Unformatted text preview: Chapter 10
Chapter
Bonding and Molecular Structure:
Orbital Hybridization and
Orbital
Molecular Orbitals
Molecular Goals
Goals
• Understand the differences between
Understand
valence bond theory and molecular orbital
theory.
theory.
• Identify the hybridization of an atom in a
Identify
molecule or ion.
molecule
• Understand the differences between
Understand
bonding and antibonding molecular
orbitals.
orbitals.
• Write the molecular orbital configuration
Write
for simple diatomic molecules.
for Orbitals and Bonding Theories
Orbitals
VSEPR Theory only explains molecular shapes.
It says nothing about bonding in molecules
It
In Valence Bond (VB) Theory (Linus Pauling)
Valence
atoms share electron pairs by allowing their
atoms
atomic orbitals to overlap.
atomic
Another approach to rationalize chemical
Another
bonding is the Molecular Orbital (MO) Theory
(Robert Mulliken): molecular orbitals are spread
out or “delocalized” over the molecule.
out Valence Bond (VB) Theory
Valence
Covalent bonds are formed by the overlap of
overlap
atomic orbitals.
atomic
Atomic orbitals on the central atom can mix and
Atomic
exchange their character with other atoms in a
molecule.
molecule.
Process is called hybridization.
hybridization
Hybrids are common:
Pink flowers
Pink
Mules
Mules
Hybrid Orbitals have the same shapes as
Hybrid
predicted by VSEPR.
predicted 1s 1s +
H H σ bond
bond 1s 1s +
H H E σ bond
bond 1s
H +
H H E H
1s
H σ bond
bond 2p + 2p F F σ bond
bond
F2 2p E
2s 1s
1s
F F
2p E
2s 1s
1s F Methane
Methane
CH4 2p
E 2s 1s C Methane
Methane
CH4
H H
2p E 2s 1s C Methane
Methane
CH4
H
H+
E 2p 2s 1s H C Methane
Methane
CH4
H
H+
E 2p 2s 1s H H– C Methane
Methane
CH4
H
H+
E Z
Y H H– X
2p
H 2s
H
1s C C 90° H
90° H
The approach is not
The
correct, because… Methane
Methane
CH4
H
109.5° C
H H H Tetrahedral Geometry
4 Identical Bonds
Identical Problem and Solution
Problem
C must have 4 identical orbitals in
must
valence shell for bonding
valence
solution: hybridization (theoretical
theoretical
mixing of the four atomic orbitals of
carbon atom, the 2s and the three 2p)
2s
2p Methane
Methane
CH4 2p
E 2s 1s Methane
Methane
CH4 2s 2p
E 2s 1s E 1s 2p Methane
Methane
CH4 2s 2p
E 2s 1s E 1s 2p Methane
Methane
CH4 2s 2p
E 2s 1s E 1s 2p Methane
Methane
CH4 2p
E 2s 1s four sp3 orbitals E 1s + –
2p + + 2s – + + three 2p + 2s =
=
four sp3 hybrid orbitals 4 identical sp3 hybrid orbitals: they are four
identical
because there was the combination of one s
and three p atomic orbitals (25% s, 75% p)
and tetrahedral geometry
tetrahedral Methane
Methane
CH4
H
2p
E 2s 1s H H
sp3 E 1s H Valence Bond (VB) Theory
Valence
Regions of High
Regions
Electron Density
(BP+LP)
(BP+LP) Electronic
Electronic
Geometry
Geometry Hybridization,
Angles(°) 2
3 Linear
Trigonal
Trigonal
planar
planar sp, 180
sp, 180
sp2
120 4 Tetrahedral 5 Trigonal
Trigonal
bipyramidal
bipyramidal sp3
109.5
sp3d
120, 90, 180 6 Octahedral sp3d2
90, 180 Predict the Hybridization of the Central Atom
Predict
in aluminum bromide
in
••
• Br•
••
Al
• Br• • Br•
••• • ••• • Electronpair shape
3 regions
trigonal planar Hybridization: sp2 Trigonal Planar Electronic Geometry, sp2
