Transcript CHE 106 Chapter 9x

CHE 106
CHAPTER NINE
MOLECULAR GEOMETRY
AND BONDING
THEORIES
Molecular Geometry
Some helpful definitions:
Bond Distance: the distance, usually given in Angstroms
or pm, between two bonded atoms.
Bond Angle: The angle formed between three bonded
atoms.
Molecular Geometry
Lewis structures are used to show us the way atoms are
arranged, but they leave much to be desired in
describing how molecules appear in three dimensional
space.
The easiest types of molecules to study are those with a
central atom, surrounded by varying number of
peripheral atoms: An.
The number of B atoms are large factor in determining
the shape.
Molecular Geometry
In general:
AB2: Linear or Bent with a bond angle of 180o.
AB3: Trigonal Planar or Trigonal Pyramidal: less than 180o.
Trigonal Planar: Bond angles of 120o and all elements
are in the same plane.
Trigonal Pyramidal: Angles of 109.5o and the central
atom is set above the three peripheral.
AB4: Tetrahedral, 109.5o.
The main goal of all of the different shapes it to get pairs of
electrons as far away from each other as possible.
Molecular Geometry
Valence Shell Electron Pair Repulsion Theory
Electrons repel one another because they are the same
charge. Our goal is to arrange electron pairs around atoms
to maximize the distance between them and minimize
repulsions.
AXE Notation:
A = Central Atom
X = number of bond pairs of electrons
E = number of lone pair of electrons
Molecular Geometry
Wherever electrons are found – bonding or non-bonding
are sometimes referred to as electron domains.
The electron domain geometry is a good place to start as
you work towards molecular geometry. Electron domain
considered all electron pairs while molecular geometry is
only concerned with the bonding pair of electrons.
Helpful tip: multiple bonds are still only considered one
electron domain.
Molecular Geometry

2 electron pairs: AX2 E0
Molecular Geometry

3 electron pairs: AX3E0
Molecular Geometry

4 electron pairs: AX4E0
Molecular Geometry

5 electron pairs: AX5E0
Molecular Geometry

6 electron pairs: AX6E0
Molecular Geometry
-Determine Lewis Structure
-Determine number of electron pairs around the central
atom
-Determine AXE notation
-Assign structure based upon parent structure and
minimizing repulsions
-Determine any distortions in bond angles.
Molecular Geometry: 2 pairs
AXE:
AX1E0: Linear
AX2E0: Linear
AX1E1: Linear
Molecular Geometry: 3 pairs
AX3E0: Trigonal Planar
AX2E1: Bent
AX1E2: Linear
Molecular Geometry: 4 pairs
Four electron domains around the central atom should
give rise to a tetrahedral arrangement. However, when
we look at molecules with 4 electron domains – but
varying number of bonding / lone pair – the bond
angles differ. H2O, NH3, CH4.
Draw the Lewis dot structures for the 3 molecules.
Compare their geometry.
Molecular Geometry: 4 pairs
Because of the presence of lone pair of electron in
ammonia and water, the bonded atoms are forced to
get closer and the bond is more compressed. The
bond angles get a little smaller.
Nonbonding electrons take up more space because they
feel less nuclear attraction. This results in more
repulsive forces and compressed bond angles.
Molecular Geometry: 4 pairs
AX4E0: Tetrahedron
Molecular Geometry: 4 pairs
AX3E1: Trigonal Pyramidal
Molecular Geometry: 4 pairs
AX2E2: Bent
Molecular Geometry: 5 pairs
When the central atom has 5 pairs, the electrons pairs can
assume one of two positions: axial or equatorial.
Axial: forms 90o angels with all equatorial domains
Equatorial: forms 120o angles with other two equatorial
domains, and 90o angles with axial.
When determining where the lone pair of electrons will
exist - they always will occupy an equatorial position
because there is less repulsive force there.
Molecular Geometry
Molecular Geometry: 5 pairs
AX5E0: Trigonal bipyramidal: two triangle pyramids
face to face.
AX4E1: See Saw
Molecular Geometry: 5 pairs
AX3E2: T Shaped
AX2E3: Linear
Molecular Geometry: 6 pairs
AX6E0: Octahedron
Molecular Geometry: 6 pairs

