Abstract

The formation of cyclopropatetrahedrane (tetracyclo[2.1.0.01,3.02,4]pentane) via four different carbene reactions is computed using the (U)CCSD(T)(full)/cc-pVTZ//(U)ωB97X-D/cc-pVTZ + 1.3686(EZPVE) theoretical model. Intrinsic reaction coordinate plots confirm that each carbene is directly linked to cyclopropatetrahedrane via a unique cyclopropanation step. Each elementary step is assessed according to the structure and energy of its transition state.
This report assesses four carbene reactions that ostensibly could form cyclopropatetrahedrane (1;1Figure 1a),2,3 a cyclopropane-fused derivative of tetrahedrane (2; Figure 1b).4−7 To date, 1 and 2 remain hypothetical constructs, although derivatives of 2(4) as well as pristine 3 and 4 (Figure 1c,d)8,9 have been prepared (cf. Table S1 in Supporting Information). Nevertheless, earlier computations suggest that 1 will be kinetically stable because (1) it occupies a deep energy minimum on the C5H4 hypersurface and (2) none of its 21 vibrational normal modes falls below ν̅ = 443 cm–1.2,3 Forming 1 will be challenging because (1) its computed strain energy (ΔstrainH° = 157 kcal/mol)2a is phenomenal and (2) the bridging CH2–group of 1 establishes a bond that connects two inverted C atoms (i.e., each C atom has four bonds pointing in the same direction;10−12Figure 1a; cf. Figures S2 and S3 in Supporting Information). Also, the long C1–C4 bond (r = 1.664 Å)2a of 1 is electron-depleted, weak, and prone to breakage when compared with typical aliphatic C–C bonds. Routes to 1 have been proposed, such as via a 2,4-dihalotricyclo[1.1.1.01,3]pentane synthon (5; Scheme 1).4,5 However, carbene routes to 1 have never been investigated.
Figure 1.

Cyclopropatetrahedrane (1) is a cyclopropane-fused derivative of tetrahedrane (2), which itself is one of the Platonic-solid-like hydrocarbons that also include cubane (3) and dodecahedrane (4).
Scheme 1. A Proposed Retrosynthesis of Cyclopropatetrahedrane (1).

Carbene reaction intermediates are uncharged, electron-deficient, and highly energetic.13−27 They are prized for their ability to form a wide variety of cyclopropanes, which can be done in two ways. The divalent C atom (:C<) can (1) insert into a homovicinal C–H bond (e.g., carbene 6 → 2) or (2) add to a C–C double bond (e.g., carbene 7 → 2) (Scheme 2).28 These two signature reactions are useful when building polycycloalkanes. Thus, an examination of carbene routes to highly strained 1 is warranted.
Scheme 2. Types of Intramolecular Carbene Cyclopropanations.

Four routes to 1 via four different hypothetical carbene reaction intermediates (Scheme 3) were evaluated using the (U)CCSD(T)(full)/cc-pVTZ//(U)ωB97X-D/cc-pVTZ + 1.3686(EZPVE) theoretical model (see Computational Methods). Paths a–c depict homovicinal C–H bond insertion reactions within carbenes 8–10, respectively, and path d depicts a C–C double bond addition reaction within carbene 11. The structures in Scheme 3 are drawn in a uniform manner to emphasize the new bonds being formed (cf. Figure 2): (1) path a, Cα–Cβ; (2) path b, Cγ–Cγ; (3) path c, Cβ–Cγ; and (4) path d, Cα–Cβ and Cβ–Cβ. Each elementary step is characterized in terms of its transition state (TS) structure, activation energy (Ea), and net energy change (ΔE) (Table 1). Intrinsic reaction coordinate (IRC) plots (Figure 3a–d) and videos (see Supporting Information) are also provided to demonstrate that each carbene is directly linked to 1.
Scheme 3. Four Carbene Routes to Cyclopropatetrahedrane (1).

Figure 2.

