Transcript 2s - UCF Chemistry

Chapter 10
Bonding and Molecular Structure:
Orbital Hybridization and
Molecular Orbitals
Goals
• Understand the differences between
valence bond theory and molecular orbital
theory.
• Identify the hybridization of an atom in a
molecule or ion.
• Understand the differences between
bonding and antibonding molecular
orbitals.
• Write the molecular orbital configuration
for simple diatomic molecules.
Orbitals and Bonding Theories
VSEPR Theory only explains molecular shapes.
It says nothing about bonding in molecules
In Valence Bond (VB) Theory (Linus Pauling)
atoms share electron pairs by allowing their
atomic orbitals to overlap.
Another approach to rationalize chemical
bonding is the Molecular Orbital (MO) Theory
(Robert Mulliken): molecular orbitals are
spread out or “delocalized” over the
molecule.
Valence Bond (VB) Theory
Covalent bonds are formed by the overlap of
atomic orbitals.
Atomic orbitals on the central atom can mix and
exchange their character with other atoms in a
molecule.
Process is called hybridization.
Hybrids are common:
Pink flowers
Mules
Hybrid Orbitals have the same shapes as
predicted by VSEPR.
1s
1s
+
H
H
 bond
1s
1s
+
H
H
E
1s
H
 bond
+
H
H
E
H
1s
H
 bond
2p
2p
+
F
F
 bond
F2
2p
E
2s
1s
F
F
2p
E
2s
1s
F
Methane
CH4
2p
E
2s
1s
C
Methane
CH4
H
H
2p
E
2s
1s
C
Methane
CH4
H
H+
E
2p
2s
1s
H
C
Methane
CH4
H
H+
E
2p
2s
1s
H H–
C
Methane
CH4
H
Z
Y
H H–
X
H+
E
2p
H
2s
H
1s
C
C
90°
H
90°
H
The approach is not
correct, because…
Methane
CH4
H
109.5°
C
H
H
H
Tetrahedral Geometry
4 Identical Bonds
Problem and Solution
C must have 4 identical orbitals in
valence shell for bonding
solution: hybridization (theoretical
mixing of the four atomic orbitals of
carbon atom, the 2s and the three 2p)
Methane
CH4
2p
E
2s
1s
Methane
CH4
2s
2p
E
2s
1s
E
1s
2p
Methane
CH4
2s
2p
E
2s
1s
E
1s
2p
Methane
CH4
2s
2p
E
2s
1s
E
1s
2p
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
because there was the combination of one s
and three p atomic orbitals (25% s, 75% p)
tetrahedral geometry
Methane
CH4
H
2p
E
2s
1s
H
H
sp3
E
1s
H
Valence Bond (VB) Theory
Regions of High
Electron Density
(BP+LP)
Electronic
Geometry
Hybridization,
Angles(°)
2
3
Linear
Trigonal
planar
4
Tetrahedral
5
Trigonal
bipyramidal
sp, 180
sp2
120
sp3
109.5
sp3d
120, 90, 180
6
Octahedral
sp3d2
90, 180
Predict the Hybridization of the Central Atom
in aluminum bromide

 Br
 Br

Al
 Br

Electron-pair shape
3 regions
trigonal planar
Hybridization: sp2
Trigonal Planar Electronic Geometry, sp2
Electronic Structures: BF3
B
B
F [He]
1s

1s

2s

2p

2s 2p 2p
  
2s
2p
   
1s
 
2
sp hybrid
  
Trigonal Planar Electronic Geometry, sp2
BF3
Predict the Hybridization of the Central Atom
in carbon dioxide
CO2


O C O


2 regions
Electron-pair shape, linear
Hybridization: sp (50% s, 50% p)
Linear Electronic Geometry, sp
Electronic Structures: BeCl2
Be
1s

2s

2p
Cl [Ne]
3s
3p
   
1s
 
sp hybrid


Predict the Hybridization of the
Central Atom in Beryllium Chloride
Two regions: electron-pair shape
sp hybridization
Predict the Hybridization of the Central Atom
in PF5
Five regions: Trigonal Bipyramidal Electronic
Geometry
sp3d hybridization, five sp3d hybrid orbitals
Predict the Hybridization of the Central Atom
in xenon tetrafluoride
Predict the Hybridization of the Central Atom
in xenon tetrafluoride




 F  F
 Xe 




F
F


6 regions
electron-pair shape
octahedral
Predict the Hybridization of the Central Atom
in xenon tetrafluoride




