 |
|
A theory which treats bonding as an over lapping of ligand orbitals with those of the central atom. By summing the
original wavefunctions for the bonding orbitals in constituent species, "hybrid" molecular orbitals of the compound
can be generated. These new orbitals have an intermediate character between the original s,
p, and d orbitals (if
available) in the outer energy level, and produce additional bond sites. The hybridization is named on the basis of the
orbitals involved, and the hybrid wavefunction is the (renormalized) sum of the individual wavefunctions, where each
addition may be with an arbitrary sign. The composite wavefunctions with differing signs are orthogonal, since
 |
|
 |
(1) |
But
 |
(2) |
so
 |
(3) |
The simplest example is  -hybridization. There are two possible combinations,
where the wavefunctions on the right are the solutions to Schrödinger's equation, and the normalization constants are
needed so that the hybrid wavefunction is normalized.  has the electron density is greatest between the two
nuclei. It will therefore bind the nuclei together, and is called a bonding molecular orbital.  has the
electron density greatest on the sides of the nuclei. It will therefore pull the nuclei apart, and is called an
antibonding molecular orbital. In some instances, a nonbonding molecular orbital may be generated for which the
electron density is uniformly distributed between and on the sides of the nuclei. A measure of the stability of a
compound based on the occupancy of its molecular orbitals is given by the body order.
 |
|
 |
(6) |
A diatomic hydrogen molecule fills the  orbital, and so has a bond order of 1 and is stable.
A diatomic helium molecule fills both the  and orbitals, so it has a bond order of zero and
is not stable.
More complicated bonding interactions will involve s,
p, and d orbitals. For a homonuclear diatomic compound with
hybrid orbitals constructed from  ,
 , and  p orbitals, the molecular orbital have the following form.
For heteropolar molecules or more complicated systems, the molecular orbital energy diagram can be quite complex. The
molecular orbitals for the CO2 (O1=C=O2) molecules are given by, in order of increasing energy
There are 12 electrons in the valence shell, so the levels are filled through the nonbonding orbitals. The compound is
therefore stable, with a bond order of 4. For an even more complicated example, consider benzene. For certain
compounds, electrons are delocalized. Such compounds have an extremely large number of molecular orbitals. The result,
as the number of levels goes to infinity, is a band of bonding orbitals, and band of antibonding orbitals (known as the
conduction band, since free electrons will exist here), possibly overlapping or possibly separated by a gap. In metals,
the levels overlap, and the bonding orbitals are completely filled. In semiconductors, the levels are separated by a
small "forbidden zone." The addition of a small amount of energy will therefore remove an electron from the filled
bonding orbital, through the forbidden zone, and into the conduction band.
 Crystal Field Theory, Hybridization, Ligand Field Theory, Valence Bond Theory
© 1996-2007 Eric W. Weisstein
|
