Transcript Chemistry 3722

The Chemical Bond I
Bonds as Orbital Overlap
Molecular Orbital Diagrams
Hybridization
Additional Bonding Schemes
Atomic Orbitals and Orientation

We’ve solved hydrogen-like atoms and found the orbital shapes
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Let’s get the orientation of each down
z
x
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z
Rotate
by 45°
y
y
Our orbitals had no specific orientation, except with respect to each
other
We’ll use some alternate pictures that have a specific orientation
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For example:
 2 pz  2p z   210
1


2
 2 px  2p x 
 2 py  2p y 
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2,1,1
  2,1,1 
1
i


2
2,1,1
  2,1,1 
 2,1,1
px
( X  Y  Z)
( X  Y  Z)
Chapter 12
2
Orbitals Pictures
We’ll picture the orbitals in this way
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s
py
pz
s
dz
Two
different
phases
2
dx
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2
d yz
y 2
In terms of energy, we write these as an energy level diagram
d x y
dz
d xy
d yz
d xz
E
2
2
px
2
py
pz
s
CHEM 3722
Chapter 12
3
The Energetics of Bonding I
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Can imagine the bonding process in terms of bringing two hydrogen
atoms together from far away
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As they approach, the E lowers as the atomic orbitals begin to interact
The interaction is composed of (1) nuclear-nuclear repulsion, (2)
electron-electron repulsion, and (3) electron-nuclear attraction
The most stable distance (minimum energy on this potential energy
curve) is where the attractions outweigh the repulsions
Increased electron
density between
the nuclei stabilizes
the molecule!
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Chapter 12
4
The Energetics of Bonding II
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But, need to know why an atom would bond?
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All bonds result in the lowering of energy of the electrons in the system
Not all electrons are lowered in energy, but the net result is a more
stable arrangement of the electrons
Consider the H2 molecule
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Each has one occupied orbital: 1s
Let’s ‘watch’ the energy change
Region of energy
where two electrons
can reside
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Atomic orbital
But what about He2?
Result of bonding
There is no net E-loss in
this alteration of electron
energies. That is, the
energy released in
lowering 2 e- is used to
promote the other 2.
Thus, this bond doesn’t
happen: nonbonding!
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Called molecular orbitals. Formed
from the two atomic orbitals
interacting. Note that the net effect
is two lower energy e-’s.
Chapter 12
5
Molecular Orbitals I
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To picture the MO’s, consider them as the “overlap” of the AO’s.
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Phase of overlap matters
Overlap of s-orbitals
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Since made from s-orbitals, we’ll denote this MO in similar terms
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Call the overlap a s molecular orbital
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But, we’ll use Greek letters for bonds
If overlap is out of phase, then we’ll denote it as an antibonding orbital (s*)
Other orbital can overlap similarly
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Look at p and s
Internuclear axis
s*
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s
Chapter 12
If overlap is along this axis,
then the MO formed is s.
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Molecular Orbitals II
In terms of
probability, we can
see that bonding
regions show an
enhanced electron
density between
the two nuclei. The
probability is high
that the electronnucleus attraction
will keep nuclei
together.
Antibonding regions
show a reduced
electron density
between the nuclei,
and thus the
electron-nucleus
attraction is away
from the stable
bond length.
CHEM 3722
Chapter 12
7
Molecular Orbitals III
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Any set of orbitals that overlap along the internuclear axis are
considered to be s bonds.
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And the antibonding MO is a s* bond
Here are a few other examples
s*
py  py
=
s
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Can also make a s-bond with d-orbitals
y
dx
2
y 2
 d x 2 y 2
x
CHEM 3722
Chapter 12
8
Molecular Orbitals IV
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Any set of orbitals that
overlap perpendicular to the
internuclear axis are said to
p-bond
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The antibonding orbital is p*
Any set of orbitals that
overlap at any other angle to
the internuclear axis are said
to d-bond
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The antibonding orbital is d*
Best example is two dyz
orbitals
CHEM 3722
Chapter 12
9
Putting It All Together
Carbon Monoxide
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First draw Lewis Dot Structure
O
This shows 3 bonding pairs (between nuclei) and 2 nonbonding pairs
Expect a s, a p and another p bond
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C
Now consider orientation and orbitals involved (we’ll draw 2 of 3
dimensions)
This should match Lewis Structure
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We see py-py overlap forming s bond
We see p bonds in px-px and pz-pz overlap
p-bond
pz
C
O
s-bond
px
In the other p
In the other p*
CHEM 3722
Chapter 12
10
More Diatomic MO-Diagrams
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Homonuclear diatomics show a slight change as Z increases
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p mo’s appear before s mo’s until Z = 7 (Nitrogen)
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Chapter 12
11
Polyatomic Molecules
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MO’s are easy to create for diatomics
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Things get tougher if we add atoms
Take AlCl3 as an example
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Doesn’t obey octet rule
Lewis dot structure shows three single bonds
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Thus, three s bonds
Cl
Structure looks like this:
Al
Cl
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How do p-orbitals arrange themselves this way and stay orthogonal?
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Don’t appear to be perpendicular
Make a basis set of the H-like atomic orbitals & make new orbitals
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Cl
Requires us to make linear combinations of atomic orbitals to make NEW
atomic orbitals
Call this hybridization
But why? Can we justify this?
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Chapter 12
12
Hybridization
Cl has it’s p-orbitals ready to bond to the Al, but Al has two types of
valence orbitals available: s and p (px, py, pz)
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This means that the lowest energy orbital available for overlap is the s.
But, only one Cl can bond with this orbital
To make three equal energy orbitals available to the Cl’s, Al “hybridizes”
Energy
p

