Lecture 16 C1403October 31, 2005

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Lecture 16 C1403 October 31, 2005
18.1 Molecular orbital theory molecular orbitals
and diatomic molecules
18.2 Valence bond theory hybridized orbitals and
polyatomic molecules. From steric number to
hybridization of atoms
Concepts Bond order, bond lengths, connections
of MO theory and VB theory with Lewis structures
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Potential energy curves for the ??and ? orbitals
of a diatomic molecule
Distance dependence of the energy of a ? and ?
orbital
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Making of a ?z and ?z orbital from overlap of
two 2pz orbitals
Making of a ?x and ?x orbital from overlap of
two 2px orbitals
Making of a ?y and ?y orbital from overlap of
two 2py orbitals
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The reason for the switch in the s and p MOs
Larger gap between ?2s and ?2p with increasing Z
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Bond order connection to bond energy and bond
length
Bond enthalpy bond energy energy required to
break the bonds between two atoms
Bond length distance between two nuclei in a
bond
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Some examples of configurations, bond lengths,
bond strength and bond order
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Compare the Lewis and MO structures of diatomic
molecules
C2 (?2s)2(?2s)2(?2p)4(?2p)0(?2p)0(?2p)0
N2 (?2s)2(?2s)2(?2p)4(?2p)2(?2p)0(?2p)0
O2 (?2s)2(?2s)2 (?2p)2(?2p)4(?2p)2(?2p)0
F2 (?2s)2(?2s)2 (?2p)2(?2p)4(?2p)4 (?2p)0
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What is the bond order of NO in Lewis terms and
MO theory?
Valence electrons 11
NO (?2s)2(?2s)2(?2p)2(?2p)4(?2p)1(?2p)0
BO 1/2(8 - 3) 5/2
Odd electron is in an antibonding orbital
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18.2 Polyatomic molecules
Valence bond versus molecular orbital theory
Hybridization of atomic orbitals to form
molecular orbitals
From steric numbers to sp, sp2 and sp3 hybridized
orbitals
Hybridized orbitals and Lewis structures and
molecular geometries
Double bonds and triple bonds
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Hybridization is a theory that starts with
geometry of molecules and then decides on the
hybridization of the atoms based on steric number
of the atoms
Steric number happens to be the same as the
number of hybrid orbitals
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Hybridization
If more than two atoms are involved in a
molecule, the shapes of the orbitals must match
the shape of the bonds that are needed (trigonal,
tetrahedral, etc.). The atomic orbitals do not
have these shapes, and must be mixed (hybridized)
to achieve the needed shapes
Three exemplar organic molecules
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The hybridization of a s orbital and two p
orbitals to produce three sp2 orbitals
Three hybrid Orbitals HAOs sp2
Three Atomic orbitals Aos 2s two 2p
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18.2Bonding in Methane andOrbital Hybridization
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Structure of Methane

• tetrahedral
• bond angles 109.5
• bond distances 110 pm
• but structure seems inconsistent withelectron
  configuration of carbon

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Electron configuration of carbon

• only two unpaired electrons
• should form s bonds to only two hydrogen atoms
• bonds should be at right angles to one another

2p
2s
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sp3 Orbital Hybridization
2p

• Promote an electron from the 2s to the 2p
  orbital

2s
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sp3 Orbital Hybridization
2p
2p
2s
2s
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sp3 Orbital Hybridization
2p

• Mix together (hybridize) the 2s orbital and the
  three 2p orbitals

2s
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sp3 Orbital Hybridization
2p
2 sp3

• 4 equivalent half-filled orbitals are consistent
  with four bonds and tetrahedral geometry

2s
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The CH s Bond in Methane
In-phase overlap of a half-filled 1s orbital of
hydrogen with a half-filled sp3 hybrid orbital of
carbon

sp3
s
H
C
gives a s bond.

