length are given. HOMO isosurfaces can be found in Fig. S1 (ESI†). |
X | ADE | VDE | ||||
---|---|---|---|---|---|---|
Expt. | PBE0 | B3LYP | Expt. | PBE0 | B3LYP | |
F | n.a. | −1.88 | −1.83 | n.a. | −1.29 | −1.22 |
Cl | −0.05 ± 0.05 | −0.11 | −0.09 | 0.25 ± 0.10 | 0.28 | 0.32 |
Br | 0.45 ± 0.05 | 0.34 | 0.34 | 0.75 ± 0.08 | 0.67 | 0.69 |
I | 0.85 ± 0.05 | 0.83 | 0.79 | 1.15 ± 0.07 | 1.09 | 1.04 |
Along the investigated halogen series, the theoretically predicted electronic structures show a reasonable correlation with the observed spectral bands. The first spectral band (band A) is associated with the HOMO orbital. With increasing halogen size, this orbital becomes lower in energy (more stable) so that [B6I6]2− is the most electronically stable dianion in the series. For X = Cl, three clearly distinct spectral features labeled B, C and D were observed at higher electron binding energies. Band B may be associated with the HOMO−1. The HOMO−2 and −3 are lying closer in energy and account together for band C. In the case of X = Cl, HOMO−4 and −5 have nearly the same energy, resulting in an intense sharp band (band D). In contrast to the HOMO energy, which becomes more negative from X = Cl to I, the orbitals HOMO−1 to −5 increase in energy (less stable) along the halogen series. This trend is in agreement with the observed shift in the positions of B, C and D. We note that comparison of the PES bands with HF energy levels can be used to rationalize general trends in band positions across a series of ions but cannot explain the fine structure and intensity. This requires more sophisticated models, which take into account the Jahn–Teller distortion, excited electronic states, and outgoing electron intensity wave function matrix.26,63,64
The observed trend is well reflected in the contribution of boron and halogen atomic orbitals (AOs) to the molecular orbitals (MOs). The contributions of boron and halogen AOs to the HOMO are: B: 64%, Cl: 36%; B: 56%, Br: 44%; B: 35%, I: 65%. For small halogens, the HOMO has a large boron atomic orbital contribution. The overlap with halogen orbitals increases with increase in the halogen size resulting in a stabilization of the HOMO. In contrast to the HOMO, the energy development of HOMO−1 to HOMO−5 is almost exclusively determined by the halogen-free electron pairs, which become more loosely bound along the halogen series.
The observed stabilization of the HOMO on going from the lighter to the heavier halogens accompanied by a destabilization of the lower lying orbitals (HOMO−1 to −5) is similar to the trend reported for [BnXn]2−n = 10–12.10,26 The only exception from this trend was [B12I12]2− which was found to be less electronically stable than [B12Br12]2−. The HOMOs in [B12Cl12]2− and [B12Br12]2− are very stable and only a small energy gap exists to the orbitals of the halogen's free electron pairs. Further stabilization of this orbital in the case of [B12I12]2− results in an orbital energy below the highest lying orbitals of the iodine free electron pairs. In the case of [B6X6]2−, the energy gap between the HOMO and the orbitals of the halogen free electron pairs is much larger and is still present for X = I. Therefore, electronic stability increases for [B6X6]2− from X = Br to X = I in contrast to [B12X12]2−.
[B6F6]2− is experimentally unknown. In agreement with previous computational investigations,65,66 we calculated this dianion to be electronically unstable, see Table 1. To the best of our knowledge, gas phase electronic stabilities of [B6Br6]2− and [B6I6]2− have never been predicted in the literature, but these ions are clearly shown here to be electronically stable. [B6Cl6]2− represents a particularly interesting case because it is very slightly electronically unstable (positive VDE but slightly negative ADE). The ability to observe the electronically unstable [B6Cl6]2− experimentally must result from the kinetic trapping of the excess electron (similar behavior has been observed for [C60]2−)67 due to the repulsive Coulomb barrier (RCB).68
An additional band (T) near the photon energy limit is observed exclusively in the PES spectrum of [B6Cl6]2− (Fig. 2). Band T is the result of extremely low energy electrons which do not originate from a direct photodetachment process. This can be evidenced by measurements using different laser energies.69 The energy of direct photoelectrons is dependent on the laser energy, while the kinetic energy of electrons originating from indirect detachment processes are usually not affected. Fig. S2 (ESI†) shows spectra for three different laser energies and additional information is given. We assume that the electronic excitation due to broad UV absorption bands (which can occur as a competing process to direct photodetachment) populates the electronically excited states of the dianion. These excited states have finite lifetimes allowing either coupling with the ionization continuum or internal conversion leading to emission from the hot ground state.69,70
Fig. 3(a) shows low-energy CID spectra of [B6X6]2− (X = Cl, Br, I) obtained on an ion trap mass spectrometer. The corresponding low-energy CID spectra of [B12X12]2− ions are shown in Fig. 3(b). The competition between the dissociation pathways of both [B6X6]2− and [B12X12]2− dianions is strongly dependent on the halogen atom. Specifically, we observe an exclusive loss of electron (e− loss) for [B6Cl6]2−, both e− loss and Br− loss for [B6Br6]2−, and exclusive I− loss for [B6I6]2−. Although e− loss is a dominant pathway for [B6X6]2−, it is not observed for [B12X12]2− (X = Cl–I) dianions. However, it was observed for X = F.27 In contrast, X− loss is observed for all [B12X12]2− species. In addition, a competing X˙ loss is observed for [B12Br12]2− and becomes the dominant reaction channel for [B12I12]2−.
