Molecular Structure and Energy Levels for Polyatomic

Molecular Structure and Energy Levels for Polyatomic Molecules

Dr.Qahtan Adnan Yousif Physical chemistry

goals from the lecture for computational chemistry: Aromatic Compounds Several types of aromaticity can be considered Condition necessary for aromaticity Hückel’s Molecular Orbital Theory Explain Hückel’s Rule Explain Molecular Orbital (MO) Theory Pericyclic reactions Frontier orbitals Correlation diagrams (MOs, States) Aromaticity of the Transition State

Polynuclear Hydrocarbons

Benzenoid

Isolated

Non- Benzenoid

Fused rings

Linear

Azulene

Angular

Biphenyl

Naphthalene Phenanthrene

Background • Benzene (C6H6) is the simplest aromatic hydrocarbon (or arene). • Benzene has four degrees of unsaturation (U = 4). • Benzene does not undergo the same reactions as alkenes and alkynes.

Background • Benzene does react with bromine, but only in the presence of a Lewis acid catalyst such as FeBr3.

Br Br2 FeBr3

Background • Proposed structures of benzene must account for its high degree of unsaturation and its lack of reactivity towards electrophilic addition. • Kekulé proposed that benzene was a rapidly equilibrating mixture of two compounds, each containing a six-membered ring with three alternating  bonds. • In the Kekulé description, the bond between any two carbon atoms is sometimes a single bond and sometimes a double bond.

• Although benzene is still drawn as a six-membered ring with alternating  bonds, in reality there is no equilibrium between the two different kinds of benzene molecules. • Current descriptions of benzene are based on resonance and electron delocalization due to orbital overlap.

The Structure of Benzene Any structure for benzene must account for the following facts: 1. It contains a six-membered ring and three additional degrees of unsaturation. 2. It is planar. 3. All C—C bond lengths are equal. The Kekulé structures satisfy the first two criteria but not the third, because having three alternating  bonds means that benzene should have three short double bonds alternating with three longer single bonds.

The Structure of Benzene • The resonance description of benzene consists of two equivalent Lewis structures, each with three double bonds that alternate with three single bonds. • The true structure of benzene is a resonance hybrid of the two Lewis structures, with the dashed lines of the hybrid indicating the position of the  bonds. • We will use one of the two Lewis structures and not the hybrid in drawing benzene. This will make it easier to keep track of the electron pairs in the  bonds (the  electrons).

The Structure of Benzene • In benzene, the actual bond length (1.39 Å) is intermediate between the carbon—carbon single bond (1.53 Å) and the carbon—carbon double bond (1.34 Å).

COMPARISON OF MOLECULES Benzene is Stabilized by 36 kcal/mol called the

Empirical Resonance Energy

Spectroscopic Properties of Benzene Parameters

Interesting Aromatic Compounds • Benzene and toluene, the simplest aromatic hydrocarbons obtained from petroleum refining, are useful starting materials for synthetic polymers. • Compounds containing two or more benzene rings that share carbon— carbon bonds are called polycyclic aromatic hydrocarbons (PAHs). Naphthalene, the simplest PAH, is the active ingredient in mothballs.

Interesting Aromatic Compounds Helicene and twistoflex—Two synthetic polycyclic aromatic hydrocarbons

Interesting Aromatic Compounds Selected drugs that contain a benzene ring

Stability of Benzene • Consider the heats of hydrogenation of cyclohexene, 1,3cyclohexadiene and benzene, all of which give cyclohexane when treated with excess hydrogen in the presence of a metal catalyst. • Cyclohexene and 1,3-cyclohexadiene can be hydrogenated at room temperature, however, benzene requires more forcing conditions.

Stability of Benzene • The low heat of hydrogenation of benzene means that benzene is especially stable—even more so than conjugated polyenes. • This unusual stability is characteristic of aromatic compounds. • Benzene’s unusual behavior is not limited to hydrogenation. Reaction with Br2 requires the presence of a Lewis acid catalyst.

