Noncovalent interactions in crowded olefinic radical cations

Aim. To study the effect of electronic (αand β-hyperconjugations) and steric (noncovalent interactions) factors on the structures of olefinic radical cations. Results and discussion. The effect of intramolecular dispersion interactions on the structures of crowded alkenes in the neutral and ionized forms has been studied at the density functional theory (DFT) level with and without dispersion corrections included, as well as at the MP2 theory level with medium size basis sets. The results obtained are compared to the available experimental data. An excellent agreement has been found between the experimental and MP2/DFT-computed geometries of sesquihomoadamantene, adamantylidene adamantane, bis-2,2,5,5-tetramethylcyclopentylidene, bis-D3-homocub-4-ylidene, and bis-CS-homocub-8-ylidene in the neutral and ionized forms. The experimental ionization potentials are better reproduced with the DFT-methods. Experimental part. The structure and composition of compounds were proved by the methods of 1H and 13C NMR-spectroscopy, and GC-MS-analysis. Elemental analysis was performed for the compounds obtained. Conclusions. The twisting of the olefinic moieties in the sesquihomoadamantene and adamantylidene adamantane radical cations is determined by the balance between the σ-π-hyperconjugation and residual oneelectron π-bonding and is close to that of the prototypical ethylene radical cation (29°). The twisting reaches 55° for the bis-2,2,5,5-tetramethylcyclopentylidene radical cation due to substantial steric repulsions between methyl groups. At the same time, the ionized states of bis-D3-homocub-4-ylidene and bis-CS-homocub-8-ylidene retain their planarity due to β-CC-hyperconjugation and intramolecular dispersion attractions.

Single-electron oxidation of neutral molecules leads to positively charged radical ions that are key intermediates in many fundamental chemical and biological processes [1 -3]. The ionization of olefines leads to significant geometrical distortions, and radical cations thus obtained usually are quite unstable. The simplest representative is ethylene where electron removal from the bonding highest occupied molecular orbital (HOMO) results not only in the elongation of electron-depleted C=C-bond, but is also accompanied by the twisting of the CH 2 -groups. This is due to σ-π-hyperconjugation [4], (α-hyperconjugation, two-way hyperconjugation) [5], which is maximized for the perpendicular arrangement (Fig. 1A), while the residual one-electron π-bonding stabilizes the planar form. Theory is not very successful in a balanced description between these two stabilization modes predicting a torsion angle for C 2 H 4 •+ in the range of 13 to 33°, depending on the approximation level employed [6,7]; the most trusted experimental estimate is ca. 29° [8]. Theory shows, however, that substituted ethylene radical cations do not necessary deplanarize since the stabilization may be achieved through hyperconjugation with the participation of the σ-bonds of the neighboring groups (β-hyperconjugation, Fig. 1B). As a result, our computed [9] (MP2/cc-pVQZ) CCCC torsion angle for the tetramethylethylene radical cation ( Fig. 1C) is only 11° due to an effective participation of the CH-bonds of the methyl groups in β-СH-hyperconjugation. As β-СС-hyperconjugation [10] generally is more efficient, the tetraethylethylene radical cation is almost planar (the twisting is only 1.7°, Fig. 1D). Such structural trends agree well with the density functional theory (DFT) computations at the B3LYP and M06-2X levels of the theory.
The experimental verifications of the above theoretical findings are difficult since alkene radical cations readily undergo deprotonation from the allylic positions. In this regard, the sterically hindered cage alkenes ( Fig. 2), e. g. sesquihomoadamantene 1 [11] and adamantylidene adamantane 2 [12], with allylic СН-bonds orthogonal to the olefinic p-orbitals are suitable models for structural studies [11].