![]() | ||
Fig. 3 Low-energy CID spectra (MS2) of mass-selected (a) [B6X6]2− and (b) [B12X12]2− (X = Cl, Br, and I) dianions. Ions detected at higher masses than the singly charged [BnXn-1]− are attributed to reactions with residual gases H2O and N2.27 (c) Calculated 0 K enthalpies (PBE0-GD3BJ/aug-cc-pVTZ and B3LYP-GD3BJ/aug-cc-pVTZ) for the three competing pathways shown in Scheme 1 for all the dianions examined in this study. Calculated energy ranges determined with the two methods are either shown as bars with (reaction observed) or without (reaction not observed) end caps. Black crosses mark the ADE results derived from PES (see Section 3.1). The values of the calculated enthalpies are provided in Table S3 (ESI†). Note that to enhance visibility, enthalpy ranges are shown with a minimum width of 2 kJ mol−1. |
Fig. 3(c) shows a comparison of the calculated 0 K enthalpies of the three reaction pathways for [B6X6]2− and [B12X12]2−: e−, X− and X˙ loss. To visualize the uncertainties of the computational method, we show ranges derived from B3LYP and PBE0 calculations both employing the aug-cc-pVTZ basis set. The calculated ranges of experimentally observed reactions are denoted with end-capped markers. Ranges of non-observed reactions are denoted with markers without endcaps. ADEs derived from PES (see Section 3.1) are included as crosses. In the following, we will rationalize the competition between the three pathways in the context of the calculated enthalpies and estimated heights of reverse activation barriers.
We start by discussing the competition between the two charge separation pathways: e− loss and X− loss. Electron detachment is by far more thermochemically favorable for [B6X6]2− than for [B12X12]2−, which is consistent with the lower electronic stability of [B6X6]2− as discussed in Section 3.1. For [B6X6]2− dianions, the enthalpy of the e− loss increases (becomes less favorable) with an increase in the size of the halogen atom. The relative yield of the e− loss pathway observed in CID is consistent with the calculated increase in enthalpy. However, it is remarkable that [B6I6]2− and [B12Cl12]2− show exclusive X− loss although the 0 K enthalpy for e− loss is calculated to be very similar using DFT (see Fig. 3(c)). We confirmed with MP2, SCS-MP2 and SOS-MP2 calculations that the enthalpy for X− loss is not more favorable than for e− loss (see Table S4, ESI†). Furthermore, although the reaction enthalpy of the e− loss from [B6Br6]2− is more favorable than for X− loss by 41–75 kJ mol−1 (estimated based on PBE0-GD3BJ/aug-cc-pVTZ and B3LYP-GD3BJ/aug-cc-pVTZ), both channels are observed for this precursor ion. Thermochemistry appears not to be the only factor that determines the competition between the dissociation pathways. Dissociation of multiply charged anions in the gas phase is usually influenced by the RCB, which determines the barrier for both X− and e− loss. These results indicate that X− loss from [BnXn]2− ions may be a kinetically favored pathway (smaller RCB) in comparison with e− loss.