The Criteria for Aromaticity—Hückel’s Rule Four structural criteria must be satisfied for a compound to be aromatic.

[1]

A molecule must be cyclic.

To be aromatic, each p orbital must overlap with p orbitals on adjacent atoms.

The Criteria for Aromaticity—Hückel’s Rule [2]

A molecule must be planar.

All adjacent p orbitals must be aligned so that the  electron density can be delocalized.

Since cyclooctatetraene is non-planar, it is not aromatic, and it undergoes addition reactions just like those of other alkenes.

The Criteria for Aromaticity—Hückel’s Rule [3]

A molecule must be completely conjugated.

Aromatic compounds must have a p orbital on every atom.

The Criteria for Aromaticity—Hückel’s Rule [4]

A molecule must satisfy Hückel’s rule, and contain a particular number of  electrons.

Hückel's rule:

Benzene is aromatic and especially stable because it contains 6  electrons. Cyclobutadiene is antiaromatic and especially unstable because it contains 4  electrons.

The Criteria for Aromaticity—Hückel’s Rule Note that Hückel’s rule refers to the number of  electrons, not the number of atoms in a particular ring.

The Criteria for Aromaticity—Hückel’s Rule Considering aromaticity, a compound can be classified in one of three ways:

1.

Aromatic—A cyclic, planar, completely conjugated compound with 4n + 2  electrons.

2.

Antiaromatic—A cyclic, planar, completely conjugated compound with 4n  electrons.

3.

Not aromatic (nonaromatic)—A compound that lacks one (or more) of the following requirements for aromaticity: being cyclic, planar, and completely conjugated.

The Criteria for Aromaticity—Hückel’s Rule •

1H

NMR spectroscopy readily indicates whether a compound is aromatic.

• The protons on sp2 hybridized carbons in aromatic hydrocarbons are highly deshielded and absorb at 6.5-8 ppm, whereas hydrocarbons that are not aromatic absorb at 4.5-6 ppm.

Examples of Aromatic Rings • Completely conjugated rings larger than benzene are also aromatic if they are planar and have 4n + 2  electrons. • Hydrocarbons containing a single ring with alternating double and single bonds are called annulenes.

Examples of Aromatic Rings • [10]-Annulene has 10  electrons, which satisfies Hückel's rule, but a planar molecule would place the two H atoms inside the ring too close to each other. Thus, the ring puckers to relieve this strain. • Since [10]-annulene is not planar, the 10  electrons can’t delocalize over the entire ring and it is not aromatic.

Examples of Aromatic Rings • Two or more six-membered rings with alternating double and single bonds can be fused together to form polycyclic aromatic hydrocarbons (PAHs).

• As the number of fused rings increases, the number of resonance structures increases.

Examples of Aromatic Rings • Heterocycles containing oxygen, nitrogen or sulfur, can also be aromatic. • With heteroatoms, we must determine whether the lone pair is localized on the heteroatom or part of the delocalized  system. • An example of an aromatic heterocycle is pyridine.

Examples of Aromatic Rings • Pyrrole is another example of an aromatic heterocycle. It contains a five-membered ring with two  bonds and one nitrogen atom. • Pyrrole has a p orbital on every adjacent atom, so it is completely conjugated. • Pyrrole has six  electrons—four from the  bonds and two from the lone pair.

• Pyrrole is cyclic, planar, completely conjugated, and has 4n + 2  electrons, so it is aromatic.

Examples of Aromatic Rings • Histamine is a biologically active amine formed in many tissues. It is an aromatic heterocycle with two N atoms—one which is similar to the N atom of pyridine, and the other which is similar to the N atom of pyrrole.

Examples of Aromatic Rings Both negatively and positively charged ions can be aromatic if they possess all the necessary elements.

We can draw five equivalent resonance structures for the cyclopentadienyl anion.

Examples of Aromatic Rings • Of the three species below, only the cyclopentadienyl anion satisfies Hückel’s rule.

