Transcript Document 7521644

Chapter 9
Covalent Bonding: orbitals
9.1 Hybridization and localized electron model
How do atoms share electrons between their valence shells?
The localized electron bonding model
• A covalent bond is formed by the
pairing of two electrons with opposing
spins in the region of overlap of atomic
orbitals between two atoms
•
Overlap: the two orbitals share a
common region in space
• This overlap region has high
electron charge density
• The more extensive the overlap
between two orbitals, the stronger
is the bond between two atoms
According to the model:
• For an atom to form a covalent bond it
must have an unpaired electron
• Number of bonds formed by an atom
should be determined by its number of
unpaired electrons
How does Lewis theory explain the bonds in H2 and F2?
Sharing of two electrons between the two atoms.
Overlap Of
2 1s
H2
(1s1)
(1s1)
2 2p
F2
(1s22s22p5)
(1s22s22p5)
Localized electron model – bonds are formed by sharing of e- from
overlapping atomic orbitals.
Hybridization of Atomic Orbitals
Based on ground-state electron configuration,
carbon should have only two bonds
If a 2s electron is
promoted to an empty 2p
orbital, then four unpaired
electrons can give rise to four
bonds
These four orbitals become
mixed, or hybridized to
form bonds
Hybridization of Atomic Orbitals
Most of the electrons in a molecule remain in
the same orbital locations that they
occupied in the separated atoms
Bonding electrons are localized in the region of
atomic orbital overlap
Hybridization ?
 Two or more atomic orbitals are mixed to
produce a new set of orbitals (blended
orbitals)
 Number of hybrid orbitals = number of
atomic orbitals mixed
sp3 Hybridization
Occurs most often for central atom only
The total number of hybrid orbitals is
equal to the number of atomic orbitals
combined
sp3 Hybridization
The carbon atom
in methane
(CH4) has bonds
that are sp3
hybrids
Note that in this
molecule carbon
has all single
bonds
3
sp
Hybridization
 s and p orbitals of the valence electrons
are blended.
 one s orbital is combined with 3 p
orbitals.
 sp3 hybridization has tetrahedral
geometry.
In terms of energy
2p
Energy
Hybridization
2s
sp3
Methane building blocks
1s
2s
2px 2py 2pz
Promotey
sp3 sp3 sp3 sp3
Hybridize
x
109.5o
z
Methane: Carbon
sp3 Orbital Hybridization in NH3
2p
2 sp3
7N
2s
3 Equivalent half-filled
orbitals are used to form
bonds with 3H atoms. The
4th sp3 holds the lone pair
Bonding in Ammonia
Ammonia (NH3)
is similar to
CH4
except the lone
pair of electrons
occupies the 4th
hybrid orbital
5N:
1s2 2s2 2p3
How about hybridization in H2O?
O
H
H
H
2 sp3
2p
8O
2s
H
sp2 Hybridization
Consider BF3
3B
The empty 2p orbital
remains unhybridized
sp2
is omprised of one 2s orbital
and two 2p orbitals to produce a
set of three sp2 hybrid orbitals
Formation of sp2 Hybrid Orbitals
Hybrid orbitals and geometry
The geometric distribution of the three sp2
hybrid orbitals is within a plane, directed at 120o
angles
This distribution gives a trigonal planar
molecular geometry, as predicted by VSEPR
sp2 Hybridization scheme is useful in describing
double covalent bonds, e.g. Ethylene
in CH2=CH2
Unhybridized
orbital
10.5
Nonhybridized p-orbitals
sp2 Hybridization scheme is useful in describing
double covalent bonds, e.g. Ethylene
Sigma  and pi  bonds
 Sigma bond is formed when two orbitals each
with a single electron overlap
(Head-to-head overlap). Electron density is
concentrated in the region directly between the
two bonded atoms
 Pi-bond is formed when two parallel p-orbitals
overlap side-to-side
– The orbital consists of two lopes one above the
bond axis and the other below it.
– Electron density is concentrated in the lopes
– Electron density is zero along the line joining the
two bonded atoms
H
H
C
H
C
H
2
sp




