Molecular orbitals

1. Molecular OrbitalsMolecular Orbitals
An approach to bonding in which orbitals An approach to bonding in which orbitals
encompass the entire molecule, rather than encompass the entire molecule, rather than
being localized between atoms.being localized between atoms.
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2. Molecular OrbitalsMolecular Orbitals
Molecular orbitals result from the Molecular orbitals result from the
combination of atomic orbitals. combination of atomic orbitals.
Since orbitals are wave functions, they can Since orbitals are wave functions, they can
combine either constructively (forming a combine either constructively (forming a
bonding molecular orbital), or destructively bonding molecular orbital), or destructively
(forming an antibonding molecular orbital).(forming an antibonding molecular orbital).
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3. Molecular OrbitalsMolecular Orbitals
Molecular orbitals form when atomic orbitals Molecular orbitals form when atomic orbitals
with similar energies and proper symmetry can with similar energies and proper symmetry can
overlap.overlap.
Atomic orbitals with differing energies or the Atomic orbitals with differing energies or the
wrong spatial orientation (orthogonal) do not wrong spatial orientation (orthogonal) do not
combine, and are called combine, and are called non-bondingnon-bonding orbitals. orbitals.
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4. Need for MO TheoryNeed for MO Theory
Valence bond theory fails to explain the Valence bond theory fails to explain the
bonding in many simple molecules. bonding in many simple molecules.
The oxygen molecule has a bond length and The oxygen molecule has a bond length and
strength consistent with a double bond, and it strength consistent with a double bond, and it
contains two unpaired electrons.contains two unpaired electrons.
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5. Need for MO TheoryNeed for MO Theory
Valence bond theory predicts the double Valence bond theory predicts the double
bond, but not the paramagnetism of oxygen.bond, but not the paramagnetism of oxygen.
O=OO=O
:
:
:
:
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6. Need for MO TheoryNeed for MO Theory
Resonance is another example of the Resonance is another example of the
limitations of valence bond theory. Bond limitations of valence bond theory. Bond
lengths and strengths are intermediate between lengths and strengths are intermediate between
single, double or triple bonds. single, double or triple bonds.
Molecular orbital theory is often a better Molecular orbital theory is often a better
approach to use with molecules that have approach to use with molecules that have
extended extended ππ systems. systems.
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7. Molecular Orbital TheoryMolecular Orbital Theory
In order to simplify things, we’ll consider the In order to simplify things, we’ll consider the
interaction of the orbitals containing valence interaction of the orbitals containing valence
electrons to create molecular orbitals.electrons to create molecular orbitals.
The wave functions of hydrogen atom A and The wave functions of hydrogen atom A and
hydrogen atom B can interact either hydrogen atom B can interact either
constructively or destructively.constructively or destructively.
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8. Molecular Orbital TheoryMolecular Orbital Theory
Constructively:Constructively:
ΨΨ
((σσ)) or or ΨΨ
++ = ( = (1/√2 ) 1/√2 ) [[φφ
(1s(1saa) ) + + φφ
(1s(1sbb) ) ]]
Destructively:Destructively:
ΨΨ
((σσ*)*) or or ΨΨ
-- = ( = (1/√2 ) 1/√2 ) [[φφ
(1s(1saa) ) - - φφ
(1s(1sbb) ) ]]
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9. Molecular Orbital TheoryMolecular Orbital Theory
The bonding orbital The bonding orbital
results in increased results in increased
electron density between electron density between
the two nuclei, and is of the two nuclei, and is of
lower energy than the lower energy than the
two separate atomic two separate atomic
orbitals.orbitals.
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10. Molecular Orbital TheoryMolecular Orbital Theory
The antibonding The antibonding
orbital results in a node orbital results in a node
between the two nuclei, between the two nuclei,
and is of greater energy and is of greater energy
than the two separate than the two separate
atomic orbitals.atomic orbitals.
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11. Molecular Orbital TheoryMolecular Orbital Theory
The result is an The result is an
energy level diagram with energy level diagram with
the bonding orbital the bonding orbital
occupied by a pair of occupied by a pair of
electrons. The filling of electrons. The filling of
the lower molecular the lower molecular
orbital indicates that the orbital indicates that the
molecule is stable molecule is stable
compared to the two compared to the two
individual atoms.individual atoms.