AX5E1: Square Pyramid
Molecular Geometry: 6 pairs
AX4E2: Square Planar
AX3E3: T Shaped
Molecular Geometry
Example: BF4-2 vs. XeF4
BeF4-2: AX4E0: Tetrahedron
XeF4: AX4E2: Square Planar
Molecular Geometry
Examples: I3 and SeF4
I3: AX2E3 : Linear
SeF4: AX4E1: See Saw
Molecular Geometry
Some exceptions:
Even though we count a double bond as 1 electron domain,
a double or triple bond does influence the bond angles.
Double and triple bonds take up more space, so the bond
angles will be slightly smaller than expected.
Example: COCl2
Molecular Geometry
Examples:
OF2
ClO2-1
BF3
PBr3
TeCl4
BrO4-1
SnCl4
SF6
XeOF4
Molecular Geometry
It is slightly more difficult to
determine bond angles for
larger molecules, but we can
still hone in on certain atoms to
help us get an idea of the three
dimensional molecule.
Determine the bond angles
around the three back bone
elements in CH3COOH.
Molecular Geometry

Vinyl Alcohol: CH2CHOH

Predict bond angles in Propyne
Molecular Polarity
Bond polarity is determined by electronegativity and is
a measure of how the electrons in a bond are being
shared. Expressed as dipole moments.
Molecular polarity depends on the polarity of each
bond as well as the molecular geometry. The overall
dipole moment of the molecule is the sum of each
dipole.
Molecular Polarity
Dipoles are vector quantities: both magnitude and charge.
When we add them together, we have to consider both.
Explains why CO2 is non polar and H2O is polar.
Molecular Polarity
BF3 vs. NH3
Molecular Polarity
Predict whether the following molecules are polar or
non polar:
BrCl, SO2, SF6
Orbital Overlap
In Lewis theory – covalent bonds are formed when two
nuclei are simultaneously attracted a pair of electrons.
The electron density is found between the two nuclei.
Valence Bond Theory: a chemical bond is described as
the overlap of atomic orbitals, with electrons of
opposite spins sharing space in the orbital.
Orbital Overlap
Other examples that are easy to study: HCl, Cl2.
Orbital Overlap
As the atomic orbitals overlap, there is a relationship
between the potential energy, stability and bond length
of the molecule.
As the atomic orbitals approach one another, there PE
decreases, because they are becoming more stable.
After a certain point, they get too close and the
repulsive forces take over and cause a spike in energy.
The bond length is the inter-nuclear distance that
corresponds to the minimum energy on the PE curve.
Orbital Overlap
Hybrid Orbitals
If we consider the the molecule methane: CH4
Carbon orbital diagram:
Hydrogen orbital diagram:
If you look at carbons orbital diagram, it would suggest
that carbon can only form 2 bonds. However, it often
will surround itself with 4 bonds. How is that
possible?
Hybrid Orbitals
One explanation would involve promoting one of the 2s
electrons to the empty 2p orbital – giving us four lone
electrons. Voila!
If that were the case – the 1 of the hydrogen atoms would
bond with the open 2s orbital, and the other 3 atoms would
be found in each of the 2p orbitals.
This would result in 3 bonds in p orbitals, and 1 bond in
the s orbitals. If this were the case, we would expect the
bond angles of methane to be different for the p bonds in
comparison to the s bond.
But we know - all the bond angles and lengths are identical.
Hybrid Orbitals
How can we explain the equivalent bond lengths and angles
in CH4?
The 2s and 2p orbitals actually hybridize to form 4 new
sp3 orbitals that are equivalent.
When we form hybrid orbitals – we still have the same
number of available places to bond – they just have a
different orbital geometry that allows equivalent bonds to
be formed with the 1s electrons of hydrogen.
Hybrid Orbitals
Hybrid Orbitals
Hybrid Orbitals
If we look at other molecules, we see that the hybridization of
s and p orbitals is rather common.
Example: BeF2
Be: 1s22s2  0 unpaired electrons
F: 1s22s22p5  1 unpaired electron in the 2p
As is, there should be no driving force for Be to bond with
Fluorine. However, it forms two bonds, which means two lone
pairs or electrons are available for fluorine to overlap with.
Hybrid Orbitals
Again, we could arrange the 2s2 electrons differently:
2s1 and 2p1 – but this would give us non- equivalent
bonds. And we know the molecule is linear.
Hybrid Orbitals

