Kinked polycyclic benzoids are more stable that their straight chain analogues. For example, the gaseous heat of formation of phenanthrene 1 is 49.6 kcal mol-1 while that of anthracene 2 is 55.2 kcal mol-1.1 This stability of the kinked over the straight chain is reproduced by computation: 1 is 4.24 kcal mol-1 lower in energy than 2 at BLYP/TZ2P.2 The standard explanation for this has been better resonance in 1 than in 2, leading to 1 being more aromatic than 2.
Bader has recently offered at alternative explanation. Topological electron density analysis3 (also referred to as Atoms-In-Molecules, or AIM) examines the electron density distribution to uncover chemically-relevant information. The bond path traces out the ridge of maximum electron density between two atoms, passing through the bond critical point. Bader has argued that the existence of the bond path is the necessary and sufficient condition for a chemical bond. In the AIM analysis of 1, he noted a bond path connecting the hydrogen atoms on C4 and C5.4 These are the hydrogen atoms in the bay region, labeled explicitly in the sketch above. Based on this bond path, and the fact that the bay region hydrogen atoms are stabilized due to charge transfer from carbon, Bader argued that H-H bonding in 1 stabilizes this molecule, accounting for its lower heat of formation than 2.
In a 2007 JOC paper, Bickelhaupt directly attacked this contention.2 The BLYP/TZ2P geometries of 1 and 2 are shown in Figure 1.
Figure 1. BLYP/TZ2P optimized geometries of 1 and 2.2
He approached the problem by examining the reaction of two 2-methtriylphenyl moieties combining to form either 1 or 2 (Scheme 1). The binding energy ΔE is then decomposed into two terms, ΔEprep which is the energy required to deform the triradical fragment 3 from its optimum geometry into the geometry within either 1 or 2, designated as 3(1) or 3(2), and ΔEint which is the interaction energy of the deformed fragments.
The deformation energy of the triradical fragment is nearly identical for 1 and 2. Therefore, the interaction energy to from 1 is more negative (stabilizing) than to form 2. The interaction energy for 1 was also obtained in two other ways. First, 3 was fixed to its geometry in 2 (i.e., 3(2)) with the distance of the two forming C-C bonds also that of 2. The interaction energy defined this way is -0.69 kcal mol-1, indicating a preference for aligning the fragments in the orientation of phenanthrene. Bickelhaupt further partitions the interaction energy to σ- and π-components, and finds the stabilization of the model interaction energy is dominated by π-interactions, not the σ-interactions one would expect from Bader’s model of H-H stabilization. Allowing the C-C distances between the two 3(2) fragments to adjust to those in 1 further strengthens the interaction energy to -2.49 kcal mol-1. The geometrical changes allow for the p-bonds to strengthen (by shortening the C9-C10 distance), and the repulsion between the bay area hydrogen atoms to diminish (by lengthening the C4a-C4b distance).
Bickelhaupt argues that the presence of a bond path may simply be due to two atomic basins being forced to bump into each other, whether these contacts be stabilizing or destabilizing. For example, two benzene molecules arranged such that a C-H bond points toward the C-H bond of another (see 4), a bond path will connect the two hydrogen atoms and the AIM energies of these two hydrogen atoms will indicate a net stabilization. He concludes by calling into question the basis for the claim that a bond path is the necessary and sufficient conditions for a chemical bond.
(1) Cox, J. D.; Pilcher, G. Thermochemistry of Organic and Organometallic Compounds; Academic Press: New York, 1970.
(2) Poater, J.; Visser, R.; Sola, M.; Bickelhaupt, F. M., "Polycyclic Benzenoids: Why Kinked is More Stable than Straight," J. Org.Chem. 2007, 72, 1134-1142, DOI: 10.1021/jo061637p
(3) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Clarendon Press: Oxford, UK, 1990.
(4) Matta, C. F.; Hernández-Trujillo, J.; Tang, T.-H.; Bader, R. F. W., "Hydrogen-Hydrogen Bonding: A Stabilizing Interaction in Molecules and Crystals," Chem. Eur. J. 2003, 9, 1940-1951, DOI: 10.1002/chem.200204626