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12. Molecular Orbital TheoryMolecular Orbital Theory
The bonding orbital is The bonding orbital is
sometimes given the sometimes given the
notation notation σσ
gg, where the , where the gg
stands for stands for geradegerade, or , or
symmetric with respect symmetric with respect
to a center of inversion. to a center of inversion.
+
+
-
The signs on the molecular orbitals indicate the sign of
the wave function, not ionic charge.
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13. Molecular Orbital TheoryMolecular Orbital Theory
The anti-bonding orbital The anti-bonding orbital
is sometimes given the is sometimes given the
notation notation σσ
uu, where the , where the u u
stands for stands for ungeradeungerade, or , or
asymmetric with respect asymmetric with respect
to a center of inversion. to a center of inversion.
+
+
-
The signs on the molecular orbitals indicate the sign of
the wave function, not ionic charge.
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14. Rules for Combining Atomic Rules for Combining Atomic
OrbitalsOrbitals
1.1.The number of molecular orbitals = the The number of molecular orbitals = the
number of atomic orbitals combined.number of atomic orbitals combined.
2.2.The strength of the bond depends upon the The strength of the bond depends upon the
degree of orbital overlap.degree of orbital overlap.
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15. Experimental EvidenceExperimental Evidence
Photoelectron spectroscopy (PES) is a Photoelectron spectroscopy (PES) is a
technique in which a beam of ultraviolet light technique in which a beam of ultraviolet light
with an energy of 21 eV is used to irradiate with an energy of 21 eV is used to irradiate
molecules. molecules.
The energy is high enough to eject electrons. The energy is high enough to eject electrons.
The kinetic energy of the emitted electrons is The kinetic energy of the emitted electrons is
measured, and used to determine the energy measured, and used to determine the energy
level of the electron.level of the electron.
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16. Experimental EvidenceExperimental Evidence
The technique allows The technique allows
for the measurement for the measurement
of specific ionization of specific ionization
energies (I). Each energies (I). Each
ionization energy ionization energy
represents the represents the
removal of an removal of an
electron from a electron from a
specific molecular specific molecular
orbital.orbital.
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17. Experimental EvidenceExperimental Evidence
Electrons in Electrons in
lower energy levels lower energy levels
require more energy require more energy
to be removed, and to be removed, and
are ejected with less are ejected with less
kinetic energy. kinetic energy.
hhνν
oo = I + E = I + E
kinetickinetic
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18. Period 2 Diatomic MoleculesPeriod 2 Diatomic Molecules
For the second period, assume that, due to a For the second period, assume that, due to a
better energy match, better energy match, ss orbitals combine with orbitals combine with ss
orbitals, and orbitals, and pp orbitals combine with orbitals combine with pp orbitals. orbitals.
The symmetry of The symmetry of pp orbitals permits end-on- orbitals permits end-on-
end overlap along the bond axis, or side-by-side end overlap along the bond axis, or side-by-side
overlap around, but not along, the internuclear overlap around, but not along, the internuclear
axis.axis.
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19. MOs using MOs using pp orbitals orbitals
With the With the xx axis as the bond axis, the p axis as the bond axis, the p
xx
orbitals may combine constructively or orbitals may combine constructively or
destructively. The result is a destructively. The result is a σσ bonding orbital bonding orbital
and a and a σσ anti-bonding orbital. anti-bonding orbital.
+
++ -
--
-
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20. MOs using MOs using pp orbitals orbitals
The designation The designation σσ indicates symmetric indicates symmetric
electron density around the internuclear (electron density around the internuclear (xx) axis. ) axis.
The + and – signs indicate the sign of the wave The + and – signs indicate the sign of the wave
function, and not electrical charges.function, and not electrical charges.
+
++ -
--
-
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21. MOs using MOs using pp orbitals orbitals
Some texts will use the symmetry Some texts will use the symmetry
designations of designations of gg (gerade) or (gerade) or uu (ungerade) instead (ungerade) instead
of indicating bonding or anti-bonding. of indicating bonding or anti-bonding.
