MO Theory

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CH 105: Organic Chemistry Huckel Theory For Conjugated Systems

Santosh J. Gharpure Room No. 440

Department of Chemistry, IIT Bombay, Powai Mumbai – 400076

e-mail: [email protected] [email protected]

Phone: 2576 7171

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Prof. R.B. Sunoj, IIT Bombay Prof. Pradeepkumar P. I., IIT Bombay Prof. K. M. Muraleedharan, IIT Madras Prof. Peter Volhardt, UC Berkeley Prof. J. M McBride, Yale University Oxford University Press

Acknowledgements for lecture slides

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Outline

•  Huckel Theory For Conjugated Systems

•  Stereochemistry

•  Conformational Analysis

•  Chemistry of Carbonyl Compounds

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Text Book

§  Organic Chemistry : Structure and Function by Volhardt & Schore, 5th Edition

http://bcs.whfreeman.com/vollhardtschore5e/default.asp Additional Reading §  Organic Chemistry, Clayden, Green, Warren and Wothers,

Oxford University Press Animations http://www.chemtube3d.com/

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Course Outline and Evaluation

•  Organic Chemistry till Mid August (~ August 11 )

•  Inorganic Chemistry from Mid August to Mid-Sem

•  Evaluation: Organic + Inorganic (one grade) •  For Organic: one exam (Quiz) of 25 Marks (It is final

exam for Organic!) – Duration 2 hours

•  Tentative Exam Date: August 22 (to be confirmed)

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Aromaticity: Banzene

Aroma = Characteristic Odour

IN TODAYS CONTXET “AROMATIC” IS A MISNOMER!!

C6H6: How many isomers??

???

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So What is Aromatic? – Banzene Like Molecules

Benzene is special:

Reactions:

Structure:

Kekule suggested “rapid C=C oscillation feature” What we call today as resonance

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Benzene is unusually unreactive. Does this mean that it is also especially stable

thermodynamically? Look at ΔH° hydrogenation:

Special stability is now called aromaticity. All cyclic 6e arrangements are aromatic, including transition states.

Cyclohexane

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The concepts of hybridization of atomic orbitals and the theory of resonance, developed in the 1930s, provided the first adequate description of benzene’s structure.!

Banzene: Structure

•  The carbon skeleton is a planar regular hexagon.!•  All C-C-C and H-C-C bond angles 120°.!

sp2-sp2

σ σ

sp2-1s109 pm

120°

120°120°

139 pm

CC

CC

C CH

H H

H

H H

All C-C bonds 1.39 Å All C-H bonds 1.09 Å

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•  (a) The carbon framework with the six 2p orbitals.!•  (b) Overlap of the parallel 2p orbitals forms one torus

above the plane of the ring and another below it!•  this orbital represents the lowest-lying pi-bonding

molecular orbital.!

Banzene: Structure

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Is Banzene UNIQUE? How about other Annulenes?

Annulenes: Monocyclic hydrocarbons with alternating single and double bonds

cyclobutadiene [4]-annulene

cyclooctatetraene [8]-annulene

benzene [6]-annulene

Highly Unstable Bonds are localized

Isolated in argon matrix

Not “Aromatic” Tub shaped

Localized Bonds

Just conjugation not enough!

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Huckel Theory For Conjugated Systems

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Picture courtesy: world of stock

Symmetry of objects

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Symmetry in Nature

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Symmetry

Symmetry Elements A geometrical entity such as a line, a plane or a

point, with respect to which one or more symmetry operations may be carried out

1.  Plane of symmetry (σ)

2.  Center of symmetry or (inversion symmetry)-(i) 3.  Axis of symmetry (C)

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Symmetry in Molecules

BF

F

F1

2

3

BF

F

F

1

23 BF

F

F1

2

3

Rotation (C)

BF

F

F1

2

3

BF

F

F12

3

Reflection (s)

BF

F

F12

3

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Molecular Symmetry

One C6 axis, Six C2 axes One σh, Six σv

One i

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Orbital Symmetry

σ

σ*

Symmetric along the axis

For any bonding molecular orbital (BMO) there should be a corresponding antibonding molecular orbital (ABMO)

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More on sigma orbitals

σ

Symmetric along the axis

σ-type overlaps contain no nodes along the internuclear axis.