hybridization
C2H4
Double bond acts as one pair.
trigonal planar
Have to end up with three blended
orbitals.
 Use one s and two p orbitals to make sp2
orbitals.
 Leaves one p orbital perpendicular.
In terms of energy
2p
Energy
Hybridization
2s
2p
sp2
sp Hybridization
The geometric distribution of the two sp hybrid
orbitals is linear , directed at 180o angles
H-Be-H
4Be
1s2 2s2
This
distributio
n gives a
linear
molecular
geometry
In terms of energy
2p
Energy
Hybridization
2s
2p
sp
This hybridization scheme is useful
in describing triple covalent bonds
in acetylene
HC
Hybridization in
CH
Unhybridized
orbitals
Carbon–Carbon Triple Bonds
Hybridization in molecules containing
multiple bonds
 The extra electron pairs in double or triple
bonds have no effect upon the geometry of
molecules
 Extra electron pairs in multiple bonds are not
located in hybrid orbitals
 Geometry of a molecule is fixed by the electron
pairs in hybrid orbitals around the central atom
– All unshared electron pairs
– Electron pairs forming single bonds
– One (only one) electron pair in a multiple bond
CO2
O
C O
 C can make two  and two 
 O can make one  and one 
dsp3/sp3d Hybridization
This hybridization allows for expanded valence
shell compounds – typical for group 5A elements,
e.g., 15P
A 3s electron can
be promoted to a
3d subshell,
which gives rise
to a set of five
sp3d hybrid
orbitals
Centrsl atoms without d-orbitals, N, O, F, do not form expanded octet
PCl5
sp3d sp3d sp3d sp3d sp3d
Neon
2
3s
3px 3py 3pz
dxz
dyz
90o
120o
120o
dxy
dx2-y2 dz2
Hybridized
Promoted
Trigonal
Bipyrimidal
Phosphorus Pentachloride: Phosphorus
d 2sp3/sp3d2 hybridization
This hybridization allows for expanded valence
shell compounds – typically group 6A elements,
e.g., S
A 3s and a 3p
electron can be
promoted to the
3d subshell,
which gives rise
to a set of six
sp3d2 hybrid
orbitals
Predicting Hybridization Schemes
In hybridization schemes, one hybrid orbital
is produced for every simple atomic orbital
involved
Write a plausible Lewis structure for the
molecule or ion
 Use the VSEPR method to predict the
electron-group geometry of the central atom
 Count # of e-pairs around the atom
 Multiple bond is counted as one pair
Choose the hybrid set having same
number of orbitals
Success of the localized electron model
 Overlap of atomic orbitals explained the
stability of covalent bond
 Hybridization was used to explain the
molecular geometry predicted by the
localized electron model
 When lewis structure was in adequate,
the concept of resonance was introduced
to explain the observed properties
Weakness of the localized electron model
 It incorrectly assumed that electrons are
localized and so the concept of
resonance was added
 Inability to predict the magnetic
properties of molecules like O2
(molecules containing unpaired
electrons)
 No direct information about bond
energies
9.2 Molecular Orbital Theory
 Molecular orbitals (MOs) are mathematical
equations that describe the regions in a molecule
where there is a high probability of finding
electrons
 Involves diagramming molecular energy levels
 Used to explain magnetic and spectral properties
of molecules
 Used to predict the existence of certain molecules
 Atomic orbitals of atoms are combined to give a
new set of molecular orbitals characteristic of the
molecule as a whole
– The number of atomic orbitals combined
equals the number of molecular orbitals
formed. (Two s-orbitals
Two molecular orbitals)
Molecular orbitals
 Two atomic orbitals combine to form a bonding
molecular orbital and an anti-bonding MO*.
– Electrons in bonding MO’s stabilize a molecule
– Electrons in anti-bonding MO’s destabilize a
molecule
 The combined orbitals must be of comparable
energies. e.g., 1s(H) with 2s(Li) is not allowed
 The molecular orbitals are arranged in order of
increasing energy.
 The electronic structure of a molecule is
derived by feeding electrons to the molecular
orbitals according to same rule applied for
atomic orbitals
Molecular orbitals
 Each molecular orbital can hold a maximum of
two electrons with opposite spins
 Electrons go into the lowest energy molecular
orbital available
 Hund’s rule is obeyed
 Molecular orbital model will be applied only to
the diatomic molecules of the elements of the
first two periods of the Periodic Table
Formation of molecular orbitals by
combination of 1s orbitals
The hydrogen molecule
HB
Destructive
interference
HA
Antibonding MO2 = region of
diminished electron density
Electron density is concentrated away from
Internuclear region
Electron density
is concentrated
between nuclei
Bonding MO1 =
enhanced region of
electron density
Destructive interference
Energy level diagram in hydrogen (H2).
A bonding molecular orbital has lower energy and greater
stability than the atomic orbitals from which it was
formed.
An antibonding molecular orbital has higher energy and
lower stability than the atomic orbitals from which it was
formed.
The Molecular Orbital Model
• We use labels to indicate shapes, and
whether the MO’s are bonding or
antibonding.
– MO1 = 1s
– MO2 = 1s* (* indicates antibonding)
• Can write them the same way as atomic
orbitals
– H2 = 1s2
Bond order
 Bond Order =1/2 (bonding e – antibonding e)
(number of bonds)
 Higher bond order = stronger bond
Bond order for H2
Bond order for He2+ and He2
*1s
1s
1s
Energy
Energy
*1s
1s
1s
1s
AO of
He
MO of
He+
1s
AO of
He+
He2+ bond order = 1/2
AO of
He
MO of
He2
AO of
He
He2 bond order = 0
Predicting Species Stability Using MO Diagrams
PROBLEM:
PLAN:
Use MO diagrams to predict whether H2+ and H2- exist.
Determine their bond orders and electron configurations.
Use H2 as a model and accommodate the number of electrons in
bonding and antibonding orbitals. Find the bond order.
SOLUTION:
bond order
= 1/2(1-0)
= 1/2