+
++ -
--
-
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22. MOs using MOs using pp orbitals orbitals
For these orbitals, the bonding orbital is For these orbitals, the bonding orbital is
geradegerade, or symmetric around the bond axis., or symmetric around the bond axis.
+
++ -
--
-
σ
g
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23. MOs using MOs using pp orbitals orbitals
For these orbitals, the anti-bonding orbital is For these orbitals, the anti-bonding orbital is
asymmetric about the bond axis, and is asymmetric about the bond axis, and is
designated as designated as σσ
uu. Note that the designations of . Note that the designations of uu
or or gg do notdo not correlate with bonding or anti- correlate with bonding or anti-
bonding.bonding.
+
++ -
--
-
σ
g
σ
u
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24. ππ Molecular Orbitals Molecular Orbitals
The orbital overlap side-by-side is less than The orbital overlap side-by-side is less than
that of overlap along the bond axis (end-on-that of overlap along the bond axis (end-on-
end). As a result, the bonding orbital will be end). As a result, the bonding orbital will be
higher in energy than the previous example.higher in energy than the previous example.
side-by-side
overlap
+
+
+
-
-
-
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25. ππ Molecular Orbitals Molecular Orbitals
ππ orbitals are asymmetric with respect to the orbitals are asymmetric with respect to the
bond axis. There is electron density surrounding bond axis. There is electron density surrounding
the bond axis, with a node along the internuclear the bond axis, with a node along the internuclear
axis.axis.
side-by-side
overlap
+
+
+
-
-
-
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26. ππ Molecular Orbitals Molecular Orbitals
Some texts use the subscripts Some texts use the subscripts gg and and uu instead instead
of bonding and anti-bonding. In this example, of bonding and anti-bonding. In this example,
the bonding orbital is ungerade, or asymmetric the bonding orbital is ungerade, or asymmetric
about a center of symmetry.about a center of symmetry.
side-by-side
overlap
+
+
+
-
-
-
π
u
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27. ππ Molecular Orbitals Molecular Orbitals
The anti-bonding orbital is The anti-bonding orbital is geradegerade, or , or
symmetric about a center of symmetry.symmetric about a center of symmetry.
side-by-side
overlap
+
+
+
-
-
-
π
u
π
g
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28. Molecular Orbital DiagramMolecular Orbital Diagram
This is a molecular This is a molecular
orbital energy level orbital energy level
diagram for the diagram for the pp
orbitals. Note that the orbitals. Note that the
σσ bonding orbital is bonding orbital is
lowest in energy due to lowest in energy due to
the greater overlap the greater overlap
end-on-end.end-on-end.
2p 2p
σ
g
π
u
π
g
σ
u
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29. Molecular Orbital DiagramMolecular Orbital Diagram
The alternate The alternate
notation is provided notation is provided
on the right side of the on the right side of the
energy level diagram.energy level diagram.
2p 2p
σ
g
π
u
π
g
σ
u
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30. Molecular Orbital DiagramsMolecular Orbital Diagrams
1.1.Electrons preferentially occupy molecular Electrons preferentially occupy molecular
orbitals that are lower in energy.orbitals that are lower in energy.
2.2.Molecular orbitals may be empty, or contain Molecular orbitals may be empty, or contain
one or two electrons.one or two electrons.
3.3.If two electrons occupy the same molecular If two electrons occupy the same molecular
orbital, they must be spin paired.orbital, they must be spin paired.
4.4.When occupying degenerate molecular When occupying degenerate molecular
orbitals, electrons occupy separate orbitals orbitals, electrons occupy separate orbitals
with parallel spins before pairing.with parallel spins before pairing.
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31. Molecular Orbital DiagramsMolecular Orbital Diagrams
Although molecular orbitals form from inner Although molecular orbitals form from inner
(core) electrons as well as valence electrons, (core) electrons as well as valence electrons,
many molecular orbital diagrams include only many molecular orbital diagrams include only
the valence level.the valence level.
