the chemical bond i bonds as orbital overlap molecular orbital diagrams hybridization additional...
TRANSCRIPT
The Chemical Bond I
Bonds as Orbital OverlapMolecular Orbital DiagramsHybridizationAdditional Bonding Schemes
CHEM 3722 Chapter 12 2
Atomic Orbitals and Orientation We’ve solved hydrogen-like atoms and found the orbital
shapes Let’s get the orientation of each down
Our orbitals had no specific orientation, except with respect to each other
We’ll use some alternate pictures that have a specific orientation For example:
2 210
2 2,1,1 2,1, 1
2 2,1,1 2,1, 1
2
12
21
22
z
x
y
p z
p x
p y
p
p
pi
y
zz
yx
Rotate by 45°
X Y Z( )
X Y Z( )
2,1,1xp
CHEM 3722 Chapter 12 3
Orbitals Pictures We’ll picture the orbitals in this way
In terms of energy, we write these as an energy level diagram
ypzp
2zd
2 2x yd
yzd
s
Two different phases
s
E
2zd 2 2x y
d yzdxyd
xzd
s
yp zpxp
CHEM 3722 Chapter 12 4
The Energetics of Bonding I Can imagine the bonding process in terms of bringing two
hydrogen atoms together from far away 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 Increased electron density electron density
between the between the nuclei stabilizes nuclei stabilizes the molecule!the molecule!
CHEM 3722 Chapter 12 5
The Energetics of Bonding II But, need to know why an atom would bond?
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 Each has one occupied orbital: 1s Let’s ‘watch’ the energy change
But what about He2?
Atomic orbitalRegion of energy
where two electrons can reside
Result of bonding
Called molecular orbitals. Formed from the two atomic
orbitals interacting. Note that the net effect is two lower
energy e-’s.
There is no net E-loss There is no net E-loss in this alteration of in this alteration of electron energies. electron energies. That is, the energy That is, the energy
released in lowering 2 released in lowering 2 ee-- is used to promote is used to promote
the other 2. Thus, this the other 2. Thus, this bond doesn’t happen: bond doesn’t happen:
nonbonding! nonbonding!
CHEM 3722 Chapter 12 6
Molecular Orbitals I To picture the MO’s, consider them as the “overlap” of the
AO’s. Phase of overlap matters
Since made from s-orbitals, we’ll denote this MO in similar terms But, we’ll use Greek letters for bonds
Call the overlap a molecular orbital If overlap is out of phase, then we’ll denote it as an antibonding
orbital (*) Other orbital can overlap similarly
Look at p and s
Overlap of s-Overlap of s-orbitalsorbitals
Internuclear axisInternuclear axis
If overlap is along this If overlap is along this axis, then the MO formed axis, then the MO formed isis ..
CHEM 3722 Chapter 12 7
Molecular Orbitals IIIn terms of
probability, we can see that
bondingbonding regions show an
enhanced electron density between the two
nuclei. The probability is high that the electron-
nucleus attraction will keep nuclei together.