Trigonal
Electronic Structures: BF3
1s
↑↓ B 1s
B
↑↓
F [He] ↑ 2s 2p
↑↓
↑
2s 2p 2p
↑↑ 2s
2p
↑↓ ↑↓ ↑↓ ↑ 1s
⇒ ↑↓ sp2 hybrid
↑↑ ↑ Trigonal Planar Electronic Geometry, sp2
Trigonal
BF3 Predict the Hybridization of the Central Atom
Predict
in carbon dioxide
in
CO2
••
••
OCO
••
••
2 regions
Electronpair shape, linear Hybridization: sp (50% s, 50%
Hybridization:
p)
p) Linear Electronic Geometry, sp
Linear
Electronic Structures: BeCl2 Be 1s
↑↓ 2s 2p
↑↓ Cl [Ne] 3s
↑↓ 3p
↑↓ ↑↓ ↑ 1s
⇒↑
↓ sp hybrid
↑↑ Predict the Hybridization of the
Central Atom in Beryllium Chloride
Central
Two regions: electronpair shape
sp hybridization Predict the Hybridization of the Central Atom
in PF5
in
Five regions: Trigonal Bipyramidal Electronic
Five
Geometry
sp3d hybridization, five sp3d hybrid orbitals
sp Predict the Hybridization of the Central Atom
Predict
in xenon tetrafluoride
in Predict the Hybridization of the Central Atom
Predict
in xenon tetrafluoride
in
•••
F
•••
•••
F
••• ••
F•
•• • •
Xe ••
•
•• F •
••• 6 regions
electronpair shape
octahedral Predict the Hybridization of the Central Atom
Predict
in xenon tetrafluoride
in
•••
F
•••
•••
F
••• ••
F•
•• • •
Xe ••
•
•• F •
••• 6 regions
electronpair shape
octahedral sp3d2 hybridization Predict the Hybridization of the Central
Atom in SF6
Atom
Six regions: Octahedral Electronic Geometry
Six
 sp3d2 hybridization,
sp
six sp3d2 hybrid orbitals Consider Ethylene, C2H4
Consider Consider Ethylene, C2H4
Consider
H
H C C H
H Consider Ethylene, C2H4
Consider
H C C H
3 regions
trigonal planar H
H Consider Ethylene, C2H4
Consider
H C C H H
H 3 regions
trigonal planar sp2 hybridization Consider Ethylene, C2H4
Consider
H
H C C H
H 3 regions
trigonal planar sp2 hybridization 2p
E 2s 1s
1s 2s 2p
E 2s 1s
1s E 1s 2p 2p
E 2s 1s
1s sp2 E 1s 2p sp2
sp
2p sp2
sp2 2p
sp2
sp2
sp sp2 σ bond framework
bond π bond
bond π bond
bond Compounds Containing Double Bonds
Compounds
Thus a C=C bond looks like this and is made
Thus
of two parts, one σ and one π bond. Consider Acetylene, C2H2
Consider
H C C H Consider Acetylene, C2H2
Consider
H C 2 regions
linear C H Consider Acetylene, C2H2
Consider
H C C H 2 regions
linear sp hybridization Consider Acetylene, C2H2
Consider
H C C H 2 regions
linear sp hybridization 2s 2p
E 2s 1s
1s E 1s 2p 2p
E 2s 1s
1s sp
E 1s 2p 2p
sp
sp 2p sp σ bond framework
bond π bonds
bonds Compounds Containing Triple Bonds
Compounds
A σ bond results from the headon overlap of
headon
two sp hybrid orbitals.
two
The unhybridized p orbitals form two π bonds
The
(sideon overlap of atomic orbitals.)
Note that a triple bond consists of one σ and
two π bonds. π bonds
bonds Generally
Generally
• single bond is a σ bond
single
• double bond consists of 1 σ and 1 π
double
bond
bond
• triple bond consists of 1 σ and 2 π
triple
bonds
bonds Molecular Orbital (MO) Theory
Molecular
When atoms combine to form molecules,
When
atomic orbitals overlap and are then
combined to form molecular orbitals.
combined
# of orbitals are conserved.
A molecular orbital is an orbital associated
molecular
with more than 1 nucleus.
with
Like any other orbital, an MO can hold 2
Like
electrons.
electrons.