Attempts to isolate and characterize radical cation 2 •+ failed due to its short lifetime (less than 5 seconds) [13]. In contrast, radical cation 1 •+ characterized through X-ray crystallography is quite stable [11,13]. The high stability of 1 •+ primarily is due to the steric crowding caused by the CH 2 -groups that surround the C=C bond [13]. Still, the cage is flexible enough to provide a torsion angle of 29° for effective α-hyperconjugation. Even more significant devia- tions from planarity were observed for the extremely sterically crowded radical cation of bis-2,2,5,5-tetramethylcyclopentylidene (3, Fig. 2). The ESR-spectrum of 3 •+ displays "almost perpendicular arrangement of five-membered rings" [14] due to the additional steric repulsion between the methyl groups. Although this hypothesis is only partly confirmed by our computations (vide infra), the reasons for the occurrence of planar vs. twisted forms of olefinic radical cations and the role of noncovalent interactions (NCI, primarily London dispersions) still remains open. Herein, we present our study of the neutral and ionized dia-mondoid olefins 1 -2, highly crowded 3, as well as homocubane dimers 4 and 5, as their structures comprise fundamentally different C=C-bond surroundings.

Results and discussion
For comparison, alkenes 1 and 2 in the neutral and ionized states were studied using various DFT levels, as well as the MP2 ab initio method (Fig. 3). Previously, we found that DFT reproduced the experimental ionization potentials of large saturated hydrocarbons well [15 -19]. Correct descriptions of radical cations derived from 1 and 2 require taking into account both electron correlation and noncovalent interactions (NCI) [13,20] between the groups that surround the C=C bonds. Hydrocarbon 1 provides an opportunity to test the applicability of the recently developed DFT implementations to olefinic radical cations, such as 1 •+ , since its X-ray crystal structure is available [13]. We used a popular functional B3LYP with empirical corrections for dispersions (B3LYP-D3 [21]) and M06-2X [22], which was parameterized to account for the medium-range electron correlation. Previously, we used a similar approach to estimate the dispersion contributions in saturated diamondoid dimers [20, 23 -25] and graphane clusters [26].
Although there is torsional strain caused by the repulsive [27] intramolecular H•••H contacts of 1.85 -2.00 Å across the C=C bond (2.4 Å corresponds to the minimum on the vdW potential [27]), this fragment remains planar in neutral hydrocarbons 1 and 2. Inclusion of dispersion does not alter this picture, and all methods reproduce the experimental geometries of the neutrals well ( Fig. 3). In contrast, the results for radical cations 1 •+ and 2 •+ are strongly method-dependent. Upon ionization the twisting of the olefinic moiety leads to an insignificant increase of the intramolecular H•••H distances up to 2.1 Å, which is still significantly less than the optimal 2.4 Å. The B3LYP method underestimates the torsional angle even with empirical dispersion corrections included. While MP2 substantially overestimates the length of the central electron-depleted C=C bond, the M06-2X reproduces the experimental interatomic distances and torsion angles of 1 •+ exceptionally well.
We also probed the computational reproducibility of the experimental adiabatic potentials [28,29] of 1 and 2 (Table). Both B3LYP and M06-2X results agree well with the experimental values and accounting for dispersion has almost no effect; again, the M06-2X is slightly more accurate.
The above findings demonstrate that dispersion corrections only insignificantly affect the geometries of radical cations 1 •+ and 2 •+ . In contrast, due to excessive repulsions between the methyl groups, the olefinic moiety of 3 substantially deplanarizes even in the neutral form 3a (Fig. 4). The neglect of dispersion reduces significantly the value of the torsion angle (3.4° at B3LYP vs. ca. 7° with B3LYP-D3(BJ) (Fig. 4). Note that computations with molecular mechanics on 3a gave an intermediate twisting value of 5.5° [31].
Unexpectedly, we found another highly twisted (ca. 40°) C=C bond rotamer 3b, which, surprisingly, was only 6 -7 kcal·mol -1 less stable than 3a. Such small differences may be associated with additional destabilization of 3a due to the presence of very close H•••H-contacts (~1.8 Å); such short contacts are not present in more twisted form 3b. Ionization reorders the relative stability of conformers due to the partial elimination of the π-bonding that flattens the rotation potential: "planar" 3a •+ becomes less stable than twisted conformer 3b •+ . The computed π-bond twisting in 3b •+ is smaller than "the almost perpendicular arrangement cyclopentane fragments" predicted based on the ESR data [14], but still is exceptionally high (ca. 55° at all levels).
