Pyramidalization angle

One more structural dilferentiation that can influence functionalization is the tip vs. sidewall region. The tips are the two ending parts of the tube in these two regions, the curvature is increased and the shape more resembles that of a hemisphere, with reactivity expected to be similar to that of fullerenes. In contrast, sidewalls present reduced pyramidalization angles and therefore different behaviors towards functionalization. Reactions involving the use of harsh conditions can result in a fracture of the tubes, enabling production of shorter tubes with open tips, where the aromatic pattern is interrupted and carbon atoms are more reactive. 

Figure 3.3 Bonding structures for different carbon materials (a) diamond, (b) graphite, (c) carbon nanotubes and (d) fullerenes. Scheme of the pyramidalization angle (0p) in deformed sp bonding in comparison with a trigonal structure.

On the other hand, and as discussed before, the chemical reactivity of CNT sidewalls increases vhth the tube curvature (i.e. decrease of the tube diameter), due to the increase of the pyramidalization angle and greater strain energy per atom [37,38]. Such pyramidalization of the CNT atoms causes the exohedral lobes of the orbitals to be larger than their endohedral counterparts. The reactivity of the surface is thus enhanced by the pronounced exposure of the hybrid orbitals from the exterior, which favors the orbital overlap vhth incoming reactants [38]. 

The question of the correctness of such an explanation of the nonplanarity of 2-azirine and the planarity of pyrrole was analyzed in Mo et al. [89JMS(201)17]. The evolution of the MOs as a function of the pyramidalization angle in nitrogen was traced. For both 2-azirine and pyrrole nitrogen pyramidalization leads to the stabilization of all 7t-MOs of the planar structure and, conversely, to the destabilization of several [Pg.368]

C-Y bond contractions and of the planarization of the a-carbon as measured by the % progress in the change of the pyramidal angle a. The pyramidal angle is defined as shown in 56 where the dashed lines are the projection... 

The conclusions based on energy calculations are supported by the calculation of aromaticity indices such as HOMA142,143 and NICS(l)144,145 values as well as the pyramidal angle of the transition state. The pyramidal angle, a, is defined as illustrated for the benzenium ion (59) and the transition state (60) for reaction 33a (B = benzene) this angle is 0° in the aromatic species. 

TABLE 6. Pyramidalization angles (0 and j/) for compounds containing strongly pyramidalized double-bond carbon atoms... 

An interesting series of polycyclic olefins with notable pyramidalization in the lower members is represented by the superphanes 37142 and 38143. Their pyramidalization angles are shown in Table 6. While 37 could be obtained as a solid at ambient temperature... 

Figure 4. Rehybridization as a function of pyramidalization angle. The rc-orbital axis vector (poavI approximation), is defined as that vector which makes equal angles to the three a-bonds at a conjugated carbon atom (Haddon 1988). The common angle to the three a-bonds (which are assumed to lie along the internuclear axes), is denoted 0OT. The average pyramidalization angle [(< — 90)°] shown for representative fullerenes (C ), was obtained from eqn (2) of Haddon et al. (19866) for n > 60.

The quadrupolar quasi-static coupling in NF3 — 7.068 MHz— is very close to the value obtained from microwave measurements — 7.07 MHz — this feature may be interpreted as a clue that intermolecular effects are negligible in this compound unless, by a fortuitous coincidence, thes intermolecular effects are cancelled by some other mechanism, such as a molecular deformation in the solid (the coupling is very sensitive to slight variations of the pyramidal angle, as discussed below). 

Fig. 11. Calculated pyramidalization angles at the substituted (Or) and unsubstituted (Oh) silicon atoms in mono-substituted silenes, H2Si=SiHR (6-3 IG //6-3 IG )...

In contrast, the sidewall pyramidalization angle is much less than the endcap, on the order of 3-6°, depending on the diameter/chirality of the SWNT. For an armchair (5,5) SWNT, two types of C-C bonds are present along the sidewalls - either parallel or perpendicular to the nanotube axis. Each of these bonds exhibits a different... 

Figure 6.57. Schematic of (a) a metallic (5,5) SWNT, (b) the pyramidalization angles of typical sp and sp carbon atoms, (c) the K orbital misalignment angles along C1-C4 in the (5,5) SWNT and its capping fullerene, C q. Reproduced with permission from Niyogi, S. Hamon, M. A. Hu, H. Zhao, B. Bhowmik, R Sen, R. Itkis, M. E. Haddon, R. C. Acc. Chem. Res. 2002, 35, 1105. Copyright 2002 American Chemical Society.

Further studies along these lines have demonstrated that the capillary action is related to the diameter of the inner cavity of the nanotube [176]. This was explained in terms of the polarizability of the cavity wall which is related to the radius of curvature, through the pyramidalization angle (bond-bending angle) and the polarizability of the filling material. 

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