Tricyclo[2.1.0.02,5]pent-3-ylidene: Stereoelectronic Control of Bridge-Flapping within a Nonclassical Nucleophilic Carbene

Tricyclo[2.1.0.02,5]pent-3-ylidene is a carbene foreseen to rearrange to pyramidane (c-C4H4)C, a highly strained molecule featuring an inverted C atom. Modeling of the carbene, using the (U)MPWB1K/cc-pVTZ//(U)MPWB1K/6-311G(d) theoretical model, indicated a large singlet–triplet energy gap (ΔES–T = −45 kcal/mol), a high gas-phase proton affinity (PA = 258 kcal/mol), and a preference for electron-poor alkenes. These properties are consistent with those of nucleophilic carbenes. Structural differences between the Cs-symmetric singlet (ωflap = ±44 deg) and C2v-symmetric triplet (ωflap = 0 deg) stem from nonclassical electron delocalization in the former and the lack thereof in the latter. Degenerate bridge-flapping of the singlet’s main bridge, which comprises the reactive divalent C3 atom, is computed to be slow due to a high activation barrier of the C2v-symmetric transition state (TS) (Ea = 17 kcal/mol). The position of the conformeric equilibrium is subject to stereoelectronic control. 1-Substituted derivatives of the carbene (R ≠ H) are sensitive to σ inductive effects. A proximal conformation is preferred when R is electron-donating and a distal one is favored when R is electron-withdrawing. Finally, carbene rearrangements via 1,2-C atom shift or enyne fragmentation were computed. The C2v-symmetric bridge-flapping TS has the proper geometry to initiate enyne fragmentation.

An MO correlation diagram between 1 1 and 2 has been reported at the MINDO/3 level of theory. 11,12 However, 1 1 was treated as having C 2v symmetry 11 instead of the C s symmetry found using ab initio methods. Thus, a new comparison was warranted. Frontier MO details for C ssymmetric 1 are shown in Figure 4a,b and Table 3 and those for C 4v -symmetric 2 are found in Figure 4c,d and Table  4. The LUMO{+1} of 1 and LUMO of 2 are essentially the same. In contrast, their HOMOs are spatially different. The electron lone-pair density within each HOMO resides mainly in the protruding lobe of each one's σ orbital, whose position is governed by symmetry. These high-lying HOMOs are ostensibly the source of the hydrocarbons' large gas-phase PA values. Note that the HOMO of 2 corresponds with the HOMO{−5} of 1 ( Figure 5). Inspection of the HOMO{−1} level of 2 reveals a doubly degenerate pair of perpendicular MOs that feature in-between σ/π overlap (Table 4), which is the source of its banana-like bent bonds. 85,86 The degeneracy within 2 is broken in 1, however, due to the presence of the carbene's electron lone pair, which is orthogonal in the HOMO{−1} but aligned in the HOMO{−2} (Table 3). Once again, 1 may be viewed as "iso-pyramidane" given these frontier MO similarities. 1d The very large ΔE S−T value for 1 of −45 kcal/mol (Table 1) means that the ground state 1 1 should react as a nucleophile. This can be demonstrated, for example, from pericyclic [ π 2 s + ω 2 a ] cycloadditions 36 of 1 with a representative set of alkenes. 46−49 The smaller ΔE value for each of the two possible donor (D)−acceptor (A) interactions denotes which one is dominant (eqs 3 and 4): 49 (1) D carbene (σ) with A alkene (π*) or (2) D alkene (π) with A carbene (p). The sign of the resulting ΔΔE value, found using eq 5, indicates whether the carbene acts as an (+)-electrophile or a (−)-nucleophile. 87 A 2-D chart comparing carbene 1 with other alkenophiles is then assembled to reveal philicity trends (Table 5). 51,52 They indicate that 1 is more nucleophilic than 4, 88 Stereoelectronic control has been modeled computationally and observed experimentally when carbene 4 bears the remote γ-substituent R. 64 Specifically, σ inductive effects bias the prox-Scheme 4. Protonation of 1 or 2 Gives Carbocation 6 a a Note that carbocation 6 represents both Brønsted−Lowry conjugate acids 1H + and 2H + , which are identical to each other (i.e., 1H + ≡ 2H + ), according to quantum chemical computations.   