Since α-hyperconjugation affects mostly the structures of highly twisted forms, accounting dispersions has only little influence on the geometry of 3b •+ . Note that for bis-2,2,4,4-tetramethylcyclobutylidene, the cyclobutane analog of 5, where the methyl groups are more distant, the twisting in the radical cation is only 29 -30° [32], i. e. essentially the same as in ethylene.
The conclusion can be made that α-hyperconjugation determines the structures of 1 •+ and 2 •+ as the neighboring C-C bonds undergo only little changes upon ionization. The cage moieties have only little effect on the degree of twisting of the olefinic fragments in the corresponding radical cations 1 •+ and 2 •+ (ca. 29°, which is close to that for parent ethylene). Even in the almost planar form 3a •+ the β-hyperconjugation is insufficient as the C-CH 3 bond lengths in the neutral (1.54 -1.55 Å) and ionized (1.56 -1.57 Å) forms are close.
The D 3 -trishomocubylidene dimer 4 exists in two diastereomeric forms 4a and 4b (Fig. 5). Computations at our levels of theory reproduce satisfactorily the experimental X-ray crystal structure geometries of neutral hydrocarbons [33]. Remarkably, the olefinic moiety of 4b is slightly twisted (3 -4°). As the noncovalent CH•••HC contacts across the C=C bond are close to the optimal value of 2.5 Å and are positioned in the attractive part of the vdW potential, such twisting must derive from antibonding interactions in the D 2 -symmetric helical HOMO-1 of 4b.
The ionization of 4a and 4b is accompanied by only moderate geometric distortions. The С 1 -radical cation 4а •+ , (the deviation from С 2 -symmetry is in- significant) is slightly twisted (13 -14°). Two pairs of β-C-C bonds contribute substantially to the stabilization of 4а •+ as it is seen from their elongations up to 1.58 -1.60 Å. Reoptimization with С 2 -symmetry constraints leads to a minimum that is twisted less (3 -5°), but structurally and energetically close to the С 1 -form.
Significant deviations are obtained for 4а •+ at DFT and MP2, as the latter predicts an almost planar olefinic moiety. These findings, as well as the pronounced elongation of the neighboring β-C-C-bonds of the cage (up to 1.59 Å) suggest that β-CC-hyperconjugation makes a significant contribution to the structure 4а •+ . The same applies to the structure of 4b •+ , which retains the D 2 -symmetry of a neutral hydrocarbon and is characterized by only minor twisting upon ionization. Thus, hydrocarbons 4a and 4b display stabilization of the planar ionized states through participation of the neighboring C-C-bonds as in the prototypical case of tetraethylethylene (D, Fig. 1). Dispersion interactions thereby play a stabilizing role since the H•••H interactions over the C=C bonds are attractive.
The previously unknown C S -trishomocubane dimer 5 was obtained through a titanium(III)-promoted McMurry dimerization [34,35] of C S -trishomocubane-8-one 6 [36,37]. As the nature of the titanium salt and of the reducing agent affects the outcome of dimerizations to sterically hindered alkenes [33,38], we chose the most effective TiCl 4 -Zn system in THF for coupling (Fig. 6).