Comparison of low- and higher-energy CID of [B6Br6]2− shown in Fig. 4(a) and (b) provides interesting insights into the competition between the Br− loss and e− loss, respectively. The branching ratio of the e− loss to Br− loss pathways changes from ∼5 in the low-energy CID spectrum (Fig. 4(a)) to ∼0.1 in the higher-energy CID spectrum (Fig. 4(b)). Fig. 4(c) shows a schematic drawing of the potential energy surface, which rationalizes this observation. It is well-established that low-energy CID favors fragmentation pathways with energetically low-lying transition states (TS). The higher abundance of the e− loss product [B6Br6]˙− in comparison with [B6Br5]− in the low-energy CID spectrum (Fig. 4(a)) indicates that the TS for the e− loss (TS1) is lower in energy than the TS for the Br− loss (TS2). However, considering that Br− loss is still observed in the spectrum, we expect the difference between TS1 and TS2 to be small (within several kJ mol−1) and considerably smaller than the difference between the reaction enthalpies (41–75 kJ mol−1). Therefore, the reverse activation barrier, which is dominated by the RCB for charge separation reactions, appears to be substantially smaller for Br− loss than for e− loss (RCB2 < RCB1).
This assertion is further supported by higher-energy CID experiments shown in Fig. 4(b), in which [B6Br5]− is the dominant fragment and [B6Br6]˙− is a minor product. Kinetically favored fragmentation pathways often become dominant in higher-energy CID experiments due to the relatively high internal energies accessible in these experiments. The drastic difference in the [B6Br6]−/[B6Br5]− branching ratio observed in low-energy and higher-energy CID suggests that although the energy of TS1 is lower than that of TS2, the formation of the [B6Br5]− fragment is entropically more favorable than the e− loss pathway. An entropically-preferred TS is usually associated with a smaller reverse activation barrier (here smaller RCB). As a result, at higher internal energies, Br− loss becomes the dominant dissociation channel. Based on these experimental findings, we propose that the Br− loss has a considerably smaller RCB than the e− loss channel. The difference between the heights of the RCBs is expected to be close to the enthalpy difference of e− and X− loss (41–75 kJ mol−1) resulting in comparable energies of TS1 and TS2. In the following, we rationalize this finding using PES and different computational methods.
Although it is not possible for us to determine the RCB for the Br− loss experimentally, the magnitude of the RCB for e− loss can be estimated by comparing photoelectron spectra measured at different laser energies (EL). Photoelectron spectra of closo-[B6Br6]2− measured at 193 nm (EL = 6.4eV) and 157 nm (EL = 7.9eV) are shown in Fig. 5. It is established that the presence of an RCB suppresses spectral bands at binding energies larger than (EL − RCB).72 Note that a higher binding energy (x-axis) correlates with a lower kinetic energy of the detected electrons. Electrons with extremely low kinetic energy cannot overcome the RCB which leads to signal suppression at high binding energies. Electrons with kinetic energies only slightly below the barrier height may tunnel through the RCB, which results in partial signal suppression. Three areas are marked in the 193 nm spectrum in Fig. 5. A complete signal suppression occurs for bands between 4.9 and 6.5 eV binding energy (region I). The intense signal at 4.5 eV in the 157 nm spectrum is visible in the 193 nm spectrum but is partially suppressed, meaning that the kinetic energy of electrons in this region of the PES spectrum is close to but still below the RCB height (region II). No considerable change in the signal is observed below 4.2 eV (region IV), meaning that the corresponding photoelectrons are not affected by the RCB. Since no significant band between 4.2 and 4.5 eV is present (region III, corresponding to 2.0–2.3 eV kinetic energy at 193 nm), this region determines the uncertainty of the experimental value. Therefore, based on the signal suppression in the PE spectra, we estimate that the height of the RCB for electron loss from [B6Br6]2− is in the range of 2.0 eV to 2.3 eV. A list of the heights of RCBs estimated based on the observed suppression of the electron loss from [B6X6]2− and [B12X12]2− (X = Cl, Br, I) at different laser wavelengths is shown in Table S5 (ESI†) and the corresponding spectra for [B6X6]2− are shown in Fig. S3 (ESI†).
For a theoretical evaluation of the RCB height, we calculated the potential energy of a negative test charge based on the electrostatic potential (ESP) of [B6Br6]−. The ESP was calculated along three different possible detaching directions: through the middle of the B–B bond, through the middle of the B-triangle and along the B–X bond. The results for the three different pathways are visualized in Fig. S4 (ESI†). The lowest barrier for electron detachment of 2.5 eV is found along the B–X bond. The calculated barrier is slightly higher than the RCB estimated from suppression effects in photoelectron spectra (2.0–2.3 eV). Because the polarizability of the ion is not taken into account, RCB calculations based on the ESP typically overestimate the barrier height.