Examples of Aromatic Rings • The tropylium cation is a planer carbocation with three double bonds and a positive charge contained in a seven-membered ring. • Because the tropylium cation has three  bonds and no other nonbonded electron pairs, it contains six  electrons, thereby satisfying Hückel’s rule.

The Basis of Hückel’s Rule • Why does the number of  electrons determine whether a compound is aromatic? • The basis of aromaticity can be better understood by considering orbitals and bonding.

The Basis of Hückel’s Rule • Thus far, we have used “valence bond theory” to explain how bonds between atoms are formed. • Valence bond theory is inadequate for describing systems with many adjacent p orbitals that overlap, as is the case in aromatic compounds. • Molecular orbital (MO) theory permits a better explanation of bonding in aromatic systems. • MO theory describes bonds as the mathematical combination of atomic orbitals that form a new set of orbitals called molecular orbitals (MOs). • A molecular orbital occupies a region of space in a molecule where electrons are likely to be found.

The Basis of Hückel’s Rule • The combination of two p orbitals can be constructive—that is, with like phases interacting—or destructive, that is, with opposite phases interacting.

• When two p orbitals of similar phase overlap side-by-side, a  bonding molecular orbital results. • When two p orbitals of opposite phase overlap side-by-side, a * antibonding orbital results.

The Basis of Hückel’s Rule • The * antibonding MO is higher in energy because a destabilizing node results, which pushes nuclei apart when orbitals of opposite phase combine. Combination of two p orbitals to form π and π* molecular orbitals

The Basis of Hückel’s Rule Consider benzene. Since each of the six carbon atoms in benzene has a p orbital, six atomic p orbitals combine to form six  MOs. The six molecular orbitals of benzene

The Basis of Hückel’s Rule • The most important features of the six benzene MOs:

  

  

The larger the number of bonding interactions, the lower in energy the MO. The larger the number of nodes, the higher in energy the MO. Three MOs are lower in energy than the starting p orbitals, making them bonding MOs, whereas three MOs are higher in energy than the starting p orbitals, making them antibonding MOs. Two pairs of MOs with the same energy are called degenerate orbitals. The highest energy orbital that contains electrons is called the highest occupied molecular orbital (HOMO). The lowest energy orbital that does not contain electrons is called the lowest unoccupied molecular orbital (LUMO).

Diamond and Graphite • The two most common elemental forms of carbon are diamond and graphite. • Their physical characteristics are very different because their molecular structures are very different.

Buckminsterfullerene—Is it Aromatic? • Buckminsterfullerene (C60) is a third elemental form of carbon. • Buckminsterfullerene is completely conjugated, but it is not aromatic since it is not planar. • It undergoes addition reactions with electrophiles in much the same way as ordinary alkenes.

HISTORY OF SEMI-EMPIRICAL MOLECULAR ORBITAL THEORY 1930’s  1952 

Hückel Dewar

treated  systems only PMO; first semiquantitative

application  1960’s Hoffmann Extended Huckel; included bonds  1965 Pople CNDO; first useful MO program  1967 Pople INDO

HISTORY... 1975  1977  1985

Dewar Dewar Dewar

1989  1970’s

Stewart Zerner





MINDO/3; was widely used MNDO AM1; added vdW attraction & H-bonding PM3; larger training set ZINDO; includes transition metals, parameterized for calculating UV-Vis spectra

HARTREE-FOCK SELF-CONSISTENT FIELD (SCF) METHOD...  Computational  

 

methodology:

guess the wavefunction (LCAO orbital coefficients) of all occupied orbitals compute the potential (repulsion) each electron would experience from all other electrons (taken as a group in the H-F approximation) solve for Fock operators to generate a new, improved wavefunction (orbital coefficients) repeat above two steps until the new wavefunction is not much improved; at this point the field is called self-consistent. (SCF theory)

SEMI-EMPIRICAL MO CALCULATIONS: FURTHER SIMPLIFICATIONS Neglect core (1s) electrons; replace integral for Hcore by an empirical or calculated parameter  Neglect various other interactions between electrons on adjacent atoms: CNDO, INDO, MINDO/3, MNDO, etc.  Add parameters so as to make the simplified calculation give results in agreement with observables (spectra or molecular properties). 