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32. Molecular Orbital DiagramsMolecular Orbital Diagrams
For OFor O
22, there , there
will be a total of will be a total of
12 valence 12 valence
electrons that electrons that
must be placed in must be placed in
the diagram.the diagram.
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33. Molecular Orbital DiagramsMolecular Orbital Diagrams
For OFor O
22, there , there
will be a total of will be a total of
12 valence 12 valence
electrons that electrons that
must be placed in must be placed in
the diagram.the diagram.
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34. Molecular Orbital DiagramsMolecular Orbital Diagrams
For OFor O
22, there , there
will be a total of will be a total of
12 valence 12 valence
electrons that electrons that
must be placed in must be placed in
the diagram.the diagram.
2p 2p
2s 2s
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35. MO Diagram for OMO Diagram for O
22
2p 2p
2s 2s
σ
g
σ*
u
σ
g
π
u
π*
g
σ*
u
The molecular
orbital diagram for
oxygen shows two
unpaired electrons,
consistent with
experimental data.
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36. Bond OrderBond Order
Bond order is an indicator of the bond Bond order is an indicator of the bond
strength and length. A bond order of 1 is strength and length. A bond order of 1 is
equivalent to a single bond. Fractional bond equivalent to a single bond. Fractional bond
orders are possible.orders are possible.
The bond order of the molecule =The bond order of the molecule =
(# e(# e
--
in bonding orbtls) in bonding orbtls) - - (# e(# e
--
in anti-bonding orbtls) in anti-bonding orbtls)
22 22
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37. MO Diagram for OMO Diagram for O
22
2p 2p
2s 2s
σ
g
σ*
u
σ
g
π
u
π*
g
σ*
u
The bond order of
O
2
is:
8-4 = 2
2
This is consistent
with a double
bond.
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38. MO Diagram for OMO Diagram for O
22
2p 2p
2s 2s
σ
g
σ*
u
σ
g
π
u
π*
g
σ*
u
This energy level
diagram works well
for atoms in which
the 2s and 2p levels
are fairly far apart.
These are the
elements at the right
of the table: O, F and
Ne.
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39. Experimental EvidenceExperimental Evidence
Oxygen is paramagnetic, consistent with having Oxygen is paramagnetic, consistent with having
two unpaired electrons. In addition, two unpaired electrons. In addition, photoelectron photoelectron
spectroscopyspectroscopy (PES) can be used for determining orbital (PES) can be used for determining orbital
energies in molecules. The molecule is bombarded with energies in molecules. The molecule is bombarded with
UV or X-rays to remove an electron from the molecule. UV or X-rays to remove an electron from the molecule.
The kinetic energy of the emitted electron is measured The kinetic energy of the emitted electron is measured
and subtracted from the incident radiation to determine and subtracted from the incident radiation to determine
the binding energy of the electron.the binding energy of the electron.
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40. Photoelectron SpectroscopyPhotoelectron Spectroscopy
The result is a spectrum of absorptions which are The result is a spectrum of absorptions which are
correlated to the molecular orbitals of the molecule. In correlated to the molecular orbitals of the molecule. In
addition, electrons ejected from bonding orbitals show addition, electrons ejected from bonding orbitals show
more vibrational energy levels than electrons emitted more vibrational energy levels than electrons emitted
from anti-bonding or non-bonding orbitals.from anti-bonding or non-bonding orbitals.
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41. Muhammad Asif Pakistan

42. MO diagram for Li through NMO diagram for Li through N
The elements on the left side of period 2 The elements on the left side of period 2
have a fairly small energy gap between the 2s have a fairly small energy gap between the 2s
and 2p orbitals. As a result, interaction between and 2p orbitals. As a result, interaction between
s and p orbitals is possible. This can be viewed s and p orbitals is possible. This can be viewed
in different ways. in different ways.
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43. MO diagram for Li through NMO diagram for Li through N
In some approaches, the s orbital on one atom In some approaches, the s orbital on one atom
interacts with the p orbital on another. The interaction interacts with the p orbital on another. The interaction
can be constructive or destructive.can be constructive or destructive.
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44. MO diagram for Li through NMO diagram for Li through N
In another approach, the s and p orbitals on In another approach, the s and p orbitals on
the the samesame atom interact in what is called atom interact in what is called orbital orbital
mixingmixing. .
