Bonding and Antibonding interactions; Idea about σ, σ*, π, π *, n – MOs; HOMO, LUMO and SOMO; Energy levels of π MOs of different conjugated acyclic and cyclic systems; Hückel’s rules for aromaticity; Frost diagram

1. ORGANIC CHEMISTRY
CHEMISTRY HONOURS COURSE
Energy levels of π MOs of different conjugated systems
Dr. Santarupa Thakurta
Assistant Professor
Department of Chemistry
Prabhu Jagatbandhu College
West Bengal
MOLECULAR ORBITAL THEORY

2. Electron as wave
2

3. Linear Combination of Atomic Orbitals (LCAO)
3

4. Three types of molecular orbitals are possible:

5. Antibonding:
destabilizing.
Higher Energy
pi type anti-bond sigma type anti-bonding
Bonding : Atoms are
directly attached to each
other - strongly bonding
interactions, stabilizing
the system. Lower energy.
Non bonding: distant atomic orbitals,
atoms not directly attached to each other.
Their interaction is weak and does not
affect the energy of the system.
non-bonded
pi type bond sigma type bonding
or
or
or or

6. 6

7. 7

8. 8

9. Sketch And Energy Levels Of  MOs Of Acyclic p Orbital System
1. C=C: -Molecular Orbital of Ethylene
9

10. 2. Conjugated Diene: Pi-Molecular Orbital of 1,3-Butadiene
10
1,3-Butadiene contains two double bonds that are conjugated. It is "built" from 4 sp2
hybridised C atoms, each contributing a p atomic orbital containing one electron.
LCAO method

11. The Lowest-Energy Molecular Orbital has p orbitals
with phases in complete alignment with each other:
there are zero nodes between the p orbitals themselves.
A physical interpretation of this orbital is that an
electron in this orbital is delocalized over the length of
the pi system.
The phases flip in the centre of the pi orbital.
Two adjacent non-interacting pi bonds, where
the electrons are each confined to pi orbitals
spanning two carbons each, with a node in the middle
Nodes are placed symmetrically with respect to
the centre. This gives a 2-carbon pi orbital in the
centre flanked by two one-carbon orbitals on the sides.
The Highest-Energy Molecular Orbital (π4*):
four p orbitals with alternative phases of each.
This creates a pi system with three nodes.

12. 12
The Highest Occupied Molecular Orbital (HOMO) and The
Lowest-Unoccupied Molecular Orbital (LUMO)
HOMO is π2.
The HOMO can be considered as being a little bit like the “valence electrons” of the pi
system: they’re the most readily lost. If butadiene participates in a reaction where it is
the electron-donor (nucleophile), its electrons are going to come from that orbital.
LUMO is π3.
If butadiene participates in a reaction where it is the electron acceptor (electrophile),
the electrons will be donated to that orbital.

13. An alternative way to consider "building" the π molecular orbitals is by combining the
π molecular orbitals of two ethene molecules.
This requires that we make an in-phase and an out-of-phase combination for both the π
and π* of ethene.
This method of construction also shows why the HOMO-LUMO gap of
butadiene is smaller than that of ethene. 13

14. A  to * transition in excitation of Ethene .
A  to * transition in excitation of Butadiene .
 Absorption of UV-Vis radiation results in promotion of electrons from a lower-energy,
occupied MO to a higher-energy, unoccupied MO.
 The λ tells us the energy E required to promote an electron from HOMO to LUMO.
 As this HOMO-LUMO gap (E) decreases , λ increases (E= hc/λ).
 The molecule absorbs in the visible region and we see the complementary colour.
UV-Visible Spectroscopy :
measures a molecule’s absorption of light at different wavelengths λ

15. In general, as conjugated pi systems become larger, the energy gap for a π - π*
transition becomes increasingly narrow, and the wavelength of light absorbed
correspondingly becomes longer (E= hc/λ).
In other words, excitation of an electron from HOMO to LUMO (i.e. absorbing a
photon, which gives rise to the colour of the molecule) takes less energy as the number
of double bonds increases.
15
724 (173)
552 (132)
448 (107)
385 (92)
290
268
217
165
m ax
Structural Formula
Name
(3E,5E)-1,3,5,7-Octatetraene
(3E)-1,3,5-Hexatriene
1,3-Butadiene
Ethylene
(nm)
Energy
[kJ (kcal)/mol]

