Antibonding Antisymmetrized

The electronic states introduced by hydrogen in the band structure of Si are quite different depending upon the location of the impurity in the lattice. For H at the bond center we can, to a first approximation, treat the problem as involving only three states (Schaad, 1974 Fisch and Licciardello, 1978) the semiconductor bonding (b) and antibonding (a) states (which, in turn, are symmetric and antisymmetric combinations of hydrid orbitals on the two atoms) and the hydrogen Is orbital. The cor-... 

So we find that the ground state (n) orbital would be symmetric (S) with respect to the mirror plane m and antisymmetric (A) with respect to C2 axis. On the other hand the antibonding orbital (k ) would be antisymmetric with respect to m and symmetric with respect to C2 axis. 

Figure 3.2 Symmetric and antisymmetric wave fnnctions, describing the two electrons in a pair of atoms and leading to bonding and antibonding electron configurations.

This function is zero for all points equidistant front the two nuclei (that is, it has a nodal plane). The orbital y>j is large in the region between the nuclei (where lsA and 1% overlap and the electrostatic potential is low) and is generally referred to as a bonding orbital. Similarly, y>t, which keeps its electron away from the internuclear region, is antibonding. The two functions and yj2 are analogous to the symmetric and antisymmetric orbitals for the one-dimensional model. A similar transformation can be applied and two equivalent orbitals constructed. These are... 

Ethylene, the first member of the series, is already familiar. Two adjacent p orbitals interacting will yield a bonding orbital, symmetric with respect to reflection in the mirror plane lying midway between the two carbons and perpendicular to the C—C axis, and an antibonding orbital antisymmetric with respect to that mirror plane. Figure 10.18 illustrates the interaction and the resulting orbitals. 

Figure 11.1 (a) The ethylene it bonding orbital is symmetric (S) with respect to reflection in the mirror plane a, and antisymmetric (A) with respect to reflection in the mirror plane a, (b) The ethylene it antibonding orbital is antisymmetric (A) with respect to reflection in both a and a. ... 

The symmetry conservation principle allows us to reconstruct qualitatively how the orbital tt1 will change.18 Since it starts out antisymmetric under C2, it remains so it can do this only if it ends up as an antisymmetric orbital of the product, say it (Figure 11.8). As the two end carbons rotate, the contribution of the p orbitals on those end carbons must decrease, finally to disappear altogether. Similarly, in 7t2, the contribution of the two central p orbitals will decrease, leaving only the end two, which will have rotated onto each other to yield the product a orbital. The changes in the antibonding orbitals may be visualized in a similar way. 

Figure 11.22 Union of a single carbon at both ends of a three-carbon chain. The nonbonding orbital is antisymmetric with respect to the mirror plane bisecting the system and cannot interact with the symmetric p orbital. Alternatively, a bonding interaction at one end is exactly cancelled by an antibonding interaction at the other. No stabilization results to a first approximation, the cyclic system is less stable than the open chain (Figure 11.21) by 2 AE and is therefore antiaromatic.

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