Either approach yields the same result. The Either approach yields the same result. The
σσ bonding and anti-bonding orbitals are raised in bonding and anti-bonding orbitals are raised in
energy due to the interaction with a energy due to the interaction with a pp orbital. orbital.
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45. MO diagram for Li through NMO diagram for Li through N
σ
g
σ
g
σ*
u
σ*
u
π
u
π*
g
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46. MO diagram for NMO diagram for N
22
σ
g
σ
g
σ*
u
σ*
u
π
u
π*
g
N
2
has 10
valence
electrons.
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47. Experimental EvidenceExperimental Evidence
The photoelectronic The photoelectronic
spectrum of nitrogen is spectrum of nitrogen is
consistent with a consistent with a
molecular orbital molecular orbital
approach. approach.
Electrons emitted Electrons emitted
from bonding orbitals from bonding orbitals
show vibrational show vibrational
excitations.excitations.
σ
g
π
u
σ*
u
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48. Experimental EvidenceExperimental Evidence
σ
g
π
u
σ*
u
σ
g
σ
g
σ*
u
σ*
u
π
u
π*
g
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49. Heteronuclear Diatomic Heteronuclear Diatomic
MoleculesMolecules
The more electronegative atom will have The more electronegative atom will have
orbitals of lower energy, and therefore orbitals of lower energy, and therefore
contribute more to the bonding orbitals.contribute more to the bonding orbitals.
The less electronegative atom has orbitals of The less electronegative atom has orbitals of
higher energy, and contributes more to the anti-higher energy, and contributes more to the anti-
bonding orbitals.bonding orbitals.
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50. Rules for Combining Atomic Rules for Combining Atomic
OrbitalsOrbitals
For heteronuclear molecules:For heteronuclear molecules:
1. The bonding orbital(s) will reside 1. The bonding orbital(s) will reside
predominantly on the atom of lower orbital predominantly on the atom of lower orbital
energy (the more electronegative atom).energy (the more electronegative atom).
2. The anti-bonding orbital(s) will reside 2. The anti-bonding orbital(s) will reside
predominantly on the atom with greater orbital predominantly on the atom with greater orbital
energy (the less electronegative atom).energy (the less electronegative atom).
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51. HFHF
The 2s and 2pThe 2s and 2p
xx orbitals orbitals
on fluorine interact with on fluorine interact with
the 1s orbital on hydrogen. the 1s orbital on hydrogen.
The pThe p
yy and p and p
zz orbitals orbitals
on fluorine lack proper on fluorine lack proper
symmetry to interact with symmetry to interact with
hydrogen, and remain as hydrogen, and remain as
non-bonding orbitals.non-bonding orbitals.
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52. HFHF
The anti-bonding The anti-bonding
orbital resides primarily on orbital resides primarily on
the less electronegative the less electronegative
atom (H).atom (H).
Note that the Note that the
subscripts subscripts gg and and uu are not are not
used, as the molecule no used, as the molecule no
longer has a center of longer has a center of
symmetry.symmetry.
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53. Carbon monoxideCarbon monoxide
In carbon In carbon
monoxide, the bonding monoxide, the bonding
orbitals reside more on orbitals reside more on
the oxygen atom, and the oxygen atom, and
the anti-bonding the anti-bonding
orbitals reside more on orbitals reside more on
the carbon atom. the carbon atom.
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54. Carbon monoxideCarbon monoxide
CO is a highly CO is a highly
reactive molecule with reactive molecule with
transition metals. transition metals.
Reactivity typically Reactivity typically
arises from the arises from the hhighest ighest
ooccupied ccupied mmolecular olecular
oorbital (HOMO), when rbital (HOMO), when
donating electrons.donating electrons.
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55. Carbon monoxideCarbon monoxide
When acting as an When acting as an
electron pair acceptor, electron pair acceptor,
the the llowest owest
uunoccupied noccupied mmolecular olecular
oorbital (LUMO), is rbital (LUMO), is
significant.significant.