16. A common feature of all natural colored organic compounds is a system of extensively
conjugated pi-electrons. Some very brightly coloured molecules such as carotene,
chlorophyll and lycopene have very long conjugated double bonds.
16

17. Frontier Molecular Approach:
HOMO of one reactant is looked upon as being analogous to the
outer (valence) electrons of an atom.
The reaction is envisaged as involving the overlap of this HOMO –
an potential e’ donor with the LUMO – a potential e’ acceptor of
the other reactant.
HOMO-LUMO Gap:
The HOMO of the nucleophile reacts with the LUMO of the
electrophile and the closer in energy they are, the stronger the
interaction- faster reaction.
17

18. The addition reaction of Br2 occurs faster with butadiene than ethylene.
-15°C
3,4-Dibromo-1-butene
(54%)
(1,2-addition)
1,4-Dibromo-2-butene
(46%)
(1,4-addition)
+
+
1,3-Butadiene
CH2 = CH- CH= CH2 Br2
CH2 - CH= CH- CH2
CH2 - CH- CH= CH2
Br Br Br Br
The unsaturated compounds act as nucleophile and Br2 act as electrophile.
So consider the energy gap between HOMO of olefin:  BMO and LUMO of Br2 :  ABMO
Now, HOMO of butadiene is at higher energy than HOMO of ethene.
So the energy gap is smaller in case of butadiene and it reacts faster than ethene.

19. 3. Conjugated Triene:
Pi-Molecular Orbital Of 1,3,5-hexatriene
19

20. 4. Molecular Orbital of Allyl System: Cation, Anion, Free radical
Since there were now three 2pz AO’s in the basis set, there are three MO’s which result
from their combination by overlap.
Only one MO is bonding 1, and there are an antibonding 3 and a nonbonding MO 2.
NBMO 2 : encompasses only the end carbons, there is node at middle carbon. It has
same energy as the basis set AO, i.e., has not benefit from delocalization.
20

21. HOMO LUMO
Cation 1 2
Anion 2 3
Free radical 2 3
21

22. 5. Molecular Orbital of Pentadienyl System:
Cation, Anion, Free radical
22

23. Sketch And Energy Levels Of  MOs Of Cyclic p Orbital System :
a.neutral systems
1.  Molecular Orbital of Benzene
Degenerate Orbitals: orbitals that have the same energy 23

24. 24

25. 25
Why Is Benzene More Stable Than Hexatriene?
Two molecular orbitals can have the same number of nodal planes, and therefore have the
same energy. This is described by saying the orbitals are degenerate.
This is really the key difference in the molecular orbital picture of a cyclic system versus an
acyclic system: two units can co-exist on the same level. The highest occupied molecular
orbitals (HOMO) of benzene (2 and 3 : one node) are lower in energy than the highest
occupied molecular orbital (HOMO) of hexatriene (3: two nodes).
And for our purposes, that lower energy of the pi-electrons translates into lower reactivity.
Aromaticity:
cyclic conjugated organic compounds such as benzene, that exhibit special
stability due to resonance delocalization of pi-electrons.
Aromatic stability - extensive delocalization – high resonance energy

26. Stability of Benzene :
The π-bonds of benzene are resistant to the normal reactions of alkenes and alkynes
Benzene undergoes electrophilic substitution reactions rather than electrophilic addition
Stability of Benzene: Heats of Hydrogenations
calc'd value= 354 KJ/mol - 148 KJ/mol added stability
26

27. Structure of Benzene :
Double Bond Equivalent: Number of double bonds and/or rings
in the compound (CaHbNcOd)
D.B.E. = a+1-(b-c)/2
D.B.E. of C6H6 = 6+1-(6-0)/2 = 7-3 = 4 (3 double bonds, 1 ring)
•All bonds are ~139 pm (intermediate between C-C and C=C)
•Electron density is distributed evenly between the six carbons
•Structure is planar, hexagonal
•C–C–C bond angles are 120°
•Each carbon is sp2
and has a p orbital perpendicular to the plane of the six-
membered ring
27

