Page 288 - Instant notes

Physical chemistry 274

As with the bonding orbital, the probability function for this molecular orbital is given
by:
2
2
2
P(r)=(ψ(A)− (B)) dτ=ψ(A) dτ+ψ(B) dτ−2ψ(A)ψ(B)dτ
The negative term now corresponds to a decrease of electron density in the internuclear
volume of the molecule. The electron density decrease raises the energy of the molecule
above that of the free atoms. There is now a node—a line of zero electron density—in the
molecular orbital, between the two atoms (Fig. 1c).
It is usual to denote an antibonding orbital with an asterisk to distinguish it from the
bonding orbital. In the case, therefore, of two s orbitals interacting to form both a bonding
and an antibonding orbital, both molecular orbitals will be σ orbitals. The antibonding
orbital is denoted as σ*, allowing its immediate distinction from the bonding orbital, σ.

Potential energy curves

The degree of stabilization conferred on a molecule by the overlap of atomic orbitals is
heavily dependent upon the extent to which the orbitals are allowed to overlap. The
extent of the orbital overlap is in turn determined by the internuclear distance.
A potential energy curve may be plotted for a molecule, and is constructed by plotting
the energy of the molecule as a function of internuclear distance. For the bonding orbital
at relatively large separations, the energy decreases as the nuclei are brought together,
and the atomic orbital overlap increases. The total wavefunction for the molecule also
includes an internuclear repulsion term, which increases with increasing nuclear
proximity, and the energy of the