C2v-symmetric cyclopropatetrahedrane (1) comprises (a) one 2°-C atom (α), (b) two 4°-C atoms (β), and (c) two 3°-C atoms (γ). (ORTEP structure shows 50% ellipsoids.)
Table 1. Computed Data for Carbene Isomerizations to 1a,b.
| Carbene | IRC path | ν̅ TS (cm–1) | Ea (kcal/mol) | ΔE (kcal/mol) |
|---|---|---|---|---|
| 8 | a | 1164i | 15.8 | –50.2 |
| 9 | b | 915i | 14.2 | –24.5 |
| 10 | c | 961i | 3.5 | –29.2 |
| 11 | d | 329i | 27.8 | 10.0 |
Figure 3.
Four IRCs were computed using the CCSD(T)/cc-pVTZ//ωB97X-D/cc-pVTZ theoretical model. Routes (a)–(c) depict homovicinal C–H bond insertion reactions within carbenes 8–10, respectively, while route (d) depicts a C–C double bond addition reaction within carbene 11.
Path a involves the hypothetical carbene (tetrahedryl)carbene (8).29 A homovicinal C–H bond insertion reaction via TSa was confirmed by its one, and only one, imaginary frequency (Table 1, path a), by animating the corresponding vibration, and by plotting the IRC, which links 8 directly to 1 (i.e., 8 → TSa → 1; Figure 3a (blue)).
An intriguing aspect of the carbene itself was found. Its computed singlet–triplet energy gap (ΔES–T)30 of −6.7 kcal/mol, corrected for the experimental ΔES–T of CH2 (eq 1; see Supporting Information),31 indicates that alkylcarbene 8 has a singlet ground state, and decidedly so. Hyperconjugation32−35 between the C1′–C4′ “banana” bond and the vacant p orbital of the carbene’s divalent C atom is a contributing factor (cf. Figure S1 in Supporting Information). The :CH-group of the lowest energy conformation of 8 is bent 41 deg toward the C1′–C4′ bond in comparison to the ·C·H-group of triplet (tetrahedryl)carbene (i.e., 38) (Scheme 3, path a) even though this deformation causes the C1′ atom’s four bonds to point in one direction (i.e., C1′ is an inverted C atom; cf. Figure S2 in Supporting Information). The distorted geometry of 8 may assist the formation of TSa since a triangular array comprising the C1, C1′, and C4′ atoms is already established (Figure 3a (blue)). Thus, the high ΔH⧧ may be more prohibitive than ΔS⧧ for the homovicinal C–H bond insertion reaction 8 → 1.
| 1 |
Path b involves the hypothetical carbene tricyclo[1.1.1.01,3]pent-2-ylidene (9). A homovicinal C–H bond insertion reaction via TSb was confirmed by its one, and only one, imaginary frequency (Table 1, path b), by animating the corresponding vibration, and by plotting the IRC, which links 9 directly to 1 (i.e., 9 → TSb → 1; Figure 3b (green)).
Path c involves the hypothetical carbene trans-tricyclo[2.1.0.01,3]pent-2-ylidene (10). A homovicinal C–H bond insertion reaction via TSc was confirmed by its one, and only one, imaginary frequency (Table 1, path c), by animating the corresponding vibration, and by plotting the IRC, which links 10 directly to 1 (i.e., 10 → TSc → 1; Figure 3c (yellow)).
Path d involves the hypothetical carbene 4-methylenebicyclo[1.1.0]but-2-ylidene (11). A cycloaddition reaction via TSd was confirmed by its one, and only one, imaginary frequency (Table 1, path d), by animating the corresponding vibration, and by plotting the IRC, which links 11 directly to 1 (i.e., 11 → TSd → 1; Figure 3d (red)). However, in contrast to those of the homovicinal C–H bond insertion reactions (Table 1, paths a–c), the net ΔE computed for this elementary step is positive. This indicates a thermodynamic preference for a cycloreversion of 1 (i.e., 1 → 11). However, 1 → 11 is computed to have a high ΔH‡ (18.1 kcal/mol; see Supporting Information). Of course, this enthalpy barrier is not insurmountable even in a frozen Ar matrix (T = ca. 10 K) under photolytic conditions.36