28. 2. Pi Molecular Orbital of Cyclobutadiene
28
HOMO( 2 and 3): one node, non-bonding, singly occupied
HOMO (2): one node, bonding,
completely filled

29. Can you see why cyclobutadiene is unstable?
Cyclic conjugated molecules: not all cyclic conjugated systems are
aromatic (no special stability)
29
• First, the highest occupied molecular orbitals (HOMO) of cyclobutadiene are
degenerate pair of non-bonding orbitals, intermediate in energy between the lowest
(π1, bonding) and highest (π4, antibonding) energy orbitals.
• “Non-bonding” implies that filling these orbitals with electrons does not result in
any stabilization of the molecule.
• Second, note that each of the HOMO orbitals is singly occupied.
• Therefore this orbital picture predicts that cyclobutadiene should have a di-radical
nature. A species containing two free radicals is extremely reactive!

30. 30
Hückel 4n + 2 Rule for Aromaticity
“Hückel (1937) carried out MO calculations on monocyclic systems CnHn containing n π
electrons and each carbon providing one electron, and as result connected aromatic stability with
the presence of (4n+2) π electrons in a closed shell, where n is an interger.”
Aromatic Requirements
Structure must be cyclic with conjugated pi bonds.
Each atom in the ring must have an unhybridized p orbital.
The p orbitals must overlap continuously around the ring. (Usually planar structure)
Must contain 4n+2 π-electrons, where n is an integer
Compound is more stable than its open-chain counterpart.
Example: benzene vs. 1,3,5-hexatriene
Anti-aromatic :
Cyclic, conjugated, flat molecules that contain 4n π-electrons (where n is an integer)
Antiaromatic compounds are cyclic, conjugated, with overlapping p orbitals around the ring,
but the the compound is less stable than its open-chain counterpart.
Example: cyclobutadiene vs. 1,3-butadiene

31. 31
Theoretical justification
Energies of MOs of cyclic conjugated systems have a pattern:
• There is one orbital of lowest energy followed by a degenerate pair
of orbitals in order of increasing energy.
• Finally there is one orbital of highest energy.
• Filling of the orbitals takes place as per Hund’s rule.
4n+2 π-electrons: aromatic
The lowest energy MO and all degenerate pair of orbitals are occupied
by two electron each- All BMO s are completely filled which results
stabilisation.
4n π-electrons: antiaromatic
There are two singly occupied degenerate orbitals - highly unstable.

32. Annulenes
Annulenes are completely conjugated monocyclic hydrocarbons. They have the general
formula CnHn (when n is an even number) or CnHn+1 (when n is an odd number). The
IUPAC naming conventions are that annulenes with 7 or more carbon atoms are named
as [n]annulene, where n is the number of carbon atoms in their ring, though sometimes
the smaller annulenes are referred to using the same notation, and benzene is
sometimes referred to simply as annulene
• [4]Annulene (cyclobutadiene) is antiaromatic : 4  e-
’s
• [6]Annulene (benzene) is aromatic : 6  e-
’s
32
Larger 4n annulenes are not antiaromatic because they are flexible
enough to become nonplanar. Such cyclic systems show non
aromatic behavior.
Non-aromatic
Nonaromatic compounds do not have a continuous ring of
overlapping p orbitals and may be nonplanar.

33. [8]Annulene (cyclooctatetraene), a conjugated 8 pi electron cyclic system –
would be antiaromatic, but it’s nonaromatic.
The molecule is not planar, it typically adopts a "tub" conformation.
The lack of conjugation allows the 8 π electron molecule to avoid antiaromaticity.
33
[10]Annulene or cyclodecapentaene, a conjugated 10 pi electron cyclic system –
should display aromaticity, but it is non-aromatic
It is not aromatic because various types of ring strain destabilize an all-planar geometry.
Cis isomer (2): angle strain. Trans isomer (3): steric strain.
The nonplanar structure (4) is the most stable of all the possible isomers.