STEPS IN PERFORMING A SEMI-EMPIRICAL MO CALCULATION Construct a model or input structure from MM calculation, X-ray file, or other source (database)  optimize structure using MM method to obtain a good starting geometry  select MO method (usually AM1 or PM3)  specify charge and spin multiplicity (s = n + 1), where n = # unpaired electrons, usually 0, so s usually is 1.  select single point or geometry optimization  set termination condition (time, cycles, gradient)  select keywords (from list of >100) if desired. 

SOME APPLICATIONS... Calculation of reaction pathways (mechanisms)  Determination of reaction intermediates and transition structures  Visualization of orbital interactions (formation of new bonds, breaking bonds as a reaction proceeds)  Shapes of molecules including their charge distribution (electron density) 

…MORE APPLICATIONS QSAR (Quantitative Structure-Activity Relationships)  CoMFA (Comparative Molecular Field Analysis)  Remote interactions (those beyond normal covalent bonding distance)  Docking (interaction of molecules, such as pharmaceuticals with biomolecules)  NMR chemical shift prediction. 

As we will see, ab initio and DFT calculations generally give better results than Semi-empirical MO calculations

6 4

six p-orbitals

2

5

3 1

Degenerate orbitals: orbitals that have the same energy

Ψ1: zero nodes Ψ2 and Ψ3: one node

Bonding

Ψ4 and Ψ5: two nodes Ψ6: three node

Anti-bonding

48

Cyclobutadiene and Cyclooctatetraene Not all cyclic conjugated systems are aromatic (no special stability)

cyclobutadiene 4 -electrons Cyclobutadiene: highly reactive two different C-C bonds

138 pm 151 pm

benzene 6 -electrons

+

cyclooctatetraene 8 -electrons Diels-Ald er -78 °C

not aromatic

aromatic

not aromatic

Cyclic conjugation is necessary, but not sufficient criteria for aromaticity.

Hückel's Rule: Aromatic: Cyclic Conjugated: “alternating single and double bonds” Planar: maximum overlap between conjugated  -bonds Must contain 4n+2 -electrons, where n is an integer (Hückel’s rule) Anti-aromatic: cyclic, conjugated, planar molecules that contain 4n -electrons (where n is an integer). Destabilized (highly reactive) relative to the corresponding open-chain conjugated system

Frost Circles: relative energies of the molecular orbitals of cyclic, conjugated systems 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 benzene:

anti-bonding MO's non-bonding level bonding MO's Benzene 6 -electrons The bonding MO's will be filled for aromatic compounds, such as benzene.

Cyclobutadiene:

anti-bonding MO non-bonding MO's bonding MO

Cyclobutadiene 4 -electrons For anti- aromatic compounds, such as cyclobutadiene and cyclooctatetraene, there will be unpaired electrons in bonding, non-bonding or antibonding MO's. Cyclooctatetraene: anti-bonding MO non-bonding MO's bonding MO Cyclooctatetraene 8 -electrons

Annulenes - monocyclic, conjugated, planar polyenes that conform to Hückel's rule. [10]annulene H H H

H H

[14]annulene H

H H

[18]annulene

H

H

H

H

H

10 -electrons 4n+2 = 10, n=2.

