In diatomic species, there is only one important coordinate, defined
as the internuclear axis. We discuss the molecular orbitals in terms
of the overlap of the atomic orbitals along this axis. In polyatomic
species, this description must be extended to allow for the fact
that there are many internuclear axes.
Let us consider the water molecule, H2O. A simple description
would suggest that the two O-H bonds are formed from the overlap
of an O(2p) orbital and an H(1s) orbital. The bonding orbitals would
be described by the expression
The valence electrons, 8 in H2O (the O
2s (2) + O 2p (4) + H 1s (1+1)), are contained in the molecular
orbitals to create two bonds O-H (2 x 2 = 4 electrons), and the
remaining 4 are contained in the non-bonding O(2s) and one remaining
If this description were accurate, the H-O-H bond
angle would be 90o, as the two p orbitals involved in
the bonding are perpendicular to each other. However, the actual
bond angle is 104.5o. This can be explained by noting
that the O-H bonds actually result from the overlap of the H(1s)
orbital and a hybrid orbital on O.
in the sp-valence system
|If we treat the s and p valence
orbitals as contributing to bonding in the molecule, they
can form four molecular orbitals (there are four basis atomic
orbitals and hence four molecular orbitals).
Often, the molecular orbitals are not simply formed from
overlap of the basis atomic orbitals and the atomic orbitals
an another atom, but are formed from the overlap of hybrid
orbitals on the central atom and the other atom.
These hybrid orbitals are so-called because they are
formed from mixing together the basis atomic orbitals
on the central atom, to give another basis set which better
reflects the geometry of the molecule.
In the sp-valence system, the 4 orbitals (1 s and 3 p
orbitals) can mix in different ways to give different
types of sp-hybrid orbital
are formed from the mixing of the s orbital and one of the
p orbitals (the pz orbital). The two orbitals
formed, h1 and h2, are directional,
pointing in opposite directions along an axis through the
atom (the z-axis).
are formed from the mixing of the s orbital and two of the
p orbitals (the pz and py orbitals).
The three orbitals formed, h1, h2
and h3, are directional, pointing to the corners
of a planar triangle in the yz-plane.
are formed from the mixing of the s orbital and the three
p orbitals. The four orbitals formed, h1, h2,
h3 and h4, are directional, pointing
to the vertices of a regular tetrahedron centered on the
origin. These orbitals are shown as arrows on the diagram
In water, there is sp3 hybridization,
forming two bonding orbitals, where the H-O-H bonding angle is
close to the tetrahedral angle of 109.5o (the reduction
to 104.5o can be explained by VSEPR),
and two non-bonding orbitals, which contain lone pairs of electrons.
Hence, each bonding orbital is described by a wavefunction with
This picture of the formation of the molecular orbitals
from hybrid atomic orbitals is a good approximation for the first
period elements, but lower down the periodic table, where the degree
of overlap between the s and p orbitals is smaller, the picture
of bonding through the original basis s and p atomic orbitals is
a better one.
Let us consider the series ethane,
ethene, and ethyne.
These have single, double and triple bonds between the C atoms respectively.
This can be explained in terms of the hybridization of the C(2s)
and C(2p) orbitals.
Ethyne, C2H2, forms three σ
bonds: they are H(1s)-C1(sp1), C1(sp1)-C2(sp1)
and C2(sp1)-H(1s). This means that the C atoms
are sp1 hybridized to form the linear sp1
orbitals shown above, and the ethyne molecule is linear.
The remaining p orbitals on C overlap to form a set of two π
bonding orbitals, which are degenerate, and so overall there are
three bonds between the C atoms.
Ethyne, C2H4, forms five σ
bonds: they are H(1s)-C1(sp2) (x2), C1(sp2)-C2(sp2)
and C2(sp2)-H(1s) (x2). This means that the
C atoms are sp2 hybridized to form the trigonal planar
sp2 orbitals shown above, and the ethene molecule is
therefore planar. The remaining p orbitals
on the C atoms overlap to form a π bonding
orbital and so overall there are three bonds between the C atoms.
The molecule as a whole is planar
as this geometry maximizes the amount of overlap between the C p
orbitals, and therefore creates the strongest π
In ethane, C2H6, both C atoms
are sp3 hybridized, so all the bonds in the molecule
are σ bonds. The three C-H and one C-C
bond about each C atom are tetrahedrally arranged, and the two tetrahedra
are joined by a shared vertex. The two tetrahedra are free to rotate
about the C-C axis.
Molecular Orbital diagrams of polyatomic species
In the diatomic species, in constructing the molecular
orbital diagram, we simply show the energies of the atomic orbitals
of the two species on either side of the diagram and the energies
of the molecular orbitals in the center. Lines are drawn to connect
the molecular orbitals with their basis atomic orbitals.
In the polyatomic case, it is not so simple, as we
would need more dimensions to show the overlap in this way. Instead,
the MO diagram is generally drawn with two sets of basis atomic
orbitals on either side, and again with the resultant molecular
orbitals in the center. These basis orbitals are hybrid orbitals
of the atoms, and reflect the symmetry of the molecule.
A simple MO diagram for water is as shown in the table.
|MO diagram for water
Thus we can see in the center of the diagram the
2 bonding orbitals (containing 4 electrons) the two non-bonding
orbitals (containing 4 electrons) and the 2 antibonding orbitals
(which are vacant) formed from the basis set of six O(2s), O(2p)
(x3) and H(1s) (x2) atomic orbitals.