Magnetic Shielding Analysis of Bonding in [1.1.1]Propellane

Abstract

The bonding in [1.1.1]propellane, bicyclo[1.1.0]butane, bicyclo[1.1.1]pentane, tetrahedrane, and cyclopropane is investigated by analyzing changes in the off-nucleus isotropic magnetic shielding within the space surrounding each of these molecules and, for [1.1.1]propellane, by examining also the diamagnetic and paramagnetic contributions to this shielding. Any shielding arising from the two "exo" sp³-like hybrid atomic orbitals on the bridgehead carbon atoms that have been used to support the idea of an inverted bond between these two atoms is found to be almost entirely contained within the [1.1.1]propellane cage and to contribute to a strongly shielded central region. This strongly shielded region suggests the establishment of a mainly covalent bonding interaction involving all carbon atoms that cannot be straightforwardly decomposed into contributions from individual carbon-carbon bonds. The emergence of the strongly shielding central region is traced by comparing the shielding variations in and around molecules with one three-membered carbon ring (cyclopropane), two fused three-membered carbon rings (bicyclo[1.1.0]butane), and three fused three-membered carbon rings ([1.1.1]propellane).

Figure 1

Geometries of [1.1.1]propellane 1, bicyclo[1.1.0]butane 2, bicyclo[1.1.1]pentane 3, tetrahedrane 4, and cyclopropane 5 with C–C distances (in Å) from ^aexperimental geometries (gas-phase electron diffraction for 1(31) and 3, microwave spectrum analysis for 2(33) and 5(25)), and from ^bB3LYP-D3(BJ)/def2-TZVP and ^cCASSCF(2,2)/def2-TZVP optimized geometries. C_b and C_m in 1–3 and 5 denote bridgehead and methylene carbon atoms, respectively.

Figure 2

Isotropic shielding isosurfaces for 1–5 at σ_iso(r) = ±16 ppm (positive/negative isovalues in blue/orange) and σ_iso(r) = 50 ppm (darker) [B3LYP-GIAO/6-311++G(d,p)//B3LYP-D3(BJ)/def2-TZVP].

Figure 3

Isotropic shielding contour plots in the σ_v, σ_h, or d σ_d symmetry planes of 1, 3–6 and in one of the CCC planes of 2, from calculations at the B3LYP-GIAO/6-311++G(d,p)//B3LYP-D3(BJ)/def2-TZVP and CASSCF(2,2)-GIAO/6-311++G(d,p)//CASSCF(2,2)/def2-TZVP levels. Lines show bonds in the plotting plane. σ_iso(r) range between ca. −20 and 180 ppm, red/orange (deshielded) to blue (shielded).

Figure 4

Total electron density (ρ) and Laplacian of the total electron density (∇²ρ) contour plots in the σ_v symmetry plane of 1, from calculations at the B3LYP/6-311++G(d,p)//B3LYP-D3(BJ)/def2-TZVP and CASSCF(2,2)/6-311++G(d,p)//CASSCF(2,2)/def2-TZVP levels. Lines show bonds in the plotting plane. ρ range between 0 and 75 a.u. (ρ, blue), ∇²ρ range between ca. −10⁵ and 300 a.u. (∇²ρ, red to blue).

Figure 5

Contour plots of the diamagnetic (a, c, e, g) and paramagnetic (b, d, f, h) contributions to the isotropic shielding in 1 in the σ_v (a–d) and σ_h (e–h) symmetry planes from calculations at the CASSCF(2,2)-GIAO/6-311++G(d,p)//CASSCF(2,2)/def2-TZVP level. (a, b, e, f) were calculated with gauge origin at the center of mass; (c, d, g, h) were calculated with individual gauge origins at r for each σ(r). Lines show bonds in the plotting plane. The σ_iso^d(r) and σ_iso^p(r) ranges are between ca. −600 and 600 ppm, red/orange (deshielded) to blue (shielded), axes in Å.