Consider 2 hydrogen atoms bonding to form
Consider
H2 Molecular Orbital Theory
Molecular
• Combination of atomic orbitals on different atoms forms
Combination
molecular orbitals (MO’s) so that electrons in MO’s belong
to the molecule as a whole.
to
• Waves that describe atomic orbitals have both positive
Waves
and negative phases or amplitudes.
and
• As MO’s are formed the phases can interact
As
constructively or destructively.
constructively
destructively Molecular Orbitals
Molecular
There are two simple types of molecular
There
orbitals that can be produced by the overlap
of atomic orbitals.
of
Headon overlap of atomic orbitals
Headon
produces σ (sigma) orbitals.
Sideon overlap of atomic orbitals
Sideon
produces π (pi) orbitals.
Two 1s atomic orbitals that overlap produce
two molecular orbitals designated as:
two
σ 1s or bonding molecular orbital
σ 1s* or antibonding molecular orbital. +
H H subtract add
add subtract
antibonding add
add bonding subtract
antibonding
σ *1s
add
add bonding σ 1s Molecular Orbital Energy Level Diagram
Molecular Now that we have seen what these MO’s look
Now
like and a little of their energetics, how are
the orbitals filled with electrons?
the
Order of filling of MO’s obeys same rules as
Order
for atomic orbitals.
for
Including
Aufbau principle: increasing energy
Pauli’s Excluion: two unaligned e per orbital,
two
with opposite spins (+1/2 and 1/2)
with
Hund’s Rule: maximum spin; unpaired
electrons in degenerate orbitals have same
electrons
spin (+1/2 or 1/2)
spin
Thus the following energy level diagram results for
the homonuclear diatomic molecules H2 and He2. σ *1s
E E
1s
1s 1s
σ 1s H H2 H σ *1s
E E
1s
1s 1s
σ 1s H H2 H σ *1s
E E
1s
1s 1s
σ 1s H H2 H σ *1s
E E
1s
1s 1s
σ 1s H H2 H (σ 1s ) 2
1s
σ *1s
E E
1s
1s 1s
σ 1s H H2 H (σ 1s ) 2
1s
total spin = 0
σ *1s
E E
1s
1s 1s
σ 1s H H2 H • Diamagnetic: slightly repelled by a
Diamagnetic:
magnetic field
magnetic
– total spin = 0
• paramagnetic: attracted to a magnetic field
– total spin not 0
(bonding e– – antibonding e–)
(bonding
antibonding • Bond Order =
Bond
────────────────────
────────────────────
2 Bond Order and Bond Stability
Bond
The larger the bond order, the more stable the
The
molecule or ion is.
molecule
Bond order = 0 implies there are equal numbers of
Bond
electrons in bonding and antibonding orbitals,
electrons
~ same stability as separate atoms: no bond formed
same
no
Bond order > 0 implies there are more electrons in
Bond
bonding than antibonding orbitals.
bonding
Molecule is more stable than separate atoms.
The greater the bond order, the shorter the bond
The
length and the greater the bond energy.