p
p
p
sp2
s
So we use the H-like orbitals to generate
three different but energetically equivalent
atomic orbitals
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In math terms, the linear combinations are…
sp 2 


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Chapter 12
sp2
sp2
1
s
2
pz
3
s
1
1
py  pz
4
2
s
1
1
py  pz
4
2
3
1
3
1
3
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sp2 hybrids and AlCl3
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We can picture the hybrid orbitals as spreading out perpendicular to
the remaining p-orbital
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They are in the xy-plane
Three lobes must get as far apart as possible
This is a trigonal planar arrangement of hybrid orbitals
Can see how the orbitals ‘do’ this pictorially, too
sp2 hybrid orbital
of Aluminum
p-orbital of Chlorine
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Chapter 12
14
sp hybrids
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If need two identical bonding orbitals, use an s and a p orbital in an
sp hybrid
 For example, LiH2
1
sp 
(s  p z )
2


1
2
(s  p z )
Pictorially, the linear combination goes like
CHEM 3722
Chapter 12
15
Multiple Bonds
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In sp and sp2 hybridization, there remains a p-orbital (or two)
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Can this orbital involve itself in some sort of bonding?
Sure, but not along the internuclear axis, so must be p-bonding!
This is the basis for double and triple bonds
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For example, consider ethane
CHEM 3722
Chapter 12
16
sp3 hybrids
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If need four identical bonding orbitals, use an s and all three p orbitals in an
sp3 hybrid
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For example, H2O
sp 3  1 (s  p x  p y  p z )
2
 1 (s  p x  p y  p z )
2
 1 (s  p x  p y  p z )
2
 1 (s  p x  p y  p z )
2
O
H
H
O
H
H
CHEM 3722
Chapter 12
17
Other Bonding Types
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So far, only showed covalent bonding
Other bonds
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Metallic
Ionic
Coordinate Covalent
Three center, two electron bonds
Ionic Bonds
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Purely Coulombic interactions
Electrons are not “shared” they are transferred (in a sense)
NaCl is perfect example
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NaCl = Na+--Cl- or Na---Cl+
We know first ionic species is best, but both are probably present in any
sample
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CHEM 3722
NaCl has character of both, but has mainly the character of Na+ -- Cl-
Chapter 12
18
Coordinate Covalent
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Often the e’s shared in a covalent type bond don’t come from both
atoms, but instead from one atom, molecule, or ion
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For Example: W(CO)6
Usually occurs with a transition metal as central atom (d-orbitals are
the key)
O C
M
CO-M sigma bond
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O
C
M
M to CO pi backbonding
O C
M
CO to M pi bonding
(rare)
Species that donates both electrons is called a ligand
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CO and O2 are both ligands for Hemoglobin, and this is why CO can
suffocate you when inhaled in great amounts
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Not only is it a substitute ligand, it also bonds better because the O can pull
electron density from the C. This makes the Carbon antibonding MO a better
electron donar AND it makes the ‘backbonding’ more stabilizing
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CHEM 3722
Backbonding is the donation of electron density of the metal back to the ligand
In regular O2, the nonpolar nature of the molecule limits these effects
Chapter 12
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3 Center, 2 Electron Bonds
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Most bonds are between two atoms
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They are 2 center, 2 electron bonds (2c-2e bonds)
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A center is a nucleus
3c-2e bonds occur when two electrons hold together 3 nuclei
Most common examples: Al2H6 and B2H6
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The second is called diborane
BH3 is hard to make because diborane is so stable in comparison
Orbital overlap looks like
H
H
H
B2
B1
H
sp3 hybrid orbital of boron 1
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s-orbital of H
Chapter 12
H
H
sp3 hybrid orbital of boron 2
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