AntibondingAntibonding 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 8
Molecular Orbitals III Any set of orbitals that overlap along the internuclear axis
are considered to be bonds. And the antibonding MO is a * bond
Here are a few other examples
Can also make a -bond with d-orbitals
x
y2 2 2 2x y x y
d d
=
py py
CHEM 3722 Chapter 12 9
Molecular Orbitals IV Any set of orbitals that
overlap perpendicular to the internuclear axis are said to -bond The antibonding orbital is
* Any set of orbitals that
overlap at any other angle to the internuclear axis are said to -bond The antibonding orbital is
* Best example is two dyz
orbitals
CHEM 3722 Chapter 12 10
Putting It All Together Carbon Monoxide
First draw Lewis Dot Structure This shows 3 bonding pairs (between nuclei) and 2 nonbonding pairs Expect a , a and another bond
Now consider orientation and orbitals involved (we’ll draw 2 of 3 dimensions) This should match Lewis Structure
We see py-py overlap forming bond
We see p bonds in px-px and pz-pz overlap
C O
C O
-bondpz
px
-bond
In the other *
In the other
CHEM 3722 Chapter 12 11
More Diatomic MO-Diagrams Homonuclear diatomics show a slight change as Z increases
mo’s appear before mo’s until Z = 7 (Nitrogen)
CHEM 3722 Chapter 12 12
Polyatomic Molecules MO’s are easy to create for diatomics
Things get tougher if we add atoms Take AlCl3 as an example
Doesn’t obey octet rule Lewis dot structure shows three single bonds
Thus, three bonds Structure looks like this:
How do p-orbitals arrange themselves this way and stay orthogonal? Don’t appear to be perpendicular
Make a basis set of the H-like atomic orbitals & make new orbitals Requires us to make linear combinations of atomic orbitals to
make NEW atomic orbitals Call this hybridization
But why? Can we justify this?
AlClCl
Cl
CHEM 3722 Chapter 12 13
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) 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”
So we use the H-like orbitals to generate three different but energetically equivalent atomic orbitals In math terms, the linear combinations
are…
2 1 233
1 1 14 23
1 1 14 23
z
y z
y z
sp s p
s p p
s p p
Energ
y
s
p pp
sp2 sp2 sp2
p
CHEM 3722 Chapter 12 14
sp2 hybrids and AlCl3 We can picture the hybrid orbitals as spreading out
perpendicular to the remaining p-orbital 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 orbitalof Aluminum
p-orbital of Chlorine
CHEM 3722 Chapter 12 15
sp hybrids If need two identical bonding orbitals, use an s and a p
orbital in an sp hybrid For example, LiH2
1( )
2
1( )
2
z
z
sp s p
s p
Pictorially, the linear combination goes like
CHEM 3722 Chapter 12 16
Multiple Bonds In sp and sp2 hybridization, there remains a p-orbital (or
two) Can this orbital involve itself in some sort of bonding? Sure, but not along the internuclear axis, so must be -bonding!
This is the basis for double and triple bonds For example, consider ethane
CHEM 3722 Chapter 12 17
sp3 hybrids If need four identical bonding orbitals, use an s and all three p
orbitals in an sp3 hybrid For example, H2O
OHH
3 1 ( )2
1 ( )2
1 ( )2
1 ( )2
x y z
x y z
x y z
x y z
sp s p p p
s p p p
s p p p
s p p p
H
H
O
CHEM 3722 Chapter 12 18
Other Bonding Types So far, only showed covalent bonding Other bonds
Metallic Ionic Coordinate Covalent Three center, two electron bonds
Ionic Bonds Purely Coulombic interactions Electrons are not “shared” they are transferred (in a sense) NaCl is perfect example
NaCl = Na+--Cl- or Na---Cl+
We know first ionic species is best, but both are probably present in any sample NaCl has character of both, but has mainly the character of Na+ -- Cl-
CHEM 3722 Chapter 12 19
Coordinate Covalent Often the e’s shared in a covalent type bond don’t come
from both atoms, but instead from one atom, molecule, or ion For Example: W(CO)6
Usually occurs with a transition metal as central atom (d-orbitals are the key)
Species that donates both electrons is called a ligand CO and O2 are both ligands for Hemoglobin, and this is why CO
can suffocate you when inhaled in great amounts 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 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
CHEM 3722 Chapter 12 20
3 Center, 2 Electron Bonds Most bonds are between two atoms
They are 2 center, 2 electron bonds (2c-2e bonds) A center is a nucleus
3c-2e bonds occur when two electrons hold together 3 nuclei
Most common examples: Al2H6 and B2H6
The second is called diborane BH3 is hard to make because diborane is so stable in
comparison Orbital overlap looks like BB
H
H
HHH H
sp3 hybrid orbital of boron 2
sp3 hybrid orbital of boron 1
s-orbital of H
21