Instead, we hydridize one “s” orbital and one “p”
orbital, which gives rise to 2 “sp” orbitals. Which are
now equivalent.
sp Hybrid Orbitals

sp hybrid orbitals formed from the combination of
one s and one p orbital (linear arrangement).
+
+
linear
Hybrid Orbitals
Each singly occupied “sp” orbital is now available to
bond with the lone electron in the 2p orbital of
fluorine.
The two sp orbitals face away from one another, so this
will imply a linear arrangement.
Hybrid Orbitals
SP2 hybridization: BF3 : Boron: 1s22s22p1
sp2 Hybrid Orbitals

sp2 hybrid orbitals formed from the combination of
one s and one p orbital (linear arrangement).
+
+
+
trigonal planar
sp3 Hybrid Orbitals

sp2 hybrid orbitals formed from the combination of
one s and one p orbital (linear arrangement).
+
+
+
+
tetrahedral
Hybrid Orbitals
The three hybridizations we have discussed work well
for smaller elements, which only involve the s and p
valence electrons and obey the octet rule.
For molecules that are hypervalent, we need more than
just the four orbitals made available to use with sp, sp2
and sp3 hybridizations.
One way of increasing the available hybrid orbitals is by
incorporating the d orbitals as well.
Hybrid Orbitals
To accommodate five or more bonded atoms: the
central atom can use its ns and np orbitals (n is the
outer most shell) as well as the n-1 d orbitals.
To accommodate 5: we use an “s”, three “p” and one
“d” orbital to create equivalent: sp3d orbitals.
To accommodate 6: sp3d2 orbitals
sp3 Hybrid Orbitals
Hybrid Orbitals
Hybrid Orbitals
Hybrid Orbitals

Draw Lewis Structures

Determine VSEPR geometry using AXE notation




Determine the hybrid orbitals needed to fit the
geometry:
sp = linear
sp2 = trigonal planar
sp3 = tetrahedral
sp3d = trig. Bipyramid
sp3d2 = octahedron.
Hybrid Orbitals
Examples:
1. Indicate the orbital hybridization around the central
atom in NH2-.
2. Predict the electron domain geometry and
hybridization of the central atom in SO3-2.
Multiple Bonds
When two nuclei come together to form a bond
through orbital overlapping, the electron density can
either be concentrated along the internuclear axis or
above/ below the internuclear axis.
Sigma Bond: Electron density along axis s
Pi Bond: Electron density above and below p
Multiple Bonds
Whether the bond is considered a s or a p bond
depends on what type of orbitals are overlapping.
When s orbitals overlap in H2, the p orbitals overlap in
HCl or the p and sp orbitals overlap – these all give rise
to sigma bonds.
All of these orbital overlaps lead to electron density
located right in between the two nuclei.
Multiple Bonds
Pi bonds occur when the orbital overlap occurs perpendicular
to the internuclear axis.
The electron cloud density is located above and below the axis.
These bonds tend to be weaker than sigma bonds. Pi bonds can
only be formed after a sigma bond, because the sigma bond is
what brings the p orbitals together in the first place.
Some general helpful hints:
Single bonds are sigma bonds
Double bonds: 1 sigma, 1 pi
Triple Bonds: 1 sigma and 2 pi.
Multiple Bonds
Ethylene: C2H4
There are three electron domains. Giving a trigonal
planar structure around each carbon atom, indicating
an sp2 hybridization.
Recall carbon valence electrons:
Multiple Bonds
Each carbon has 3 sp2 orbitals prepared for bonding and 1 leftover p
orbital.
First a carbon – carbon sigma bond is formed by the overlap of each
carbons sp2 orbital.
Then the 4 hydrogens overlap and bond with the remaining sp2 orbitals.
The leftover p orbitals on each carbon will also overlap, but they are
oriented above and below the axis, hence forming a pi bond.
Multiple Bonds
Multiple Bonds


Sigma bonds are thought as end to end overlap
between the nuclei, which allows them to spin and
rotate without losing their overlap.
Because pi bonds are a side to side overlap, they are
not able to rotate. By spinning, they would “come
apart.” the The presence of pi bonds locks the
carbon atoms in their place… which is why this
molecule is a planar molecule.
Multiple Bonds
Acetylene: C2H2 – linear molecule containing a triple
bond. Linear geometry indicates sp hybrization,
leaving two p orbitals available for overlap.
Multiple Bonds
For the following molecules:
Draw Lewis Structure
Predict hybridization around central atom
Using an orbital diagram, show this hybridization
Identify the number of sigma and pi bonds in your
Lewis dot structure and your orbital diagram.
NH3, PF5, IF2-, CO3-2, HCN, TeF5-1, I3-, ClF3
Multiple Bonds



