Chemistry Reference
In-Depth Information
core orbitals becomes tiresome, and so it is common practice to list the equivalent ideal gas
symbol for the core electrons and then only quote the detail of the valence orbitals, so that:
O: 1s
2
2s
2
2p
4
becomes
O: [ He] 2s
2
2p
4
S: 1s
2
2s
2
2p
6
3s
2
3p
4
becomes
S: [ Ne] 3s
2
3p
4
and
Se: 1s
2
2s
2
2p
6
3s
2
3p
6
3d
10
4s
2
4p
4
becomes
Se: [ Ar] 3d
10
4s
2
4p
4
This makes it easier to recognize why atoms from the same group of the periodic table,
such as these examples, have similar chemical properties.
The radial node in the 2s function gives it a minor peak in the probability density below
the Bohr radius, which is not present for 2p. This means that a 2s electron will spend more
time close to the nuclear centre than will one in a 2p atomic orbital. This, in turn, implies
that the 2s orbital has a lower energy than the 2p orbital. The main peak in 2s is at just
under 3 Å, a little beyond the peak in the 2p radial function; so, despite its lower energy, it
is still available to mix with orbitals from neighbouring atoms in molecules.
These pictures of the orbital radial probabilities will be useful in understanding the
relative energies of the AOs in the next section.
7.3.2 The Relative Energies of Atomic Orbitals in Different Elements
For the MO diagram of H
2
in Figure 7.10 the atomic energy levels for the two atoms are
drawn at the same level, since they are identical atoms. For molecules containing atoms of
different types we must estimate the relative energy of the constituent atomic states.
There are experimental probes of the electronic energy levels of atoms and molecules.
Perhaps the simplest is provided by the ionization energies of the elements which have
been obtained by determining the photon energies required to eject electrons from essen-
tially isolated (gas-phase) atoms. The photon energy is simply related to the light frequency
ν
(s
−
1
) by the Planck constant
h
. For example, by measuring the lowest frequency radiation
with which it is possible to ionize Li atoms, we are probing the ionization event
Li( 2s
1
)
Li
+
(2s
0
)
e
−
+
h
ν
→
+
(7.25)
To a first approximation, the lowest photon energy
hf
at which ionization occurs gives a
direct estimate of the energy of the orbital from which the photoelectron was ejected. For
atoms with occupied 2p orbitals there are two primary ionization energies; for example,
carbon can be ionized as follows:
C( 2s
2
2p
2
)
+
ν
s
→
C
+
(2s
2
2p
1
)
+
e
−
h
(7.26)
or,
C( 2s
2
2p
2
)
C
+
(2s
1
2p
2
)
e
−
+
h
ν
p
→
+
(7.27)
where the subscripts s and p indicate that the required energy to ionize from a 2s state will
be different from that required to ionize a 2p electron.
