 2.1. H2 and He2 - the Simplest Examples The simplest
example of the LCAO approximation is the combination of
two s-AOs to form s-
(bonding) and s*- (antibonding) MOs. This is shown
in Figure 2.2 for the dihydrogen molecule. Figure 2.2a
shows the simple orbital
interaction diagram, whereas Figure 2.2b shows 3D-electron density contour
plots for
the AOs and MOs.
It is useful
to define the conventions used in Figure 2.2a and all
other orbital interaction diagrams in this book. The
thick horizontal lines represent orbital energy levels
and, although it is not explicitly shown, the diagram
implies a vertical energy scale. The dashed connecting
lines signify orbital interactions. Thus, the two s-orbitals,
which have the same energy, interact with each other to
form the s- and s*-MOs.
The s-MO is stabilised by DE1
relative to the energy level of the two AOs and the s*-MO is destabilised by DE2. It is
important to note that DE1 is always slightly
smaller than DE2. If we now add
the electrons to the orbital interaction diagram, we find
that H2, with two electrons (see Figure 2.3a),
can form a closed-shell singlet state in which the
electrons are paired in the stabilized s-orbital to give a strong bond (the total
energy of the two electrons is lower than in the two
separated atoms). If, however, we consider He2,
with four electrons (see Figure 2.3b), we must doubly
occupy both the s- and the s*-orbitals.
Because E1 is smaller than E2, this
situation gives a higher energy than for the four
electrons in the two separated atoms. He2 thus
does not form a bond.
The
stabilisation and destabilisation energies, E1
and E2, depend on the overlap between the AOs. The closer the
two atoms approach each other, the larger the overlap and
the larger the energy splitting. This effect can be
tested using demonstration 1.
H2 and He2 -The
Simplest Examples |