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(i) (ii) (iii)

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Types of Orbitals: Ethylene

σ

σ*

π

π*

H

H

H

Nonbonding orbital: e.g., pz-orbital (AO) on BH3

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Significance of Orbital Energies

Nucleophiles have higher energy filled nonbonding orbitals (Ready to donate electrons to suitable electrophiles)

e.g., nonbonding MO in NH3 that contains the lone pair of electrons is responsible for the nucleophilic nature of the molecule

Electrophiles are characterized by lower energy unfilled nonbonding orbitals

e.g., empty nonbonding MO in BF3

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Electron Rich to Electron poor

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Types of Orbitals: Formaldehyde

πCO

πCO*

C O

z

xy

In xy-plane

C O

C O

C

C

n’O

nO

Filled levels

Empty levels

Frontier MOs

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Ethylene MOs

Ethylene shows interesting properties due to the presence of a π-bond

The C-C p-orbital is the Highest Occupied Molecular Orbital (HOMO) of the alkene

Linear Combination of p-orbitals, leading to C-C π-orbital can be represented as,

2 x

Nodal Plane (nodes)

Out of-phase combination ofp-orbitals to give a π-orbital

π-orbital lower in energythan p-orbital

π* orbital higher in energythan p-orbital

Increasing Energy ofOrbitals

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Ethylene MOs

Increasing Energy ofOrbitals

Total Number of π-electrons = 2 Total Number of π-orbitals = 2Both electrons will occupy the lowest energy MO, i.e., BMO

π* (Antibonding molecular orbital)

π (Bonding molecular orbital)

_

_

_ _

+

+

+ +

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How about MOs for allyl system?

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Can we construct butadiene MOs?

φ1 φ2

ψ1φ1 φ2+ =

HOMOψ2

φ1 φ2_ =

φ3 φ4

LUMOψ3

φ3 φ4+ =

ψ4φ3 φ4_ =

HOMO is higher in energy than the HOMO of

ethylene

LUMO is lower in energy than the LUMO of

ethylene

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Butadiene MOs Total number of pπ-orbitals = 4 Total number of π-electrons = 4

1

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4

Butadiene is more reactive than ethylene

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Generalizations for Acylic Polyenes

The lowest energy orbital is always symmetric with respect to the principal mirror plane

The number of nodes increases by ONE on going from

one orbital to the next higher energy orbital

Nodes must be symmetrically located with respect to the central mirror plane

In systems with an odd number of atoms, the

antisymmetric levels always have a node at the central carbon atom.

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HOMO-LUMO Gap

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Extended Conjugation and Colour (E.g. 1)

If the conjugation is extended further, the gap between HOMO and LUMOwill decrease to allow the compound to absorb visible light and hencebe COLOURED.

Lycopene, the red pigment present in tomatoes and other berries

β-carotene, the red pigment present in carrots and other vegetables

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Extended Conjugation and Color (E.g. 2)

The colour of the blue jeans come from the pigment indigo

Jeans are generally dyed by immersion in a vat of reduced indigo,which is colourless since there is no conjugation.

When the cloth is hung up to dry, the oxygen in the air oxidizes thepigment to indigo and the jeans turn blue.

NH

HN

O

O

NH

HN

O

O

Air

Colourless Indigo precursor Indigo

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Polyenes to Solids CH103

R. B. Sunoj

When Number of atoms (N) in a polyene become infinitely large, the difference between neighboring energy levels (MO-levels) is infinitely small. But the band has a finite

width

N = 2

N = 3

N = 4

N = 5

N = 6

N →∞ Band

Is it possible to calculate the ‘width’ of the band, in an approximate fashion?

This will help us find

‘overlap regions’ between s and p bands

Q.