In all of these bonds, the electrons are localized;
meaning they are still completely associated with the
two atoms that came together to form the bond.
However, there are many cases where the electrons
are considered delocalized – the electrons are far
more fluid within the molecule.
This is the case when molecules have pi bonds and
two or more resonance structures, like Benzene.
Multiple Bonds
Multiple Bonds
Multiple Bonds


Because the electrons are spread out amongst all 6
carbon atoms in the ring, they are considered
delocalized. These pi bonds lock the surrounding
carbon atoms into a particular rigid structure.
These delocalized electrons are responsible for many
of the odors of organic compounds and the rigidity
of pi bonds gives many organic compounds their
properties.
Hybrid Orbitals Summary
Every bonded pair of atoms shares at least one electron
pair
- every bond has one sigma bond localizing the
electrons between the atoms bonds.
- there is a close relationship between molecular
geometry and the hybrid orbitals that were formed.
Sigma bonds contribute to the the bonding of two atoms
Multiple bonding is only possible if pi bonds are
introduced, which may result in delocalized electrons.
Every pi bond involves two 2 overlaps (2 lobes in p orbital)
Molecular Orbitals
Although orbital hybridizations and VSEPR theory
allow us to make sense of many of the observed
properties of molecules, there are certain things that
are not able to be explained with these theories.
Molecular orbital theory relies on interpreting electrons
as wave functions and are associated with the whole
molecule rather than just the central atom (axe
notation).
Molecular Orbital
Molecular orbitals are formed whenever atomic orbitals
overlap.
In a molecule of hydrogen, we have two 1s orbitals
overlapping, which gives us two MO’s.
Because molecular orbital theory uses the idea that
electrons are waves, when we combine these two
orbitals that overlap can either be constructive or
destructive.
Molecular Orbital
If the addition of the wave functions of the 1s orbitals,
this MO is a constructive combination. It’s energy is
lower and more stable than the two 1s orbitals on their
own. This is called a bonding MO.
The other MO is formed when the two orbitals overlap
and cancel each other out. This is called destructive
combination and results in an antibonding orbital. This
has higher energy than the atomic orbitals.
Molecular Orbital
Molecular Orbital
In this diagram, the bonding MO shows an electron
density in between the two nuclei and the electrons are
attracted to both nuclei. It is energetically favorable and
more stable than the 1s orbitals by themselves.
The antibonding MO shows electron density on
opposite sides of the molecules and a node in the
region between the two nuclei. Electrons are not
present in the area where the bond should exist. They
are repelled and have higher energy and are unstable.
Molecular Orbital
Because in both of these MO the electron density is
located along the internuclear axis, they are referred to
a sigma molecular orbitals.
Bonding: s1s
Antibonding: s*1s
Molecular orbital diagrams or energy level diagrams are
used to relate the energy of atomic and molecular
orbitals.
Molecular Orbital
Energy level diagram for H2
Molecular Orbital
Energy level diagram for He2: why diatomic helium
cannot exist
Molecular Orbital
Bond Order = ½ (# of bonding electrons – # of antibonding
electrons).
Bond Order of 1 = single bond, 2 = double bond, 3 = triple
bond. Typically whole numbers, however can be a fraction: ½,
3/2, or 5/2.
If a bond order is calculated to be zero, that bond does not
exist. The higher the bond order, the greater the stability.
Example: H2 has a bond order of 1, He2 has a bond order of 0.
Molecular Orbitals
Other new terminology:
Diamagnetic: molecular orbitals contain no unpaired
electrons. These molecules would be weakly repelled by a
magnetic field.
Paramagnetic: contains at least one unpaired electron.
Strongly attracted into magnetic fields.
Molecular Orbital
Our study of molecular orbitals will focus on the diatomic
molecules of Period 2 elements. The valence electrons are located
in the 2s and 2p. Some things to consider:
1.
2.
3.
4.
5.
The number of MO orbitals = atomic orbitals combined.
Atomic orbitals combine best with orbitals of similar energy.
As the overlap increases, the effectiveness increases and the
bond energy decreases: making it more stable bonding MO
and more unstable antibonding.
Each MO can hold 2 electrons with spins paired (Pauli
exclusion)
When MO’s of same energy level are populated, one electron
per orbitals before spin pairing (Hunds rule)
Molecular Orbitals for Li2
Li2 molecules exist in the vapor phase when lithium
metal is heated to its boiling point. Electron
configuration is 1s22s1.
We can assume that because the 1s and 2s atomic
orbitals are different energies, the 1s orbitals from each
lithium will overlap and the 2s orbitals will overlap
separately.
Molecular Orbitals for Li2
Molecular Orbitals
One thing to notice about the molecular orbital diagram is
the difference between the bonding and antibonding
orbitals at the 1s level compared to the 2s level.
The 2s MO bonding and antibonding orbitals have much
greater difference in their energy. Because the 2s orbitals
are larger than the 1s, they are able to overlap to a greater
extent. This results in a much greater energy discrepancy
between the bonding and antibonding orbitals.
Molecular Orbitals for Li2