3a). This, in turn, influences both intramolecular and intermolecular product selectivities ( Table 6). The nature of R is the determining factor: (1) σ I < 0 (−) if R = R EDG and (2) σ I > 0 (+) if R = R EWG . 92 A similar situation for carbenes 1-R was researched. Its bridge-flapping may be subject to σ inductive effects too. Note that carbenes 1-R would not be diastereoselective, however, since they lack    Bridge-flapping transition states TS(1/1) flap and TS(prox-1-R/dist-1-R) flap were computed for 1 and a set of 1-substituted derivatives 1-R, respectively, and verified by IRC analyses (Figure 6). Conformational effects caused by the following Rgroup substituents were explored: SiMe 3 , PMe 2 , H, Me, OMe, and Br. When R = H, the degenerate step 1 → [TS(1/1) flap ] ‡ → 1 gives a symmetric curve since ΔE flap = [0] ( Figure 6). However, when R ≠ H, then ΔE flap ≠ 0 (eq 6) because the distinct conformers prox-1-R and dist-1-R have different energies (i.e., E prox ≠ E dist ). For example, ΔE flap increases by 4.3 kcal/mol with 1-SiMe 3 but decreases by 6.7 kcal/mol with 1-Br (cf. eq 6, Table 7, and Figure 6). The preference for a proximal or distal conformation is influenced by the σ inductive effect of substituent R, which can be quantified by a σ I value. 92 Hence, a conformational bias based on the proximity of C3 to substituted C1 or unsubstituted C5 is observed. A proximal (prox) conformation is established when the divalent C atom (>C:) leans toward substituted C1, while a distal (dist) conformation exists when >C: is tilted toward unsubstituted C5. It is evident from the energy profiles that prox-1-R is energetically preferred when R is an EDG, while dist-1-R is favored when R is an EWG. Hence, ΔE flap decreases as R becomes more electron-withdrawing. These trends accord well with those of carbenes 4-R.
Carbene 1 comprises (cyclopropyl)carbene (7)       The Journal of Organic Chemistry pubs.acs.org/joc Article ring enlargement or ring contraction via a 1,2-C atom shift reaction and cyclopropanation via a 1,3-C−H bond insertion reaction (Scheme 6). (Cyclopropyl)carbenes can also react via enyne fragmentation reactions when structural circumstances are favorable. The most important of these is orbital alignment. 96 The rigid C s -symmetric carbene nortricyclylidene (9) is a perfect example of this and yields the C s -symmetric enyne (cyclopent-3-en-1-yl)ethyne (10) almost exclusively (Scheme 7). 94−96 Presently, IRC calculations show that (cycloprop-2-en-1-yl)ethyne (11) is formed from the C ssymmetric carbene 1 1 via a shared TS, 75,110 namely, C 2vsymmetric TS(1/1) flap . At this bifurcation point, either bridgeflapping will continue or enyne fragmentation will commence toward TS(1/11) frag (Scheme 8a and Figure 8a). Depictions of Scheme 6. Rearrangements of (Cyclopropyl)carbene (7) and Cyclobutylidene (8) Scheme 7. Enyne Fragmentation within Nortricyclylidene (9) The Journal of Organic Chemistry pubs.acs.org/joc Article the properly aligned orbitals of the combined bridge-flapping/ enyne fragmentation transition states are found in Figure 9.  (1) were computed using DFT. The divalent C atom of singlet 1 is stabilized by nonclassical electron delocalization from flanking bent bonds comprising well-aligned σ/π-type orbitals. This interaction is responsible for the singlet carbene's bent C ssymmetric structure. Its main bridge is tilted ±43.5 deg from a C 2v -symmetric geometry, which triplet 1 and the bridgeflapping TS do have. The energy barrier for flapping (E a = 17.0 kcal/mol) is much higher than that computed for adamantylidene (E a = 1.1 kcal/mol), whose main bridge is tilted only ±19.7 deg from a C 2v -symmetric geometry. Thus, bridgeflapping conformerism within singlet 1 is relatively slow. The sizeable ΔE S−T (−44.9 kcal/mol) and gas-phase PA (258 kcal/mol) values computed for 1 suggest that the singlet is nucleophilic. This is further supported by a 2-D philicity chart of tabulated ΔΔE values obtained from the frontier MO energies of singlet 1 and representative sets of carbenes and alkenes. Computations reveal that singlet 1 will react more quickly and completely with electron-poor alkenes than with electron-rich alkenes.