 F  F
 Xe 




F
F


3
2
sp d
6 regions
electron-pair shape
octahedral
hybridization
Predict the Hybridization of the Central
Atom in SF6
Six regions: Octahedral Electronic Geometry
- sp3d2 hybridization,
six sp3d2 hybrid orbitals
Consider Ethylene, C2H4
Consider Ethylene, C2H4
H
H
C
H
C
H
Consider Ethylene, C2H4
H
H
C
C
H
3 regions
trigonal planar
H
Consider Ethylene, C2H4
H
H
C
C
H
H
3 regions
trigonal planar
2
sp
hybridization
Consider Ethylene, C2H4
H
H
C
H
C
H
3 regions
trigonal planar
sp2
hybridization
2p
E
2s
1s
2s
2p
E
2s
1s
E
1s
2p
2p
E
2s
1s
sp2
E
1s
2p
sp2
2p
sp2
sp2
2p
sp2
sp2
sp2
 bond framework
 bond
 bond
Compounds Containing Double Bonds
Thus a C=C bond looks like this and is made
of two parts, one  and one  bond.
Consider Acetylene, C2H2
H
C
C
H
Consider Acetylene, C2H2
H
C
2 regions
linear
C
H
Consider Acetylene, C2H2
H
C
C
H
2 regions
linear
sp hybridization
Consider Acetylene, C2H2
H
C
C
H
2 regions
linear
sp hybridization
2s
2p
E
2s
1s
E
1s
2p
2p
E
2s
1s
sp
E
1s
2p
2p
sp
2p
sp
 bond framework
 bonds
Compounds Containing Triple Bonds
A  bond results from the head-on overlap of
two sp hybrid orbitals.
The unhybridized p orbitals form two  bonds
(side-on overlap of atomic orbitals.)
Note that a triple bond consists of one  and
two  bonds.
 bonds
Generally
• single bond is a  bond
• double bond consists of 1  and 1 
bond
• triple bond consists of 1  and 2 
bonds
Molecular Orbital (MO) Theory
When atoms combine to form molecules,
atomic orbitals overlap and are then
combined to form molecular orbitals.
# of orbitals are conserved.
A molecular orbital is an orbital associated
with more than 1 nucleus.
Like any other orbital, an MO can hold 2
electrons.
Consider 2 hydrogen atoms bonding to form
H2
Molecular Orbital Theory
• Combination of atomic orbitals on different atoms forms
molecular orbitals (MO’s) so that electrons in MO’s belong
to the molecule as a whole.
• Waves that describe atomic orbitals have both positive
and negative phases or amplitudes.
• As MO’s are formed the phases can interact
constructively or destructively.
Molecular Orbitals
There are two simple types of molecular
orbitals that can be produced by the overlap
of atomic orbitals.
Head-on overlap of atomic orbitals
produces  (sigma) orbitals.
Side-on overlap of atomic orbitals
produces  (pi) orbitals.
Two 1s atomic orbitals that overlap produce
two molecular orbitals designated as:
1s or bonding molecular orbital
1s* or antibonding molecular orbital.
+
H
H
subtract
add
subtract
antibonding
add
bonding
subtract
antibonding
*1s
add
bonding 1s
Molecular Orbital Energy Level Diagram
Now that we have seen what these MO’s look
like and a little of their energetics, how are
the orbitals filled with electrons?
Order of filling of MO’s obeys same rules as
for atomic orbitals.
Including
Aufbau principle: increasing energy
Pauli’s Excluion: two unaligned e- per orbital,
with opposite spins (+1/2 and -1/2)
Hund’s Rule: maximum spin; unpaired
electrons in degenerate orbitals have same
spin (+1/2 or -1/2)
Thus the following energy level diagram results for
the homonuclear diatomic molecules H2 and He2.
*1s
E
E
1s
1s
1s
H
H2
H
*1s
E
E
1s
1s
1s
H
H2
H
*1s
E
E
1s
1s
1s
H
H2
H
*1s
E
E
1s
1s
1s
H
H2
H
(1s ) 2
*1s
E
E
1s
1s
1s
H
H2
H
(1s ) 2
total spin = 0
*1s
E
E
1s
1s
1s
H
H2
H
• Diamagnetic: slightly repelled by a
magnetic field
– total spin = 0
• paramagnetic: attracted to a magnetic field
– total spin not 0
(bonding e– – antibonding e–)
• Bond Order = ────────────────────
2
Bond Order and Bond Stability
The larger the bond order, the more stable the
molecule or ion is.
Bond order = 0 implies there are equal numbers of
electrons in bonding and antibonding orbitals,
~ same stability as separate atoms: no bond formed
Bond order > 0 implies there are more electrons in
bonding than antibonding orbitals.
Molecule is more stable than separate atoms.
The greater the bond order, the shorter the bond
length and the greater the bond energy.
(1s ) 2
total spin = 0
diamagnetic
*1s
E
E
1s
1s
1s
H
H2
H
BO = 1/2 ( 2 – 0) = 1
*1s
E
E
1s
1s
1s
H
H2
H
Consider He2
*1s
E
E
1s
1s
1s
He
He2
He
*1s
E
E
1s
1s
1s
He
He2
He
(1s ) 2 ( *1s ) 2
*1s
E
E
1s
1s
1s
He
He2
He
diamagnetic
*1s
E
E
1s
1s
1s
He
He2
He
BO = 1/2 ( 2 – 2 ) = 0
He2 does not exist
*1s
E
E
1s
1s
1s
He
He2
He
Combination of p Atomic
Orbitals
Molecular Orbitals
The head-on overlap of two corresponding p
atomic orbitals on different atoms, say 2px
with 2px produces:
2px bonding orbital
2px* antibonding orbital
2p
2p
subtract
add
antibonding MO
subtract
add
bonding MO
subtract
antibonding MO
 *2p
add
bonding MO
 2p
Molecular Orbitals
Side-on overlap of two corresponding p
atomic orbitals on different atoms (say 2py
with 2py or 2pz with 2pz) produces:
π 2p
π
*
y
2p y
or π 2p (both are bonding orbitals)
z
or π*2pz (both are nonbonding orbitals)
2p
2p
subtract
add
subtract
antibonding MO
add
bonding MO
subtract
*2p
add
2p
subtract
*2p
add
2p
Consider Li2
*2p
*2p
2p
E
2p
2p
E
2p
*2s
2s
2s
Li
2s
Li2
Li
*2p
*2p
2p
E
2p
2p
E
2p
*2s
2s
2s
Li
2s
Li2
Li
*2p
*2p
2p
E
2p
2p
E
2p
*2s
2s
2s
Be
2s
Be2
Be
*2p
*2p
2p
E
2p
2p
E
2p
*2s
2s
2s
Be
2s
Be2
Be
*2p
*2p
2p
E
2p
2p
E
2p
*2s
2s
2s
B
2s
B2
B
*2p
*2p
2p
E
2p
2p
E
2p
*2s
2s
2s
B
2s
B2
B
*2p
*2p
2p
E
2p
2p
E
2p
*2s
2s
2s
C
2s
C2
C
*2p
*2p
2p
E
2p
2p
E
2p
*2s
2s
2s
N
2s
N2
N
Homonuclear Diatomic Molecules
In shorthand notation we represent the
configuration of N2 as
N2      
2
1s
*2
1s
2
2s
*2
2s
2
2 py
2
2 pz