H2- does exist
H2 does exist
1s
1s
AO of H
AO of H

MO of H2

+
bond order
= 1/2(2-1)
= 1/2
1s
+
AO of H-
AO of H
)1
+
1s
configuration is (1s

MO of H2-
configuration is
(1s)2(1s)1
1
bond order =
2
bond
order
½
(
Number of
electrons in
bonding
MOs
1
-
½
Number of
electrons in
antibonding
MOs
)
0
9.3 Bonding in homonuclear
diatomic molcules
 For atomic orbitals to participate in molecular
orbitals, they must overlap in space
 Thus only valence orbitals of atoms contribute
significantly to the molecular orbitals of the
molecule
 Inner orbitals are too small to overlap and thus
their electrons are assumed to be localized and
not participate in bonding
Only outer orbitals bond
 The 1s orbital is much smaller
than the 2s orbital
 When only the 2s orbitals
are involved in bonding
 Don’t use the 1s or 1s*
for Li2
 Li2 = (2s)2
 In order to participate in
bonds the orbitals must
overlap in space.
*2s
*2s
2s
Energy
2s
Li2
2s
Bonding in s-block
homonuclear
diatomic
molecules.
Li2 bond order = 1
2s
2s
2s
Be2
Be2 bond order = 0
Possible interactions between two equivalent p orbitals and
the corresponding molecular orbitals
-
+
-
Head-to-head overlap
+: High e- density
+
-: Low e- density
Side-to-side overlap
Molecular Orbital (MO) Configurations
1. The number of molecular orbitals (MOs) formed is
always equal to the number of atomic orbitals
combined.
2. The more stable the bonding MO, the less stable the
corresponding antibonding MO.
3. The filling of MOs proceeds from low to high energies.
4. Each MO can accommodate up to two electrons.
5. Use Hund’s rule when adding electrons to MOs of the
same energy.
6. The number of electrons in the MOs is equal to the
sum of all the electrons on the bonding atoms.
Expected Energy Diagram
2p
2p*
2p*
2p*
2p
2p
2p
2p
2s*
2s
2s
2s
B2
2p
2p
2s
2s
B2
 (2s)2(2s*)2 (2p)2
 Bond order = (4-2) / 2
 Should be stable.
Magnetism
 Magnetism has to do with electrons.
 Paramagnetism: substance is attracted by a
magnet.
– associated with unpaired electrons.
 Diamagnetism: substance is repelled by a
magnet.
– associated with paired electrons.
 Experimentally, B2 was found to be paramagnetic
 However, Orbital diagram shows that it is
diamagnetic?
Magnetism
 The energies of of the p2p and the s2p
are reversed by p and s interacting
 The 2s and the 2s* are no longer
equally spaced.
 Here’s what it looks like.
Correct energy diagram
2p*
2p*
2p*
2p
2p
2p
2p
2p
2s*
2s
2s
2s
B2
2p*
2p*
2p
2p
2p
2p
2s*
2s
2s
2s
MO energy level digrams for diatomic
molecules of B2 through F2
Note that for O2 and F2 2p orbital
is lower in energy than 2p orbitals
Patterns
 As bond order increases, bond energy
increases.
 As bond order increases, bond length
decreases.
 Direct correlation of bond order to bond
energy is not always there
 O2 is known to be paramagnetic.
SAMPLE PROBLEM
PROBLEM:
Using MO Theory to Explain Bond Properties
As the following data show, removing an electron from N2 forms
an ion with a weaker, longer bond than in the parent molecules,
whereas the ion formed from O2 has a stronger, shorter bond:
N2
N2+
O2
O 2+
Bond energy (kJ/mol)
945
841
498
623
Bond length (pm)
110
112
121
112
Explain these facts with diagrams that show the sequence and occupancy of MOs.
PLAN:
Find the number of valence electrons for each species, draw the MO
diagrams, calculate bond orders, and then compare the results.
SOLUTION:
N2 has 10 valence electrons, so N2+ has 9.
O2 has 12 valence electrons, so O2+ has 11.
SAMPLE PROBLEM
Using MO Theory to Explain Bond Properties
continued
N2+
N2
bonding e- lost
1/2(8-2)=3
O2 +
O2
2p
2p
2p
2p
2p
2p
2p
2p
2s
2s
2s
2s
1/2(7-2)=2.5
bond
orders
1/2(8-4)=2
antibonding
e- lost
1/2(8-3)=2.5
9.4 Bonding in heteronuclear
diatomic molecules
 Will deal with molecules of atoms
adjacent to each other in the Periodic
Table
 Simple type has them in the same energy
level, so can use the orbital diagrams
used for homonuclear molecules already
known to us
 Slight energy differences.
 NO
Energy
*
2p
The MO diagram for NO
s
*
p