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Polyenes-to-Solids Analogies

Approximate Analogs Between Molecular and Solid-State Terminologies

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Molecular Orbital Band Orbital

HOMO Valence Band

LUMO Conduction Band

HOMO-LUMO gap Band gap

Advanced and Related Topics: Organic Semiconductors, Organic LEDs, Conducting Polymers

Refer: Moore’s law (processor speed of cpus)

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Some questions of significance

Most of the reactivities of conjugated systems (say,

butadiene, or a carbonyl compound) primarily arise due to the π-molecular orbitals.

Is it possible to estimate the energies of the π-molecular orbitals?

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§  Used for the treatment of conjugated systems §  The π-system is treated independently of the σ-framework

in planar conjugated molecules §  Or π-system do not interact with the σ-skeleton

§  Interactions between pπ orbitals located on atoms which are not directly linked is zero

Sigma-Framework

pi-system

Huckel MO Theory

π-electron approximation: π-electrons move in some fixed effective potential of σ framework

Basic Approximations

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Energies of MOs in terms of Integrals The energy of each pπ-orbital before interaction is set

equal to α, (Coulomb integral) [refers to energy of an electron in the field of its own nucleus]

[can be taken as valence state ionization potential]

The interaction energy between two adjacent pπ orbitals equals to β (Resonance integral)

[refers to energy of i th electron in the field of j th nucleus] [can be taken as the interaction between atomic orbitals i and j]

[energy of an electron in the field of two or more nuclei]

αα

β

?

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Energies of MOs • The energy of the jth MO for a linear unbranched conjugated polyene with N pπ orbitals (or N number of carbon atoms) is given by

ej = α + 2βCosπN+1

j

ej = α + 2βCos2πN

j

• The energy of the jth MO for a cyclic polyene with N pπ orbitals is given by

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Note: α and β are negative (attractive !) by definition

The α and β are not calculated as numerical values, but the energies are expressed in terms of these quantities

j = 0,1, 2, …,N

j = 1, 2, …,N

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Energies of the π molecular orbitals of ethylene and butadiene by geometry

Dummy atoms at top and bottom of circle Divide semicircle into ‘n+1’ equal arcs (parts)

Energy of the electron is given by the expression:

k is the number of the atom along the sequence of n atoms

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Energies of MOs For ethylene

Energy of LUMO = α - β Energy of HOMO = α + β

For Butadiene Energy of LUMO = α - 0.62β Energy of HOMO = α + 0.62β

Linear polyenes When the number of orbitals in the chain increases, the

energies will be as, For Highest energy MO = α – 2β Lowest energy MO = α + 2β

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Energies of MOs Cyclic polyenes

Draw a circle of radius 2β and inscribe an N-vertex polygon such that two vertices are in the six o’clock

position. The points of contact between the circle and the polygon defines the energy levels

α + 2β

α - 2β

α

α + 2β

α + β

α - β

α - 2β Frost Diagram

The energy level α is at the same level as that of the center of the circle

(Note: no dummy atoms in the cyclic system!)

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Energies of MOs Calculate the total energy of π-electrons in benzene?

Total number of π-electrons = 6

Total energy = 2 * (α + 2β) +

4 * (α + β)

α + 2β

α + β

α - β

α - 2β

6α + 8β If the double bonds were localized (not conjugated)!

Equivalent to three ethylenes

Total energy = 6 * (α + β)

Additional Stabilization in Benzene (fully delocalized) = 2β

[What is the resonance stabilization energy in benzene?]

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•  Planar, fully conjugated, monocyclic systems with (4n+2)π electrons having a closed shell of electrons all in bonding orbitals are exceptionally stable. Such compounds are said to be aromatic

•  Analogous systems with 4n π electrons are described as anti-aromatic

Huckel’s Rule of Aromaticity CH105 R. B. Sunoj

Modern definition of aromaticity:

Compounds that possesses the ability to sustain induced ring current when subjected to magnetic field

http://nptel.ac.in/courses/IIT-MADRAS/Engineering_Chemistry_III/pdf/1_Aromaticity.pdf

i

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Huckel’s Rule of Aromaticity

Number of π electrons = 6

Satisfies Huckel’ rule, where n = 1

Aromatic

Number of π electrons = 4

Where n = 1

Anti-aromatic

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Huckel’s Rule and Aromaticity The compound must have an uninterrupted cyclic π-cloud of electrons

For the π-cloud to be cyclic, the molecule must be cyclic.