2
2p
Bond Order of N2
N2     
2
1s
*2
1s
2
2s
*2
2s
2
2 py

2
2 pz

2
2p
The greater the bond order of a bond the
more stable we predict it to be.
For N2 the bond order is
10 - 4
bo 
2
6

2
 3 correspond ing to a triple
bond in VB theory
*2p
*2p
2p
E
2p
2p
E
2p
*2s
2s
2s
O
2s
O2
O
Homonuclear Diatomic Molecules
In shorthand notation we represent the
configuration of O2 as
O2  
2
1s
*2
1s
 
2
2s
*2
2s

2
2 py

2
2 pz

2
2 px

*1
2 py

10 - 6
bo =
2
2
We can see that O2 is a paramagnetic
molecule (two unpaired electrons).
*1
2 pz
*2p
*2p
2p
E
2p
2p
E
2p
*2s
2s
2s
F
2s
F2
F
*2p
*2p
2p
E
2p
2p
E
2p
*2s
2s
2s
Ne
2s
Ne2
Ne
Bond Order for Ne2
24 - 24
BO = ─────── = 0
2
We can see that Ne2 is not stable. It does not
exist.
Delocalization and Shapes of Molecular
Orbitals
Molecular orbital theory describes
shapes in terms of delocalization of
electrons.
Carbonate ion (CO32-) is a good example.
VB Theory
MO Theory
Delocalization and Shapes of Molecular
Orbitals
Benzene, C6H6, Resonance structure - VB theory
Delocalization and Shapes of Molecular
Orbitals
This is the picture of the valence bond
(VB) theory
Delocalization and Shapes of Molecular
Orbitals
The structure of benzene is described
well by molecular orbital theory.
Heteronuclear Diatomic Molecules
• the more electronegative atom has lower energy
orbitals
• when the combining atomic orbitals are identical and
equal energy, the weight of each atomic orbital in the
molecular orbital are equal
• when the combining atomic orbitals are different kinds
and energies, the atomic orbital closest in energy to
the molecular orbital contributes more to the
molecular orbital
– lower energy atomic orbitals contribute more to the bonding
MO
– higher energy atomic orbitals contribute more to the
antibonding MO
• nonbonding MOs remain localized on the atom
donating its atomic orbitals
NO
Free-Radical
2s Bonding MO
mainly O’s 2s
atomic orbital
HF
Polyatomic Molecules
• when many atoms are combined
together, the atomic orbitals of all
the atoms are combined to make a
set of molecular orbitals which are
delocalized over the entire
molecule
• gives results that better match real
molecule properties than either
Lewis or Valence Bond theories
Ozone, O3
Delocalized
 bonding
orbital of O3