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56. Carbon monoxideCarbon monoxide
When acting as an When acting as an
electron pair donor, electron pair donor,
the the hhighest ighest ooccupied ccupied
mmolecular olecular oorbital rbital
(HOMO), is (HOMO), is
significant.significant.
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57. The highest
occupied molecular
orbital of CO is a
molecular orbital
which puts
significant electron
density on the
carbon atom.
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58. The lowest
unoccupied
molecular orbital of
CO is the π* orbitals.
The lobes of the
LUMO are larger on
the carbon atom than
on the oxygen atom.
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59. CO as a LigandCO as a Ligand
Carbon monoxide is known as a Carbon monoxide is known as a σσ donor and donor and
a a ππ acceptor ligand. It donates electrons from its acceptor ligand. It donates electrons from its
HOMO to form a sigma bond with the metal.HOMO to form a sigma bond with the metal.
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60. CO as a LigandCO as a Ligand
Carbon monoxide accepts electrons from Carbon monoxide accepts electrons from
filled filled dd orbitals on the metal into its antibonding orbitals on the metal into its antibonding
(LUMO) orbital.(LUMO) orbital.
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61. CO as a LigandCO as a Ligand
This phenomenon is called This phenomenon is called back bondingback bonding. The . The
increased electron density in the antibonding orbitals of increased electron density in the antibonding orbitals of
CO causes an increase in the C-O bond length and a CO causes an increase in the C-O bond length and a
decrease in its stretching frequency.decrease in its stretching frequency.
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62. MOs for Larger MoleculesMOs for Larger Molecules
Group theory is usually used to develop Group theory is usually used to develop
molecular orbital diagrams and drawings of molecular orbital diagrams and drawings of
more complicated molecules. When a central more complicated molecules. When a central
atom is bonded to several atoms of the same atom is bonded to several atoms of the same
element (Helement (H
22O, BFO, BF
33, or PtCl, or PtCl
44
2-2-
], group theory can ], group theory can
be used to analyze the symmetry of the orbitals be used to analyze the symmetry of the orbitals
of the non-central atoms, and then combine of the non-central atoms, and then combine
them with the appropriate orbitals of the central them with the appropriate orbitals of the central
atom.atom.
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63. MOs for Larger MoleculesMOs for Larger Molecules
The orbitals of the non-central atoms are The orbitals of the non-central atoms are
called called group orbitalsgroup orbitals. In considering a simple . In considering a simple
example, Hexample, H
22O, we obtain group orbitals using O, we obtain group orbitals using
the two the two 1s1s orbitals on the hydrogen atoms. orbitals on the hydrogen atoms.
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64. The characters for the The characters for the
group orbitals is obtained by group orbitals is obtained by
considering each hydrogen considering each hydrogen
as a spherical as a spherical 1s1s orbital. orbital.
They remain in position for They remain in position for
identity, are exchanged identity, are exchanged
during rotation, remain in during rotation, remain in
place for σplace for σ
xzxz (the molecular (the molecular
plane), and are exchanged plane), and are exchanged
for σfor σ
yzyz..
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65. Group Orbitals of WaterGroup Orbitals of Water
ΓΓ
redred and its irreducible representations are: and its irreducible representations are:
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66. Group Orbitals of WaterGroup Orbitals of Water
The AThe A
11 representation has both representation has both 1s1s orbitals with orbitals with
positive wave functions: Hpositive wave functions: H
aa+H+H
bb..
The BThe B
11 representations is H representations is H
aa+H+H
bb..
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67. Group Orbitals of WaterGroup Orbitals of Water
These group orbitals are combined with orbitals These group orbitals are combined with orbitals
on oxygen that have the same symmetry.on oxygen that have the same symmetry.
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68. Group Orbitals of WaterGroup Orbitals of Water
The 2s and 2p
z
orbital on oxygen have
A
1
symmetry, the 2p
x
orbital has B
1
symmetry,
and the 2p
y
has B
2
symmetry.