For comparison, we calculated the ESP of [B6Br5]− along the direction of the Br− detachment. The energies of the negative test charge along the detachment pathways for [B6Br5]− and [B6Br6]− are shown in Fig. 6(a). Although [B6Br5]− and [B6Br6]− have the same total charge, the electrostatic barrier is substantially smaller for [B6Br5]− than for [B6Br6]−. The origin of this effect lies in the unusual charge distribution in the [B6Br5]− ions. A [BnXn−1]− ion possesses a vacant boron atom. Although the total charge of the ion is negative, this vacant boron exhibits a significant positive partial charge. NPA indicates that the atomic charge on the vacant boron atom is +0.4 e for [B6Br5]−. This unusual phenomenon has been previously reported for [B12X11]− ions which are highly reactive and have been classified as “superelectrophilic anions”.5,8,56
![]() | ||
Fig. 6 (a) Potential energy of a negative test charge positioned at different distances from [B6Br6]− along the B–Br bond direction (black) and from [B6Br5]− along the C4v symmetry axis (magenta). Distances are given with respect to the boron scaffold center defined by the middle point between the four equivalent boron atoms. The dotted magenta line shows the potential energy of the [B6Br5]− + Br− system as a function of the center-Br− distance. (b) The electric field close to the ions [B6Br6]− (top) and [B6Br5]− (bottom). Green areas mark regions of repulsion (black: strong repulsion) from the ion on a negative test charge, while red areas mark regions of attraction. Quantitative details of the color coding can be found in Fig. S5 (ESI†). The arrows mark the direction of e−/Br− loss. |
In order to examine differences in the charge distributions of [B6Br6]− and [B6Br5]−, we calculated the electric fields outside the molecular surfaces of these ions by taking the first derivative of the ESP. The results of these calculations are shown in Fig. 6(b). Green areas represent repulsion of a negative particle, while red areas show attraction. Similar to [B12X11]− ions, [B6Br5]− is an electrophilic anion, in which a partial positive charge is localized on the vacant boron atom. In contrast, the electric field around the [B6Br6]− ion is purely repulsive. The positive charge at the binding site of [B6Br5]− substantially lowers the barrier for a negative particle.
The simple electrostatic model based on ESPs suggests that RCB2 as introduced in Fig. 4 is by 0.4 eV (= 39 kJ mol−1) smaller than RCB1 (Fig. 6(a)). For a more sophisticated calculation of RCB2, we performed a “relaxed scan” (optimization of the [B6Br5]−–Br− geometry for a fixed B–Br bond length). As shown in Fig. 6(a), the height of RCB2 was calculated to be 1.6 eV by this method. Therefore, including structural relaxation and polarization effects in the calculation lowers the calculated barrier height by additional 0.4 eV compared to the simple ESP-based model. Note that the experimentally determined RCB1 (Fig. 5(a)) was 2.0–2.3 eV. Therefore, we can estimate RCB1–RCB2 to lie in the range of 0.4–0.7 eV (= 39–67 kJ mol−1), which is consistent with the assertion that TS2 and TS1 are lying close in energy (compare Fig. 4(c)).
Collectively, both the experimental and theoretical results discussed earlier confirm that the competition between the charge separation pathways (e−vs. X− loss) is adequately described by the potential energy surface shown in Fig. 4(c). Furthermore, theoretical calculations rationalize the observed kinetic preference for the X− loss from [BnXn]2− over the e− loss. Although the reverse activation barrier for the charge separation pathways is dominated by electrostatics and both fragments ([BnXn]˙− and [BnXn−1]−) are singly charged, the positive site within [BnXn−1]− is responsible for a substantially smaller RCB. Furthermore, our results show for the first time that similar to [B12X12]2−, smaller [B6X6]2− species are precursors for “electrophilic anions” generated by abstraction of a negative substituent, X−, from the dianion.
According to the calculated reaction enthalpies shown in Fig. 3(c), loss of X˙ observed in competition with the charge separation pathways is thermodynamically the least favorable reaction channel. However, for [B12I12]2−, I˙ loss is the dominant pathway observed experimentally. Furthermore, although the enthalpy for Br− loss from [B12Br12]2− is 200–215 kJ mol−1 lower than the enthalpy for Br˙ loss, the products of Br˙ and Br− loss are both observed in comparable abundances. While fragmentation into two singly-charged ions is hindered by the RCB, fragmentation of [BnXn]2− into [BnXn−1]2−˙ and X˙ is the reverse of a radical–radical recombination, which usually has no or a very small barrier. Efficient competition of the thermochemically unfavorable X˙ loss with the more favorable charge separation pathways becomes possible if the enthalpy difference between X˙ and X− losses is comparable to the height of the RCB. For all [B6X6]2− ions, 0 K enthalpy differences between X˙ and X− loss are 4.1–4.3 eV (X = Cl) to 3.3–3.4 eV (X = I). These values are much larger than the estimated RCBs (see Fig. 6(a) and Table S5, ESI†). As a result, X˙ loss from [B6X6]2− cannot compete with charge separation pathways. The larger difference between X˙ and X− loss is a result of both an enthalpically preferred X− loss and a less preferred X˙ loss compared to [B12X12]2−, see Fig. 3(c). Structural relaxation of the fragment ions generated by X˙ and X− loss may contribute to the reaction enthalpies. However, the calculated relaxation energies (Table S6, ESI†) are very small indicating that structural relaxation is not a dominant factor in determining the enthalpies of X˙ and X− losses. An intrinsic difference in the nature of the B–X bond in [B6X6]2− and [B12X12]2− may play a role, which we evaluate in Section 3.3.