When singlet 1 is substituted at C1, the corresponding carbene 1-R adopts a proximal conformation as the divalent C atom leans toward C1 and a distal one as it bends toward C5. The thermodynamic preference for a prox or dist conformation depends on the σ inductive effect of the R-group. A proximal conformation is preferred when R is an EDG, while a distal one is favored when R is an EWG. This controllable stereoelectronic behavior parallels that for γ-adamantylidenes, which consequently undergo intramolecular and intermolecular reactions with high diastereoselectivity.  Rearrangements of polar carbene 1 were investigated. The formation of pyramidane (2) via a 1,3-C−H bond insertion TS or via a 1,3-zwitterionic TS was conclusively proven by their IRCs. That for 1 → 2 is very flat and requires a supplemental geometry optimization to reach 2. Formation of tricyclo-[2.1.0.0 2,5 ]pent-2-ene (3) via [1,2]-sigmatropic transformations of 1, for example, is unlikely since bridgehead alkenes have high strain energies. The IRC computed for bridgeflapping within 3 was found to be identical to that for transverse bridge-flapping within 1. Hence, 1 and 3 are the same molecule. This is seen from their shared ylidic resonance form, which increases in importance as carbene nucleophilicity increases, as with NHCs. Although TS(3/3) flap violates Bredt's rule, strain is mitigated during transverse bridge-flapping within 1 by a lengthening of the cyclopropane unit's C−C bonds to 1.678 Å.
The enyne fragmentation of singlet 1 was also modeled. An IRC analysis of the enyne TS showed that the elementary step begins from a TSthat for singlet 1 bridge-flapping. Thus, the C 2v -symmetric TS is a shared TS and bifurcation point. Such stringent orbital alignment will preclude enyne formation in the case of 1.
Overall, the results anticipate that 1 is a nonclassically delocalized carbene. Its electron lone pair is a source of substantial Lewis basicity, making the carbene as nucleophilic as most NHCs. The carbene will react faster and more completely with electron-poor alkenes than with electron-rich ones. Also, its 1-substituted derivatives are subject to stereoelectronic control in a similar way as for γ-substituted adamantylidenes. Finally, carbene 1 and bridgehead alkene 3 are the same entity. They have the same set of Cartesian coordinates despite having different Lewis structures.

■ COMPUTATIONAL METHODS
Quantum chemical calculations were performed using the Spartan'14 Parallel Suite (v. 1.1.8) computer program. 111 The restricted or unrestricted SCF wave functions of molecular equilibrium geometries and transition states were computed using the DFT method (U)MPWB1K 112 with a 6-311G(d) basis set. Frozen-core secondorder Møller−Plesset perturbation theory (MP2(fc)) with a 6-31G(d) basis set was used to check earlier works. 5,73 Normal-mode vibrational analyses were performed at the level of geometry optimization. The harmonic frequencies were used to obtain temperature-independent zero-point vibrational energy (E ZPVE ) 113 and temperature-dependent thermal vibrational energy (Δ vib H) values. Each reaction transition state (TS) had one, and only one, imaginary frequency ν/c whose normal mode was animated to verify the motions expected for the elementary step. Intrinsic reaction coordinates (IRCs) were subsequently generated to follow conformational bridge-flapping, enyne fragmentation, etc. Single-point energy (E) values were computed using the (U)MPWB1K/cc-pVTZ theoretical model. All E ZPVE values were scaled by Z = 0.9513 114 before being added to E (T = 0 K; p = 0 atm). Relative energy values (Δ rel E) are specified with regard to tricyclo[2.1.0.0 2,5 )]pent-3-ylidene, the 1-substituted carbene's proximal conformer, etc., which were set equal to [0]. Conversion of E values to enthalpy (H T ) values was done according to eq S1 (see the Supporting Information; computational standard state: T = 298.15 K; p = 1 atm; cf. Table  S1). All Δ vib H values were scaled by H = 0.9462 114 before being added to the ZPVE-corrected E values. The increase in kinetic energy, due to translations (3(1/2)RT) and rotations (3(1/2)RT), for each nonlinear molecule was then added. Finally, RT (i.e., "pV work" needed to expand 1 mol of ideal gas to V = 24.465 L at T = 298.15 K and p = 1 atm) was added to obtain H T (eq S1).