Bonding and antibonding orbitals

Key points: A bonding orbital arises from the constructive interference of neighbouring atomic orbit als; an antibonding orbital arises from their destructive interference, as indicated by a node between the atoms.

The orbital  is an example of a bonding orbital. It is so-called because the energy of the molecule is lowered relative to that of the separated atoms if this orbital is occupied by electrons. The bonding character of  is ascribed to the constructive interference between the two atomic orbitals and the resulting enhanced amplitude between the two nuclei (Fig. 2.8). An electron that occupies   has an enhanced probability of being found in the internuclear region and can interact strongly with both nuclei. Hence orbital overlap, the spreading of one orbital into the region occupied by another, leading to enhanced prob ability of electrons being found in the internuclear region, is taken to be the origin of the strength of bonds.

The orbital  is an example of an antibonding orbital. It is so-called because, if it is occupied, the energy of the molecule is higher than for the two separated atoms. The greater energy of an electron in this orbital arises from the destructive interference between the two atomic orbitals, which cancels their amplitudes and gives rise to a nodal plane between the two nuclei (Fig. 2.9). Electrons that occupy  are largely excluded from the internuclear region and are forced to occupy energetically less favourable locations. It is generally true that the energy of a molecular orbital in a polyatomic molecule is higher the more internuclear nodes it has. The increase in energy reflects an increasingly complete exclusion of electrons from the regions between nuclei. Note that an antibonding orbital is slightly more antibonding than its partner bonding orbital is bonding: the asymmetry arises partly from the details of the electron distribution and partly from the fact that in ternuclear repulsion pushes the entire energy level diagram upwards. The energies of the two molecular orbitals in H₂ are depicted in Fig. 2.10, which is an example of a molecular orbital energy level diagram, a diagram depicting the relative energies of molecular orbitals. The two electrons occupy the lower energy molecular orbital. An indication of the size of the energy gap between the two molecular orbitals is the observation of a spectroscopic absorption in H₂ at 11.4 eV (in the ultraviolet at 109 nm), which can be ascribed to the transition of an electron from the bonding orbital to the antibonding orbital. The dissociation energy of H2 is 4.5 eV (434 kJ mol 1), which gives an indication of the location of the bonding orbital relative to the separated atoms. The Pauli exclusion principle limits to two the number of electrons that can occupy any molecular orbital and requires that those two electrons be paired (↑↓). The exclusion principle is the origin of the importance of the pairing of the electrons in bond formation in MO theory just as it is in VB theory: in the context of MO theory, two is the maximum number of electrons that can occupy an orbital that contributes to the stability of the molecule. The H₂ molecule, for example, has a lower energy than that of the separated atoms because two electrons can occupy the orbital  and both can contribute to the lowering of its energy (as shown in Fig. 2.10). A weaker bond can be expected if only one electron is present in a bonding orbital, but nevertheless H₂ is known as a transient gas-phase ion; its dissociation energy is 2.6 eV (250.9 kJ mol 1). Three electrons (as in H₂^- ) are less effective than two electrons because the third electron must occupy the antibonding orbital  and hence destabilize the molecule. With four electrons, the antibonding effect of two electrons in  overcomes the bonding effect of two electrons in  . There is then no net bonding. It follows that a four-electron molecule with only 1s orbitals available for bond formation, such as He₂ , is not expected to be stable relative to dissociation into its atoms. So far, we have discussed interactions of atomic orbitals that give rise to molecular orbitals that are lower in energy (bonding) and higher in energy (antibonding) than the separated atoms. In addition, it is possible to generate a molecular orbital that has the same energy as the initial atomic orbitals. In this case, occupation of this orbital neither stabilizes nor destabilizes the molecule and so it is described as a nonbonding orbital. Typi cally, a nonbonding orbital is a molecular orbital that consists of a single orbital on one atom, perhaps because there is no atomic orbital of the correct symmetry for it to overlap on a neighbouring atom.

Fig. 2.8 The enhancement of electron density in the internuclear region arising from the constructive interference between the atomic orbitals on neighbouring atoms.

Fig. 2.9 The destructive interference that arises if the overlapping orbitals have opposite signs. This interference leads to a nodal surface in an antibonding molecular orbital.

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مواضيع ذات صلة

Polytypism

The close packing of spheres

Lattices and unit cells

The orbitals

Hybridization

Hypervalence

Promotion

Polyatomic molecules

Homonuclear diatomic molecules

The hydrogen molecule

The basic shapes

Resonance