Property | [B6Cl6]2− | [B12Cl12]2− | [B6Br6]2− | [B12Br12]2− | [B6I6]2− | [B12I12]2− |
---|---|---|---|---|---|---|
d/Å | 1.818 | 1.793 | 1.967 | 1.949 | 2.178 | 2.176 |
δ | 0.66 | 0.66 | 0.72 | 0.73 | 0.86 | 0.93 |
Q AIM(X)/e | −0.80 | −0.72 | −0.72 | −0.62 | −0.51 | −0.30 |
Q NPA(X)/e | −0.25 | −0.14 | −0.19 | −0.06 | −0.08 | +0.08 |
N (ELI)/e | 1.55 | 1.55 | 1.55 | 1.61 | 1.33 | 1.40 |
RJI/% | 88.5 | 85.7 | 84.1 | 79.6 | 62.7 | 51.0 |
Quantum theory of atoms in molecules (QTAIM) describes the properties of chemical bonds by means of a topological analysis of the electron density. The delocalization index δ is derived by integration over the exchange density in the two analyzed atomic QTAIM basins and is usually interpreted as the number of electron pairs delocalized between two atoms, i.e. as a covalent bond order.73 With increasing halogen size the value of δ increases, the negative atomic charges QAIM of the halogens decrease. This points to an increase in the covalent bond character and a decrease in the halide character from X = Cl to I. For a given halogen, δ of [B12X12]2− has a larger or the same value than [B6X6]2− and QAIM of the halogens is more negative for [B6X6]2−. This analysis suggests that the B–X bonds have more halide character in the [B6X6]2− clusters and a stronger covalent character in [B12X12]2−.
To confirm this assertion, we use methods complementary to the QTAIM analysis. NPA charges are often considered to be the most chemically meaningful calculated atomic charges.42 Although absolute numbers of QNPA differ considerably from the determined QAIM values, the general trend along the series is consistent and it can be concluded that the halogens in [B6X6]2− carry a larger negative charge than in [B12X12]2−. This difference is more pronounced for larger halogens. As a complementary measure of the covalent bond strength, we integrated the electron density over the electron localizability indicator (ELI-D) bond basins (N (ELI)).59 Similar to the δ values, slightly higher values for [B12X12]2− than for [B6X6]2− confirm a stronger covalent bond character in the former case. The Raub-Jansen index (RJI) uses the intersections of ELI-D bond basins and QTAIM based electron density basins to quantify bond polarity.61 A value larger than 50% shows a polarization toward the halogen atom of the B–X bond. The calculated RJIs for B–X bonds in [B12X12]2− and [B6X6]2− (Table 2) are in full agreement with the discussed trends. They show that the electron density of the bonding electrons is heavily shifted towards the halogen atom. The value decreases from X = Cl to I and for a given halogen, and it is always larger for [B6X6]2−.
The absolute values for δ, N (ELI) and RJI are very similar for a given halogen, as it would be expected for B–X bonds in very similar environments. However, the slight differences shown in Table 2 consistently show that the electron density in the B–X bond is more polarized towards the halogen in [B6X6]2− than in [B12X12]2−. The higher intrinsic halide character of X in [B6X6]2− rationalizes advantages for a heterolytic cleavage (X− loss) and disadvantages for homolytic cleavage (X˙ loss) in comparison to a less polar and more covalent B–X bonds in [B12X12]2−.
The results reported in this study deepen our understanding of the chemical and physical properties of [BnXn]2− anions as a function of size and halogen atom. In addition, we introduce the smallest known electrophilic anion, [B6X5]−, confirming that the concept of electrophilic anions extends beyond the [B12X11]− species described in previous studies. The formation of the electrophilic anion lowers the RCB for the X− loss making this reaction pathway kinetically favored over the more thermochemically favorable e− loss pathway.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0cp02581j |
This journal is © the Owner Societies 2020 |