Computational chemistry was used to assess the viability of forming cyclopropatetrahedrane (1) via four different carbene reactions. The hypothesis appears to be valid because a TS was found for each of the elementary steps (i.e., Scheme 3, paths a–d). Furthermore, the respective IRC plots (Figure 3a–d) reveal a direct link between each carbene and 1. The IRCs and ZPVE-corrected single-point energies show that the homovicinal C–H bond insertion reactions via H atom transfer are exothermic but the C–C double bond addition reaction is endothermic. The formation of 1 via a homovicinal C–H bond insertion within trans-tricyclo[2.1.0.01,3]pent-2-ylidene (10) requires an Ea of just 3.5 kcal/mol. The bent posture adopted by the electron-seeking :CH-group of (tetrahedryl)carbene (8) is akin to a house plant that is bent toward a sunlit window; each “stalk” bends to obtain what it needs. In contrast, stabilizing hyperconjugation is precluded in triplet (tetrahedryl)carbene (38) because of its half-occupied p orbital. Thus, the triplet carbene is strictly Cs-symmetric.
Computational Methods
Quantum chemical calculations were performed on 1, carbenes 8–11, transition states TSa–TSd, and intrinsic reaction coordinate (IRC) paths a–d using the Spartan’20 (v. 1.1.4) computer program.37 Restricted SCF wave functions of molecular equilibrium geometries and transition states were computed using a (100,434) DFT integration grid, the RSH-GGA functional ωB97X-D,38 and Dunning’s cc-pVTZ basis set. Unrestricted SCF wave functions were computed for triplet-state carbenes. 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 (EZPVE)39 and temperature-dependent thermal vibrational energy (ΔvibH) values. Each reaction TS had one, and only one, imaginary frequency, ν̅ TS. Its vibration was animated to verify that the motions conformed to the elementary step. An IRC was computed to ensure that the carbene followed a direct route to 1. Single-point energy (E) values were computed using the CCSD(T)(full) coupled-cluster theory method and Dunning’s cc-pVTZ basis set. All EZPVE values were scaled by z = 1.368640 before being added to E (T = 0 K; p = 0 atm). Relative energy values (ΔrelE) are specified with regard to 1 ((ΔrelE = [0]). Conversion of E values to enthalpy (HT) values was done according to eq S1 (see Supporting Information; computational standard state: T = 298.15 K; p = 1 atm; cf. Table S2). All ΔvibH values were scaled by H = 0.95640 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 HT (eq S1).
Acknowledgments
Dedicated to the memory of University of Florida Distinguished Chemistry Professor Dr. William (Bill) M. Jones (1930–2022), with the appreciation of his contributions to the advancement of carbene chemistry.
Data Availability Statement
The data underlying this study are available in the published article and its online Supporting Information.
Supporting Information Available
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.joc.2c02217.
Computational methods, Cartesian coordinates, ORTEP structures, energies/enthalpies, and geometric proof of inverted C atoms (PDF)
Energy results (XLSX)
IRC data (XLSX)
Inverted carbon atom data (XLSX)
IRC data and video (wB97X-D_cc-pVTZ.IRC_path a_(Tricyclo[1_1_0_0(2,4)but-1-yl)carbene_(8)) MOV)
IRC data and video (wB97X-D_cc-pVTZ.IRC_path b_Tricyclo[1_1_1_0(1,3)]pent-2-ylidene_(9)) (MOV)
IRC data and video (wB97X-D_cc-pVTZ.IRC_path c_Tricyclo[2_1_0_0(1,3)]pent-2-ylidene_(10)) (MOV)
IRC data and video (wB97X-D_cc-pVTZ.IRC_path d_4-Methylenebicyclo[1_1_0]but-2-ylidene_(11)) (MOV)
The authors declare no competing financial interest.
Supplementary Material
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Data Availability Statement
The data underlying this study are available in the published article and its online Supporting Information.