34. Frost Circles
A useful method for drawing energy levels of the molecular orbitals
in cyclic pi systems: “Frost Circles” (polygon method)
Inscribe the cyclic, conjugated molecule into a circle so that a vertex is
at the bottom. The relative energies of the MO’s are where the ring
atoms intersect the circle.
34

35. 35

36. Sketch And Energy Levels Of  MOs Of Cyclic p Orbital System :
b.Charged Systems -Aromatic ions (CnHn type)
1.Cyclopropenium salts
Three sp2
hybridised carbons have three component p orbitals, which can give rise to
three MOs.
Cyclopropenyl cation: 2 electron, Anion: 4 electron, Free radical: 3 electron
BMO is completely filled: stable
ABMO is partially filled: unstable

37. 2.Cyclobutenium salts
Loss of two  electrons in the separate non-bonding MOs of cyclobutadiene produces 4n+2 (n = 0)
i.e., 2 system. So the cyclobutenyl di-cation is aromatic.
3.Cyclopentadienide salts
Five sp2
hybridised carbons have five component p orbitals, which can give rise to five MOs.
Cyclopentadienyl cation: 4 electron, Anion: 6 electron, Free radical: 5 electron
BMO is partially filled: unstable
BMO is completely filled: stable

38. BMO is completely filled: stable
5. Cyclooctatetraenyl dianion
Gain of two  electrons in each non-bonding MOs of cyclooctatetraene produces
4n+2 (n = 2) i.e., 10  system. So the Cyclooctatetraenyl dianion is aromatic.
38
4. Tropylium salt
Seven sp2
hybridised carbons have seven component p orbitals, which can give rise to
seven MOs.
Cycloheptatrienyl cation: 6 electron, Anion: 8 electron, Free radical: 7 electron

39. Some Related Reactions:
Concept of Homoaromaticity
A Homoaromatic compound contains one or more sp3 hybridised carbon atoms in a
system which is otherwise a conjugated planar cycle. For an effective overlap of
orbitals to provide a close loop, the sp3 atom is forced to lie above the plane of
aromatic atoms.
39

40. Mononuclear Heterocyclic Compounds
A heterocyclic compound or ring structure is a cyclic compound that has atoms of at
least two different elements as members of its ring(s). Typical hetero atoms include
nitrogen, oxygen, and sulphur.
Because these compounds are monocyclic aromatic compounds, they must obey
Hückel's Rule. Pyrrole, furan, and thiophene appear, however, to have only 4 π
electrons (2 π bonds). In systems such as these, the extra electrons needed to produce
an aromatic condition come from the unshared electron pairs in sp2
hybrid orbitals
around the hetero atom.
40

41. 1. Pyridine is an aromatic heterocycle.
 The nitrogen is sp2
-hybridized
 Two of the three sp2
orbitals forming sigma overlaps with the sp2
orbitals of neighboring
carbon atoms
 The third nitrogen sp2
orbital contains the lone pair
 The unhybridized p orbital contains a single electron, which is part of the 6 pi-electron
system delocalized around the ring
41

42. 2. Pyrrole is a five-membered aromatic heterocycle.
 The nitrogen is sp2
-hybridized
 Two of the three sp2
orbitals forming sigma overlaps with the sp2
orbitals of neighboring
carbon atoms
 The third nitrogen sp2
orbital forms a sigma bond with H 1s orbital.
 The lone pair on nitrogen is in the unhybridized p orbital so it is involved in the six
pi-electron aromatic system
42
Therefore, pyrrole is much less basic than pyridine.

43. 1. Draw the orbitals of thiophene/furan to show that is aromatic.
 The heteroatom is sp2
-hybridized
 Two of the three sp2
orbitals forming sigma overlaps with the sp2
orbitals of neighboring
carbon atoms
 The third nitrogen sp2
orbital contains one lone pair
 The unhybridized p orbital contains another lone pair, which is part of the 6 pi-
electron system delocalized around the ring
43

44. Benzene is more aromatic than thiophene , pyrrole and
oxygen because all the π electrons are totally involved in
forming the aromatic sextet.
Whereas in other molecules, the heteroatoms being more
electronegative than carbon, they pull the electron cloud
towards themselves.
Thus, there is an uneven charge distribution.
Order of Aromaticity