For the π-cloud to be uninterrupted, every atom in the ring must have a p-orbital

For the π-cloud to form, each p-orbital must be able to overlap with the p-orbitals on either side of it. This means that the molecule must be planar.

E.g., 1

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π Molecular Orbitals of Benzene

Picture from Volhardt’s book

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Examples for Aromatic Compounds

HH

HH

HH

Phenathrene cyclopentadienyl anion

[18]-annulene Azulene

+ ____

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Aromatic Heterocyclic Compounds CH105 R. B. Sunoj

NH

O

Lone pair is part of the aromatic system

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Aromatic Heterocyclic Compounds CH105 R. B. Sunoj

N NN

Lone pair not involved in aromatic system

6π electrons 10π electrons

4n + 2 = 6, with n=1 4n + 2 = 10, with n=2

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Antiaromatic Compounds

NH

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Cyclic planar molecules with conjugated 4n π-electrons (where n is an integer) are antiaromatic

Antiaromatic compounds are less stable than the open chain counterpart

A cyclic compound that does not have a continuous conjugated p orbitals are known as nonaromatic e.g., 1,2-cyclohexadiene or 1,3-cyclohexadiene

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Criteria for Aromaticity

•  The underlying criteria for aromaticity were recognized in the early 1930s by Erich Hückel, based on molecular orbital (MO) calculations.

•  To be aromatic, a compound must –  Be cyclic. –  Have one p orbital on each atom of the ring. –  Be planar or nearly planar so that there is continuous

or nearly continuous overlap of all p orbitals of the ring.

–  Have a closed loop of (4n + 2) pi electrons in the cyclic arrangement of p orbitals.

But I don’t know MO! What do I do? Use Frost Circle

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Aromatic, Antiaromatic and Nonaromatic

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Frost Circle

◆  Frost circle: A graphic method for determining the relative order of pi MOs in planar, fully conjugated monocyclic compounds.!•  Inscribe in a circle a polygon of the same number of

sides as the ring to be examined such that one of the vertices of the polygon is at the bottom of the circle.!

•  The relative energies of the MOs in the ring are given by where the vertices of the polygon touch the circle.!

◆  Those MOs!•  Below the horizontal line through the center of the ring

are bonding MOs.!•  on the horizontal line are nonbonding MOs.!•  above the horizontal line are antibonding MOs.!

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Frost Circle

•  Frost circles describing the MOs for monocyclic, planar, fully conjugated four-, five-, and six-membered rings.!

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Antiaromaticity

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Planar cyclooctatetraene would be antiaromatic. To avoid it, the ring goes out of plane - possible as it is a larger ring. It is Non-aromatic.

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How about odd numbered rings?

However, remove an H (H+ or H-) and you may have aromatic or anitaromatic behaviour!

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POLYCYCLIC AROMATIC COMPOUNDS can follow HUCKEL 4n+2 RULE

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Effect of aromaticity on properties •  Cyclopentadiene pKa is 15 where as that of

cycloheptatriene in 46. •  Azulene has dipole moment of 1.8D. •  Tropylium bromide is actually ioninc compound. •  Pyrrole is much weaker base than pyridine. •  1,2,3,4,5-penta(trifluoromethyl)cyclopentadiene is

stronger acid than nitric acid! •  Ferrocene (Cp2Fe) undegoes electrophilc aromatic

substitution. •  When 3-chlorocyclopropene is treated with SbCl5, it

forms a stable salt. (This chemical behavior is to be contrasted with that of 5-chloro-1,3-cyclopentadiene, which cannot be made to form a stable salt.)!

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But conjugate acid of heptalene is stable!!

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THANK YOU

MO Theory

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