All four possible diastereomers 5a -d were formed in the approximate statistical ratio (GC) with a preparative total yield of 80 -90 %. The mixture was subjected to fractional crystallization from hexane resulting in the isolation of the most symmetric C i -diastereomer 5a, which structure was confirmed by the X-ray diffraction single crystal analysis (Fig. 6). The key geometric characteristics of 5a are in agreement with the computed data (Fig. 7). Neutral 5a is characterized by close to the optimal H•••H contacts around the C=C moiety, which is almost planar (the twisting is less than 2°). As a result, the geometries of 5a computed with and without dispersion corrections are very close. The ionization of 5а gives 5а •+ , which retains C i -symmetry (Fig. 7). We conclude that dispersion is stabilizing both in singlet and doublet states of 5а as the H•••H contacts across the central C=C bond remain constant (ca. 2.3 Å). The experimental adiabatic ionization potential of 5а (7.47 eV) [30] is reproduced well with M06-2X, but not at B3LYP or MP2 (Table). As expected, the С=C bond length in 5a •+ increases relative to the neutral one, however, only little twisting is found at our levels of theory: 5а •+ remains nearly planar due to the effective β-hyperconjugation with participation of the С-С-bonds of adjacent cyclobutane fragments (the respective bond lengths increase from 1.56 Å in 5a to 1.63 Å in 5a •+ , Fig. 7). Thus, the cyclobutane rings participate effectively in hyperconjugaton in 5а •+ removing the excess of the positive charge from the central bond and allowing the effective one-electron π-bonding. As a result, the distortions of the olefinic moiety of 5a •+ is even less pronounced than that in 4b •+ . Such a behavior upon ionization makes hydrocarbons 4 and 5 useful for the construction of electronic materials where the structural stiffness of the building blocks upon electron/hole transfer is critical. Derivatives of 4 and 5 may have some advantages over the diamondoid [20,39,40] derivatives previously successfully used for the construction of electron emitters and semiconductors [41 -45].

Experimental part
The NMR-spectra were recorded with a Bruker Avance II spectrometer; chemical shifts were given in ppm relative to TMS. GC-MS analyses were performed with a HP5890 GC with a HP5971A mass-selective detector. High resolution mass spectra were recorded on a Finnigan MAT 95 instrument.
C i -Trishomocub-4-ylidene 5a. Heat under argon a two-neck dry flask (100 mL) equipped with a magnetic stirrer and a reflux condenser with a bubble counter, add 25 mL of freshly distilled dry THF through a septum. Cool the solvent on an external ice bath, and add 1.35 mL (12.3 mmole) of TiCl 4 . Remove the septum, and add Zn powder (1.62 g, 24.9 mmole) in small portions. After adding Zn reflux the reaction mixture for 1 h, and then cool to ambient temperature. Add pyridine (0.5 mL) first, then the solution of ketone (5.34 mmole) in dry THF (7 mL). Reflux the mixture under argon for 12 h, cool to room temperature, and quench by dropwise addition of 10 % water solution of K 2 CO 3 (60 mL) with simultaneous cooling. Add dark blue slurry to diethyl ether (150 mL), vigorously stir for 15 min and then filter. Wash the residue with diethyl ether (3 × 50 mL). Separate the layers in the filtra-te, and extract the aqueous layer with diethyl ether (2 × 50 mL). Wash sequentially the combined organic layers with water (1 × 70 mL), hydrochloric acid (5 %, 2 × 50 mL), water (2 × 70 mL), and brine (1 × 50 mL). Dry the organic layer over Na 2 SO 4 , remove the solvent in vacuo. Purify the residue (2.0 g, 93 %) by column chromatography (hexane) to obtain olefin 5a. Three sequential crystallizations from hexane gave 0.13 g (6 %) of the pure sample.

Conclusions
The twisting of the olefinic moieties in the sesquihomoadamantene and adamantylidene adamantane radical cations is determined by the balance between the σ-π-hyperconjugation and residual one-electron π-bonding and is close to that of the prototypical ethylene radical cation (29°). The twisting reaches 55° for the bis-2,2,5,5-tetramethylcyclopentylidene radical cation due to substantial steric repulsions between methyl groups. At the same time, the ionized states of bis-D 3homocub-4-ylidene and bis-C S -homocub-8-ylidene retain their planarity due to β-CC-hyperconjugation and intramolecular dispersion attractions.
Conflict of interests: authors have no conflict of interests to declare.