Preparing for the 3nd Class


For the third lecture, please (re)read pages 441-445.
For a great web tool for visualizing H2+ molecular orbitals please use
the applet available from the website: http://www.falstad.com/qmmo/
http://www falstad com/qmmo/
CHEMISTRY 2000
Topic #1: Bonding – What Holds Atoms Together?
Spring 2009
Prof. René Boeré
2
Are empty orbitals real? – Spectroscopy!
Recap: First-period diatomic molecules and ions

1*
1*

The energy of the photon, given by E = h, must match exactly the difference
in energy between filled and empty orbital levels (just as in atoms)
In H2, ultraviolet absorption band at 109 nm, = energy difference of 11.4 eV

*
Energy
1s
1s
1
Energy
1s
1s
1
1s
h
1s
 
H2



*
1s
The possible combinations of first-period diatomic molecules are:
H2H22He23+ He22+ He2+
He2
H2+ H2
i
n
t
e
n
s
i
t
y
Predict whether each can exist, and iff so what its bond order is.
The bond energy of H2 is 436 kJ/mol (one of the strongest-known
single bonds!) The bond energy of H2+ is 255 kJ/mol. The bond
energy of He2+ is 251 kJ/mol. Explain.
 
H2*
 maximum
109 nm


1s

Unlike atomic spectra, molecular spectra are broad “humps” because of the
quantization of rotational and vibrational energy
Sometimes “fine structure” is visible on the peaks
3
1
Molecular Orbitals of Homonuclear Diatomics

Molecular Orbitals of Homonuclear Diatomics
We can combine higher energy atomic orbitals in the same way.
Compare the 2 and 2* orbitals in F2 to the 1 and 1* orbitals
in H2:
1

or
1*

p orbitals can also be combined to make molecular orbitals. The
type of molecular orbital formed will depend on the orientation
of the p orbitals.
po
orbitals
b ta s tthat
at o
overlap
e ap head-on
ead o (usually
(usua y defined
de ed as tthe
e pz
orbitals) give  molecular orbitals:
1s
1s
2
2s

or
2*
2s
What is the difference?
5
Molecular Orbitals of Homonuclear Diatomics

Molecular Orbitals of Homonuclear Diatomics
p orbitals that overlap side-on (usually defined as the px or py

orbitals) give  molecular orbitals:

6
…and here are the pretty computer-generated pictures of those
orbitals:
Combinations between s and p orbitals may also be possible.
But CAUTION:
I strongly recommend that you spend a good bit of time with the
MO viewer applet, rotating the orbitals in three dimensions to really
understand their shapes, and practice sketching these MO’s.
7
8
2
Why Pi?


Molecular Orbitals of Homonuclear Diatomics
Think about the bonding in N2. Drawing a Lewis structure tells
us that the atoms are triple bonded and each has a lone pair.
Each N atom starts with ____ electrons – ____ core electrons
(which we ignore) and ____ valence electrons (____________).
We can rotate each atom as much as we want, but we will
never be
b able
bl to position
i i them
h
such
h that
h we can make
k three
h

bonds. At best, we could make two  bonds, one with the 2s
orbitals and one with a pair of 2p orbitals:


Which p orbital combines with which other p orbital is symmetrydetermined. Since orthogonal orbitals on different atoms don’t
combine, you won’t see combination of a px orbital on one atom
and a py orbital on its neighbour, for example.
s orbitals can combine
with p orbitals when making
 MOs if the orbitals are
Figure courtesy of Prof. Marc Roussel
close enough in energy.
The figure at the right shows
2s and 2p atomic orbital
energies for the elements in
period 2
2. We can see that
there will be little mixing
between 2s and 2p orbitals
for the heavier elements in period 2.
Using
g  orbitals,, we can find a wayy to make a triple
p bond:
9
Choosing the right basis set

1.
2.
Molecular Orbitals of Homonuclear Diatomics
All atoms have infinite numbers of possible wavefunctions: which
should we use to make bonds. There are two guiding principles:
Those orbitals which are closest to each other in energy will
undergo the greatest amount of interaction.
Only orbitals within a narrow range of energy have the right
properties to undergo significant interaction – the valence
orbitals
0
H
He
Li
Be
B
C
N
O
F
Ne
Na
480
3s
2s
960
2s
1440
1s
2p

O, F and Ne have large enough energy gaps between their 2s and 2p
orbitals that they give the “normal” (valence) MO diagram:
p
bring together
E
N
E
R
G
Y
2u (2p)*
1g (2p)*
2p
2p
2g (2p)
2p
2s
2p
1u (2p)
VALENCE ZONE
2p
1920
2p
2s
1u (2s)*
2p
2400
1s
2s
2p
2880
3360
3840
10
2s
2s
2s
1s
1g (2s)
Energy level diagram
4320
S
12
3
What happens to the “core” orbitals in N2?

Molecular Orbitals of Homonuclear Diatomics
Each N atom has the electron configuration 1s22s22p3. The 1s level is
“core”.

O, F and Ne have large enough energy gaps between their 2s and
2p orbitals that they give the “normal” (valence) MO diagram:
MO description of 2nd row homonuclear diatomic molecules
bring together
E
N
E
R
G
Y
2u (2p)*
1g (2p)*
2p
2p
1u (2p)
2g (2p)
1u (2s)*
1 in H2
1 in H2
2s
1 in N2
1 in N2
1g (2s)
14
MO description of 2nd row homonuclear diatomic molecules
2u (2p)*
Mixing in some “p character” lowers the energy of the 2* MO
instead of
E
N
E
R
G
Y
Mixing in some “s character” raises the energy of the 3 MO
2u
Relative order may vary here
1g (2p)*

Sigma and pi overlap leading to bonding and antibonding MO's
Molecular Orbital Diagrams of Homonuclear
Diatomics with the two observed energy sequences
Because Li, Be, B, C and N have smaller energy gaps between
their 2s and 2p orbitals, some mixing is observed when forming
the  and * orbitals, primarily 2* and 3:

Energy level diagram
13
Molecular Orbitals of Homonuclear Diatomics

2s
2p
2p
1g (2p)*
1u (2p)
Varying
degree
of s-p
separation
2p
2g (2p)
2g
Less s-p
separation
1u (2s)*
2p
1u (2p)
1u
instead of

2s
2s
2s
2s
1g (2s)
If this effect is strong enough, the 3 orbital can end up higher
in energy than the 1 orbital, giving the MO diagram on the
next page. This is the case in Li2, Be2, B2, C2 and N2.
1g
Energy levels in original diatomic construction
15
Energy levels in re-mixed diatomic
16
4
Applying the theory

Applying the theory (2)
Now determine possible bonding (or non-bonding) descriptions for all
the second-row element diatomic molecules






Li2
Be2
B2
C2
N2
Now determine possible bonding (or non-bonding) descriptions for all
the second-row element diatomic molecules



O2
F2
Ne2
17
Properties of known 2nd row diatomics
18
Application – Unexpected behaviour in O2



Property
Li2
Be2
B2
C2
N2
O2
F2
Bond
length
(Å)
2.67
–
1.59
1.24
1.10
1.21
1.42
Bond
energy
(kJ mol–1)
110
–
272
602
941
493
138
1
0
1
2
3
2
1
Bond order
Write the Lewis diagram for O2:
Yet the MO diagram predicts the following
valence electron configuration:
What evidence can we use to decide the
better description of the bonding?
20
5