Page 78 - Science at the nanoscale

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RPS: PSP0007 - Science-at-Nanoscale
June 12, 2009
From Atoms and Molecules to Nanoscale Materials
68
z
z
z
y
y
y
x
x
x
s
p
p
x
y
Combined to generate
3
four sp hybrid orbitals
3
Figure 4.6.
Schematic showing the formation of sp hybridised orbitals.
We next consider the MO formation of a simple compound such
as methane CH 4 . In this case, MO theory predicts that the most
favorable interaction occurs only when both the C2s and 2p AOs
are involved in bonding with the H 1s orbitals:
H
C
Qualitatively, we can view the mixing of one C2s and three C2p
AOs as hybridised orbitals, hence giving rise to four sp orbitals
oriented in a tetrahedral arrangement (Fig. 4.6):

′

= c H ψ (1s) + c
(4.5)
Ψ σ Ψ (σ) = c H ψ (1s) + c x C(s) 3 ψ (2s) + c y C(p) ψ (2p) C C p 3 z z (4.4) ch04
ψ (2s) + c ψ (2p)
3
sp
C
H
C(sp )
The relative orientation of these hybridized orbitals thus deter-
mines the tetrahedral arrangement of the four C–H bonds in
methane. For more complex molecules, appropriate sets of MOs
can be iteratively determined using one-electron functions and by
minimizing the total energy of the system. The topic of MO calcu-
lation is beyond the scope of this introductory text and the read-
ers are referred to the many published MO references for further
details.
When two atoms are not similar, e.g. in the H–Cl molecule,
the electron distribution is no longer symmetrical but lies more
towards the atom with the higher electron affinity. In this case,