length (σ 1s ) 2
1s
total spin = 0
diamagnetic
σ *1s
E E
1s
1s 1s
σ 1s H H2 H BO = 1/2 ( 2 – 0) = 1
σ *1s
E E
1s
1s 1s
σ 1s H H2 H Consider He2
Consider σ *1s
E E
1s
1s 1s
σ 1s He He2 He σ *1s
E E
1s
1s 1s
σ 1s He He2 He (σ 1s ) 2 (σ *1s ) 2
1s
1s
σ *1s
E E
1s
1s 1s
σ 1s He He2 He diamagnetic
σ *1s
E E
1s
1s 1s
σ 1s He He2 He BO = 1/2 ( 2 – 2 ) = 0 He2 does not exist σ *1s
E E
1s
1s 1s
σ 1s He He2 He Combination of p Atomic
Orbitals
Orbitals Molecular Orbitals
Molecular
The headon overlap of two corresponding p
The
atomic orbitals on different atoms, say 2p x
atomic
with 2px produces:
with σ 2px bonding orbital
σ 2px* antibonding orbital 2p
2p 2p subtract
subtract add subtract antibonding MO add bonding MO
bonding subtract antibonding MO
σ *2p add bonding MO
bonding
σ 2p
2p Molecular Orbitals
Molecular
Sideon overlap of two corresponding p
Sideon
atomic orbitals on different atoms (say 2p y
atomic
with 2py or 2pz with 2pz) produces:
with
π 2p y π*2p y π 2p (both are bonding orbitals)
or
or
z
* or π 2p z (both are nonbonding
orbitals)
orbitals) 2p
2p 2p subtract
subtract add subtract
antibonding MO
antibonding
add bonding MO subtract
π *2p
add
π 2p subtract
π *2p
add
π 2p Consider Li2
Consider σ *2p
π *2p
2p
E σ 2p 2p
E π 2p
σ *2s
2s 2s
2s
Li σ 2s
Li2 Li σ *2p
π *2p
2p
E σ 2p 2p
E π 2p
σ *2s
2s 2s
2s
Li σ 2s
Li2 Li σ *2p
π *2p
2p
E σ 2p 2p
E π 2p
σ *2s
2s 2s
2s
Be σ 2s
Be2 Be σ *2p
π *2p
2p
E σ 2p 2p
E π 2p
σ *2s
2s 2s
2s
Be σ 2s
Be2 Be σ *2p
π *2p
2p
E σ 2p 2p
E π 2p
σ *2s
2s 2s
2s
B σ 2s
B2 B σ *2p
π *2p
2p
E σ 2p 2p
E π 2p
σ *2s
2s 2s
2s
B σ 2s
B2 B σ *2p
π *2p
2p
E σ 2p 2p
E π 2p
σ *2s
2s 2s
2s
C σ 2s
C2 C σ *2p
π *2p
2p
E σ 2p 2p
E π 2p
σ *2s
2s 2s
2s
N σ 2s
N2 N Homonuclear Diatomic Molecules
Homonuclear
In shorthand notation we represent the
In
configuration of N2 as
configuration N2 σ σ σ σ π
2
1s *2
1s 2
2s *2
2s 2
2 py π 2
2 pz σ 2
2p Bond Order of N2
Bond N2 σ σ σ σ π
2
1s *2
1s 2
2s *2
2s 2
2 py π 2
2 pz σ 2
2p The greater the bond order of a bond the
The
more stable we predict it to be.
more
For N2 the bond order is
10  4
bo =
2
6
=
2
= 3 corresponding to a triple
bond in VB theory σ *2p
π *2p
2p
E π 2p 2p
E σ 2p
σ *2s
2s 2s
2s
O σ 2s
O2 O Homonuclear Diatomic Molecules
Homonuclear
In shorthand notation we represent the
In
configuration of O2 as
configuration
2
*2
2
*2
2
2
2
*
*
O 2 σ1s σ1s σ 2s σ 2s π 2 p y π 2 p z σ 2 p x π 21 y π 2 1 z
p
p 10  6
bo =
=2
2
We can see that O2 is a paramagnetic
molecule (two unpaired electrons).
molecule σ *2p
π *2p
2p
E π 2p 2p
E σ 2p
σ *2s
2s 2s
2s
F σ 2s
F2 F σ *2p
π *2p
2p
E π 2p 2p
E σ 2p
σ *2s
2s 2s
2s
Ne σ 2s
Ne2 Ne Bond Order for Ne2
Bond
2× 4  2 × 4
BO = ─────── = 0
BO ───────
2 We can see that Ne2 is not stable. It does not
Ne
exist.
exist. Delocalization and Shapes of Molecular
Orbitals
Orbitals
Molecular orbital theory describes
Molecular
shapes in terms of delocalization of
electrons.
electrons
Carbonate ion (CO32) is a good example. VB Theory
VB MO Theory Delocalization and Shapes of Molecular
Orbitals
Orbitals
Benzene, C6H6, Resonance structure  VB theory Delocalization and Shapes of Molecular
Orbitals
Orbitals
This is the picture of the valence bond
This
(VB) theory
(VB) Delocalization and Shapes of Molecular
Orbitals
Orbitals
The structure of benzene is described
The
well by molecular orbital theory.
well ...
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 Fall '08
 geiger
 Chemistry, Atom, Valence, Mole, Chemical bond

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