Page 285 - Instant notes

H3
MOLECULAR ORBITAL THEORY OF
DIATOMIC MOLECULES I

Key Notes
Direct calculation of the molecular orbitals is possible only in the
+
case of H 2 . For more complex molecules, a range of
approximations must be made in order to predict the nature of the
molecular orbitals. In all cases, it is necessary to assume that the
nuclei are stationary relative to the motion of the electrons. This
is known as the Born-Oppenheimer approximation, and allows
the internuclear geometry and motion to be treated completely
separately from that of the electrons.
+
In all cases other than that of H 2 , the molecular orbitals may be
approximately derived from a linear combination of atomic
orbitals. The atomic wavefunctions are combined in a linear
combination to give a molecular orbital, ,
where c m is the mixing coefficient. c m may be varied for all the
atomic orbitals so as to minimize the energy of the resulting
molecular orbital. The variation principle states that the lowest
energy calculated orbital most accurately describes the actual
molecular wavefunction.
A molecular bonding orbital differs from the atomic orbitals from
which it is derived as it increases the probability of finding an
electron in the internuclear region. This reduces the free energy
of the electrons, and that of the molecule as a whole. Antibonding
molecular orbitals are derived by subtraction of one or more
atomic wavefunction from the others. The energy of the resulting
antibonding molecular orbital is greater than that of the atomic
orbitals, since a node in the internuclear electron density causes
an increase in the internuclear repulsion.
The stability of a molecule is heavily dependent upon the extent
to which the orbitals are allowed to overlap. The extent of the
orbital overlap is determined by the internuclear distance. At
relatively large separations, the energy decreases as the nuclei are
brought together, and the atomic orbital overlap increases,
whereas at low internuclear distances a repulsion term is
dominant. There is a point at which these two opposing effects
balance, and the molecule adopts its lowest free energy state. For
the antibonding orbital, there is a fully repulsive interaction
between the nuclei at any distance.