HC s
C
H
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Justification for Orbital Hybridization

• consistent with structure of methane
• allows for formation of 4 bonds rather than 2
• bonds involving sp3 hybrid orbitals are stronger
  than those involving s-s overlap or p-p overlap

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18.2sp3 Hybridization and Bonding in Ethane
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Structure of Ethane
C2H6
CH3CH3

• tetrahedral geometry at each carbon
• CH bond distance 110 pm
• CC bond distance 153 pm

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The CC s Bond in Ethane

• In-phase overlap of half-filled sp3
  hybridorbital of one carbon with half-filled
  sp3hybrid orbital of another.
• Overlap is along internuclear axis to give a s
  bond.

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The CC s Bond in Ethane

• In-phase overlap of half-filled sp3
  hybridorbital of one carbon with half-filled
  sp3hybrid orbital of another.
• Overlap is along internuclear axis to give a s
  bond.

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18.2sp2 Hybridization and Bonding in Ethylene
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Structure of Ethylene
C2H4 H2CCH2

• planar
• bond angles close to 120
• bond distances CH 110 pm CC 134 pm

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sp2 Orbital Hybridization
2p

• Promote an electron from the 2s to the 2p
  orbital

2s
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sp2 Orbital Hybridization
2p
2p
2s
2s
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sp2 Orbital Hybridization
2p

• Mix together (hybridize) the 2s orbital and two
  of the three 2p orbitals

2s
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sp2 Orbital Hybridization
2p
2 sp2

• 3 equivalent half-filled sp2 hybrid orbitals plus
  1 p orbital left unhybridized

2s
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sp2 Orbital Hybridization
p
2 of the 3 sp2 orbitalsare involved in s
bondsto hydrogens the otheris involved in a s
bondto carbon
2 sp2
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1.18sp Hybridization and Bonding in Acetylene
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Structure of Acetylene
C2H2

• linear
• bond angles 180
• bond distances CH 106 pm CC 120 pm

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sp Orbital Hybridization
2p

• Promote an electron from the 2s to the 2p
  orbital

2s
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sp Orbital Hybridization
2p
2p
2s
2s
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sp Orbital Hybridization
2p

• Mix together (hybridize) the 2s orbital and one
  of the three 2p orbitals

2s
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sp Orbital Hybridization
2p
2 p
2 sp

• 2 equivalent half-filled sp hybrid orbitals plus
  2 p orbitals left unhybridized

2s
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sp Orbital Hybridization
2 p
1 of the 2 sp orbitalsis involved in a s bondto
hydrogen the otheris involved in a s bondto
carbon
2 sp
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sp Orbital Hybridization
s
2 p
s
2 sp
s
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p Bonding in Acetylene
the unhybridized p orbitals of carbon are
involved in separate p bonds to the other carbon

2 p
2 sp
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p Bonding in Acetylene
2 p
2 sp

• one p bond involves one of the p orbitals on each
  carbon
• there is a second p bond perpendicular to this one

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p Bonding in Acetylene
2 p
2 sp
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p Bonding in Acetylene
2 p
2 sp
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How to determine the hybridization of an atom in
a polyatomic molecule
Draw a Lewis structure of the molecule
Determine the steric number of the atoms of the
molecule
From the steric number assign hybridization as
follows
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one s orbital and one p orbital two sp orbitals
An isoelectroic molecule
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Other examples of sp2 and sp hybridized carbon
Formaldehyde H2CO
Carbon dioxide OCO
Typo CH bond in figure below should be labeled
sp2
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sp2 hybridization and ethylene H2CCH2
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Hybridization and methane CH4
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Hybrid orbitals are constructed on an atom to
reproduce the electronic arrangement
characteristics that will yield the experimental
shape of a molecule
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Examples
BeF2 SN 2 sp
BF3 SN 3 sp2
CH4 SN 4 sp3
PF5 SN 5 sp3d
SF6 SN 6 sp3d2
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Extension to mixing of d orbitals
d2sp3 hybridization six orbitals mixed
octahedral
dsp3 hybridization Five orbitals mixed trigonal
bipyramidal
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