P-orbital participation

This is an example of a Mobius reaction system—a node along the reaction coordinate is introduced by the placement of a phase inverting orbital. As in the H - - H2 system, a single spin-pair exchange takes place. Thus, the reaction is phase preserving. Mobius reaction systems are quite common when p orbitals (or hybrid orbitals containing p orbitals) participate in the reaction, as further discussed in Section ni.B.2. 

However, we have shown how the 18-electron rule is commonly satisfied in the absence of any significant p-orbital participation, on the basis of hypervalent 3c/4e cu-bonding interactions wholly within the framework of normal-valent sd" hybridization. Results of NBO and Mulliken analyses of high-level wavefunctions for transition-metal complexes commonly exhibit only paltry occupation of the outer p orbitals (comparable in this respect to the weak contributions of d-type polarization functions in main-group bonding). 

These results depend on the assumption that at most only one of the two halogen p -orbitals participates in the bonding, while the other retains its normal occupancy of 2. If both p -orbitals participate to an equal extent, n, as for example in chloroacetylene, then equation 1 must be modified to equation 4 ... 

This does not include the nodal plane that is coplanar with the carbon chain, bisecting each p orbital participating in the n system. 

As molecular applications of the extended DK approach, we have calculated the spectroscopic constants for At2 equilibrium bond lengths (RJ, harmonic frequencies (rotational constants (B ), and dissociation energies (Dg). A strong spin-orbit effect is expected for these properties because the outer p orbital participates in their molecular bonds. Electron correlation effects were treated by the hybrid DFT approach with the B3LYP functional. Since several approximations to both the one-electron and two-electron parts of the DK Hamiltonian are available, we dehne that the DKnl -f DKn2 Hamiltonian ( 1, 2= 1-3) denotes the DK Hamiltonian with DKnl and DKn2 transformations for the one-electron and two-electron parts, respectively. The DKwl -I- DKl Hamiltonian is equivalent to the no-pair DKwl Hamiltonian. For the two-electron part the electron-electron Coulomb operator in the non-relativistic form can also be adopted. The DKwl Hamiltonian with the non-relativistic Coulomb operator is denoted by the DKwl - - NR Hamiltonian. 

On the contrary, the internal HSH angle in isolated H2S is 92°, consistent with nearly pure p-orbitals participating in each S—H bond [41]. The third mutually orthogonal / -orbital, containing a lone pair of electrons, could then orient itself toward the HY, leading to the observed angle of a near 90°. 

In the preceding three chapters we introduced the topic of compounds containing carbon-carbon tt bonds, the products of overlap between two adjacent parallel p orbitals. We found that addition reactions to these chemically versatile systems provided entries both to relatively simple products, of use in synthesis, and to more complex products, including polymers—substances that have affected modem society enormously. In this chapter we expand further on all these themes by studying compounds in which three or more parallel p orbitals participate in TT-type overlap. The electrons in such orbitals are therefore shared by three or more atomic centers and are said to be delocalized. 

Neighboring group participation (a term introduced by Winstein) with the vacant p-orbital of a carbenium ion center contributes to its stabilization via delocalization, which can involve atoms with unshared electron pairs (w-donors), 7r-electron systems (direct conjugate or allylic stabilization), bent rr-bonds (as in cyclopropylcarbinyl cations), and C-H and C-C [Pg.150]

In pyrrole on the other hand the unshared pair belonging to nitrogen must be added to the four tt electrons of the two double bonds m order to meet the six tt elec tron requirement As shown m Figure 11 166 the nitrogen of pyrrole is sp hybridized and the pair of electrons occupies a p orbital where both electrons can participate m the aromatic tt system... 

Elements beyond the second row of the periodic table can form bonds to more than four ligands and can be associated with more than an octet of electrons. These features are possible for two reasons. First, elements with > 2 have atomic radii that are large enough to bond to 5, 6, or even more ligands. Second, elements with > 2 have d orbitals whose energies are close to the energies of the valence p orbitals. An orbital overlap description of the bonding in these species relies on the participation of d orbitals of the inner atom. 

Severai common poi /atomic oxoanions, inciuding suifate, perchiorate, and phosphate, have inner atoms from the third row of the periodic tabie. In these anions, vaience d orbitais are avaiiable to participate in bonding. Figure 10-47 shows how a n orbitai can form through side-by-side overiap of a d orbital on one atom with a.7, p orbital on another atom. As with other itt bonds, electron density is concentrated above and below the bond axis. 

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