The 6 electrons in a Li2 molecule are placed as follows:

2 electrons in s1s, 2 electrons in s*1s and 2 electrons in s2s.
This arrangement gives us a bond order of ½ (4-2) = 1. A bond
order of 1 then can be interpreted to have a single bond which
is consistent with what is observed experimentally.
This bond arises from the overlap of the 2s electrons because
both the bonding and antibonding are filled at the 1s level.
Molecular Orbitals for Be2
Be has 4 valence
electrons: 1s22s2.
The Be2 molecule
therefore requires
Placing 8 electrons
in MOs.
With a bond order of
Zero, can this
Molecule exist?
Molecular Orbitals
What happens when we begin forming diatomic
molecules with elements that have valence electrons in
the p orbitals.
We can overlap p orbitals and also describe them in
terms of molecular orbitals. Because there are three p
orbitals to overlap, we will form 6 MO’s. (3 from each
of the elements in the diatomic molecule).
These MOs can also be labeled as either sigma or pi.
Molecular Orbitals
The pz orbital overlap has been decided upon to be the
overlap that concentrates the electron density along the
internuclear axis. Considered end to end overlap.
The 2pz overlap will give us a s2p and a s*2p
Molecular Orbitals
2px and 2py then are around rather than on the
internuclear axis and will form p MO.
Molecular Orbitals
Using this information, we can construct molecular orbitals
for diatomic molecules from B2 to Ne – which employ both
2s and 2p overlap.
Things to consider when looking at MO diagram:
1.
2s atomic orbitals have less energy than the 2p atomic
orbitals. The MO formed from 2s orbital are lower in
energy than any MO formed from 2p overlap.
2.
The overlap of the two 2pz orbitals is greater than the
2px and 2py, therefore more energy different between
the bonding and antibonding 2pz MOs.
3.
The p2p and p*2p MOs are “doubly degenerate”: there
are two degenerate of each.
Molecular Orbitals
Molecular Orbitals
Finally, before we can construct a MO diagram of a
diatomic molecules, we have to take into account one
more behavior that has been noticed.
The 2s orbital of one atom may interact with the 2p
orbital of the neighboring atom.
Due to 2s and 2p interaction in small molecules, the
bonding s2pz and p2px,y will switch energies with the
p2px,y having less energy (more stable) than the s2pz.
Molecular Orbitals
s*(2pz)
O thru Ne
p (2px,y)
2p
2p
p (2px,y)
Bonding orbitals from
the p’s switch energies
for the smallest
molecules due to 2s-2p
interactions
s (2pz)
s*(2pz)
p (2px,y)
Li thru N
2p
s (2pz)
2p
p (2px,y)
Molecular Orbitals for B2
Molecular Orbitals for C2
Molecular Orbitals for N2
s*(2pz)
p (2px,y)
2p
s (2pz)
2p
p (2px,y)
s*(2s)
b.o. = 8-2 = 3
2
s (2s)
2s
NA
No. 101
ENERGY
N2
2s
DIAMAGNETIC
NB
CHE
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Molecular Orbitals for O2
s*(2pz)
p (2px,y)
2p
2p
p (2px,y)
s (2pz)
s*(2s)
b.o. = 8-4 = 2
2
s (2s)
2s
OA
No. 102
ENERGY
O2
2s
OB
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Molecular Orbitals for O2
s*(2pz)
p (2px,y)
2p
Unpaired Electrons
PARAMAGNETIC
2p
p (2px,y)
s (2pz)
s*(2s)
2s
OA
No. 103
s (2s)
O2
2s
OB
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Molecular Orbitals for Period 2
p sublevel
B2
C2
N2
N2+1
1.0
2.0
3.0
2.5
s*(2pz)
p (2px,y)
s (2pz)
p (2px,y)
s*(2s)
s (2s)
bond order
No. 104
CHE
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Molecular Orbitals for Period 2
p sublevel
O2
F2
Ne2
F2+1
2.0
1.0
0.0
1.5
s*(2pz)
p (2px,y)
s (2pz)
p (2px,y)
s*(2s)
s (2s)
bond order
No. 105
CHE
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