Chemistry - A Molecular Science

Chapter 6 Molecular Structure & Bonding

Figure 6.12 Bonding in O

(^2)
(a) Lewis structure of O

. (b) Head-on overlap of the two p 2

(^) z
orbitals produces a
σ-bond, while side-on overlap of the two p
(^) y
orbitals produces a
π-bond.
poverlap p
overlap
s
overlap
z
y
OO
(a) (b)
O^2
is a diatomic molecule that contains both
and σ
bonds. The valence electron π
configuration of an oxygen atom is 2s
2 2p
4 , so there are paired electrons in the 2s and one
of the 2p orbitals. The unpaired electrons in an
oxygen atom lie in the other two p orbitals.
In Figure 6.12, the unpaired electrons are assumed to be in the p
and pz
orbitals. As the y
atoms approach along the z-axis, the p
orbitals of the two oxygen atoms overlap in an z
end-on fashion (orange line) to produce a
bond, while the pσ
orbitals overlap side-on y
(both violet lines) to produce a
bond. Thus, the O=O double bond consists of one π
and σ
one
bond. π
All bonds contain one and only one sigma bond

. Double bonds contain one

(^) σ
and one
bond. Triple bonds contain one π
and two σ
π
bonds.
The bond order of a bond is
simply the sum of the number of
and σ
bonds that it containsπ
.
ORBITAL MIXING AND HYBRIDIZATION The simple overlap of atomic orbitals used for diatomic molecules cannot be used for larger ones. Consider the molecule formed
between a carbon atom and hydrogen atoms.
Carbon has a valence electron configuration of 2s
2 2p
2 , so it has two unpaired electrons in
its p orbitals. If carbon used only atomic orb
itals with one electron, its compound with
hydrogen would be CH
, and the H-C-H bond angle would be 90 2
o (the angle between two
p orbitals). However, the simplest compound involving carbon and hydrogen is CH
, 4
which has 109
o bond angles. In order to account for molecular geometries in the valence
bond model, we must use a different set of orbitals on the central atom. These new orbitals are produced by
mixing
the atomic orbitals, but before
discussing these new orbitals, we
need to examine the process of mixing.
Recall from Chapter 2 that atomic orbitals describe algebraic functions that are
solutions to an atom’s wave equation. Mixing
orbitals is the mathematical combination of
these functions by addition and/or subtracti
on. Consider the two combinations of the
functions P and Q shown in Figure 6.13. Re
gions where the functions are positive are
shaded in blue, while negative regions are shown
in red. This is consistent with our use of
these colors to describe the sign of orbital func
tions. In Figure 6.13a, the two functions are
added to produce function R = P + Q. R is
amplified on the ends because both P and Q
have the same phase (sign) there, but it is
reduced dramatically in
the center because the
phases of P and Q are opposite there. We conclude the following:
Adding regions of the same phase (blue + blue) is
constructive
and produces a region of
increased amplitude, while adding regi
ons of opposite phase (blue + red) is
destructive
and produces a region of decreased or even annihilated amplitude.
To obtain the difference S = P - Q in Figure 6.13b, the phase of Q is reversed (its sign is
P Q
R=P
+Q
P
-Q
S=P
+(

• Q
  )=P

-Q

(a) (b)

Figure 6.13 Mixing two functions Regions where P and Q have the same phase add constructively, while regions of different phase add destructively. (a) P + Q = R

: Both P and Q have the same phase on the two

ends but opposite phases in the center. Thus, R has enhanced wings and an annihilated center. (b) P – Q = S

: The phase of Q is reversed to produce –Q, which is

then added to P. The wings have opposite phase and add destructively, while the centers have the same phase and add constructively.

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