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69. Molecular Orbitals of WaterMolecular Orbitals of Water
Since the Since the 2p2p
yy orbital on oxygen doesn’t orbital on oxygen doesn’t
match the symmetry of the group orbitals of match the symmetry of the group orbitals of
hydrogen, it will remain non-bonding. The hydrogen, it will remain non-bonding. The
other orbitals on oxygen will combine with the other orbitals on oxygen will combine with the
appropriate group orbitals to form bonding and appropriate group orbitals to form bonding and
antibonding molecular orbitals.antibonding molecular orbitals.
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70. Muhammad Asif Pakistan

71. MOs for Larger MoleculesMOs for Larger Molecules
Group theory is usually used to develop Group theory is usually used to develop
molecular orbital diagrams and drawings of molecular orbital diagrams and drawings of
more complicated molecules. A simplified more complicated molecules. A simplified
example will be shown for the example will be shown for the ππ bonding of bonding of
benzene.benzene.
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72. ππ Bonding of Benzene Bonding of Benzene
Benzene belongs to point group DBenzene belongs to point group D
6h6h. In . In
determining the orbital combinations for determining the orbital combinations for ππ
bonding, we need to obtain bonding, we need to obtain ГГ
ππ by looking only at by looking only at
the pthe p
zz orbitals on each carbon atom. orbitals on each carbon atom.
We need only consider
those orbitals on carbon
atoms that remain in place
for a given symmetry
operation.
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73. ππ Bonding of Benzene Bonding of Benzene
DD
6h6hEE2C2C
662C2C
33CC
223C′3C′
223C″3C″
22ii2S2S
332S2S
66σσ
hh3 3 σσ
dd3 3 σσ
vv
ГГ
ππ
{
z axis
C′
2C″
2
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74. ππ Bonding of Benzene Bonding of Benzene
DD
6h6hEE2C2C
662C2C
33CC
223C′3C′
223C″3C″
22ii2S2S
332S2S
66σσ
hh3 3 σσ
dd3 3 σσ
vv
ГГ
ππ66000000-2-200000000-6-60022
{
z axis
C′
2C″
2
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75. ππ Bonding of Benzene Bonding of Benzene
DD
6h6hEE2C2C
662C2C
33CC
223C′3C′
223C″3C″
22ii2S2S
332S2S
66σσ
hh3 3 σσ
dd3 3 σσ
vv
ГГ
ππ66000000-2-200000000-6-60022
{
z axis
C′
2C″
2
This reduces to: B
2g
+ E
1g
+ A
2u
+ E
2u
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76. ππ Bonding of Benzene Bonding of Benzene
Гπ: B
2g
+ E
1g
+ A
2u
+ E
2u
Group theory can be used to draw each of Group theory can be used to draw each of
the the ππ molecular orbitals. Molecular orbitals with molecular orbitals. Molecular orbitals with
fewer nodes are lower in energy (more bonding), fewer nodes are lower in energy (more bonding),
and those with more nodes are higher in energy and those with more nodes are higher in energy
(more antibonding).(more antibonding).
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77. ππ Bonding of Benzene Bonding of Benzene
Гπ: B
2g
+ E
1g
+ A
2u
+ E
2u
A
2u
fully bonding and
lowest in energy
E
1g
degenerate
bonding orbitals
with one node
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78. ππ Bonding of Benzene Bonding of Benzene
Гπ: B
2g
+ E
1g
+ A
2u
+ E
2u
E
2u
degenerate
largely anti-
bonding orbitals
with two nodes
B
2g
fully anti-
bonding orbital
with three nodes
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79. ππ Bonding of Benzene Bonding of Benzene
A
2u
E
1g
E
2u
B
2g
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80. Molecular Orbitals of ComplexesMolecular Orbitals of Complexes
Group theory is also used to construct Group theory is also used to construct
molecular orbital diagrams for the complexes of molecular orbital diagrams for the complexes of
metal atoms or ions. The symmetry metal atoms or ions. The symmetry
combinations of the atomic orbitals on the combinations of the atomic orbitals on the
ligands are determined, and then “matched” ligands are determined, and then “matched”
with appropriate atomic orbitals on the central with appropriate atomic orbitals on the central
metal. Both metal. Both σσ and and ππ bonding between the metal bonding between the metal
and ligands can be considered.and ligands can be considered.
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