p

*
possible Lewis
structures
p
s
2s
2s
AO of N
0
0
N
O
-1
+1
N
O
AO of O

Experimentally NO is
paramagnetic
2p
s
MO of NO
Bond order=
83
 2.5
2
Nitric oxide, NO
# valence e- =
5(N) + 6(O) = 11
2p
2p
2s
2s
The MO diagram for HF
Energy

Two non-bonding orbitals
are the lone pairs on F
seen in The Lewis structure
for HF
1s
Note the H1S
is less stable
than the F2P
2p

AO
of H
MO of
HF
AO
of F
Partial molecular orbital energy-level diagram for HF

• Other valence electrons of F are
assumed to be localized
Energy
•
F binds its valence
electrons more
tightly than H
1s
Note the H1S
is less stable
(has more
energy) than
the F2P
2p

AO of
H
MO of
HF
Since both electrons are lowered in
energy, HF molecule is more stable
Than individual atoms. This is the
Driving force for bond formation
AO
of F
Partial molecular orbital energy-level
diagram for HF
 The  molecular orbital containing the bonding
electron pair shows greater electron
probability close to F
 Thus, F atom will have a slight excess of –ve
charge, i.e., electron sharing is not equal
 Consequently, MO diagrams accounts for bond
polarity
The MO Energy-level
diagram for both the
NO+ and CN- ions
# valence e in NO+ = 10
Same order as homonuclear atoms
9.5 Combining the localized electron and
molecular orbital models
 sp orbitals are called the Localized electron model
  and  Molecular orbital model
 Localized is good for geometry, doesn’t deal well with
resonance.
 seeing  bonds as localized works well
 It is the  bonds in the resonance structures that can
move.
  molecular orbital can be considered to be spread
over the entire molecule rather than being
concentrated between the two atoms
 Electrons occupying the  molecular orbital belong to
the whole molecule; they are described as
Delocalized
The resonance structures for O3 and NO3-
The two extra electrons in the double bond are found in the
delocalized -orbital associated with the whole molecule
• Also, there are 3 -bonds localized between S and O atoms
• Thus bond distances are the same
•
Bonding in Benzene
The structure of benzene, C6H6, discovered by
Michael Faraday in 1825, was not figured out
until 1865 by F. A. Kekulé
Kekulé discovered that
benzene has a cyclic
structure and he proposed
that a hydrogen atom was
attached to each carbon atom
and that alternating single
and double bonds joined the
carbon atoms together
Benzene
This kind of structure gives rise to two important
resonance hybrids and leads to the idea that all
three double bonds are delocalized across all six
carbon atoms
Benzene
 A better description of bonding in benzene
results when a combination of the two models
is used for interpretation
 Six p-orbitals can be used to -molecular
orbitals
 The electrons in the resulting -molecular
orbitals are delocalized above and below the
plane of the ring.
 Thus, C-C bonds are equivalent as obtained
from experiment
 delocalized bonding
H
H
C6H6 
H
H
H
H
H
H
H
H
H
H
The lowest energy -bonding MOs in benzene and ozone.
Delocalized molecular orbitals are not confined between
two adjacent bonding atoms, but actually extend over three
or more atoms.