H H

H

14 -electrons 4n+2=14, n=3

H

H

H

H

H

HH HH

H H

H

H

H H

H

H

H H

HH HH

H

H

H

H

[16]annulene 16 -electrons 4n=16, n=4

H

H H H

H

H H

H

H H

H

H H

H

H

18 -electrons 4n+2=18, n=4

Cyclooctatetraene: Heats of hydrogenation - No special stability for cyclooctatetraene

120 KJ/mol

230 KJ/mol

97 KJ/mol

205 KJ/mol

reactivity similar to normal C=C Exists in a boat-like conformation: little overlap between double bonds

208 KJ/mol

303 KJ/mol

410 KJ/mol

Aromatic Ions H Cl H

H

+ AgBF4 H

BF4

H

H

H

H

H

H

+ AgBF4

H

H

+ H 2O

pKa ~ 16

H

H

H

H H

H

H

H

H

H

H

H H

+ H 3O +

H

H

H

+

H

H H Br

BF4

H

H

H H H

H

AgCl

H

H Cl

H

+

H

Br -

AgCl

Cyclopropenyl cation 2

H H

4n+2=2 n=0 aromatic

3 1

H

cycloprop enyl cation 2 -electrons

Cyclopentadienyl cation H H

H H

H

cyclopentad ienyl cation 4 -electrons

4

5

2

3 1

4n=4 n=1 anti-aromatic

Cycloheptatrienyl cation H H H

6

H H H

H

cycloheptatrienyl cation 6 -electrons

4 2

7 5 3 1

4n+2=6 n=1 aromatic

Cyclopropenyl anion H

H H

+

+ B:

H

H

H

B:H

4n=4 n=1 anti-aromatic

H

cyclopropenyl anion 4 -electrons

2

3 1

Cyclopentadienyl anion H

H H H

H H

H

p Ka ~ 16

+ B:

H

H H

+

B:H

4n+2=6 n=1 aromatic

H

cyclopentad ienyl anion 6 -electrons

4

5

2

3 1

Heterocyclic Aromatic Compounds Heterocycle : any cyclic compound that contains ring atom(s) other than carbon (N, O, S, P). Cyclic compounds that contain only carbon are called carbocycles N N

N H

pyridine

pyrrole

N H

imidazole

N O

S

furan

thiophene

S

N O

thiazole oxazole

Heterocyclic Aromatic Compounds and Hückel's Rule Pyridine: -electron structure resembles benzene (6 -electrons) The nitrogen lone pair electrons are not part of the aromatic system.

N pyridine

Pyrrole: 6 -electron system similar to that of cyclopentadienyl anion. There are four sp2-hybridized carbons with 4 p orbitals perpendicular to the ring and 4 -electrons and a lone pair of electrons in an unhybridized p2 orbital that is part of the aromatic sextet

N H

+ H2O

pKa ~ 5.2 N

N H N H H

+ H2O

+ H3O+

pKa ~ -4 N H

+ H3O+

Pericyclic Reactions Nu

•Polar react. (nucleophiles and electrophiles) •Radical react. R

E

R'

•Pericyclic react. (concerted, cyclic TS#) •Electrocyclic react.

•Rearrangement of polyene •Termal (react. in ground state) •Cycloadditions (i.e. Diels Alder) or photochemical (react of exited state) •Sigmatropic rearrangement

Symmetry Allowed React. Woodward Hoffmann rules Symmetry in reactants are preserved during pericyclic react. Results can generally be predicted just by looking at Front Orbitals (FMO; HOMO and LUMO) - Fukui

LUMO: Lowest uoccupied MO

HOMO: Highest occupied MO

Molecular orbitals 1,3-butadiene HOMO

LUMO -bond HOMO -bond Conrotatory Both rotate same way

Stereospesific react.

H3C

H

H

CH3

H

H

CH3

CH3

E,E

S: Symmetric A: Antisym.

H3C

Cis

H3C

H

E,Z

H

H

CH3

CH3

H

Trans

Molecular orbitals hexatriene

HOMO LUMO -bond

Disrotatory Rotation opposite way

LUMO -bond

HOMO -bond

CH3

H3C

E

E

CH3

Cis

H3C

CH3

H3C

E

CH3

CH3

Z

Trans

Symmetry allowed react No. of electrons

Reactions in the ground state

4n

Conrotatory

4n + 2

Disrotatory

Photochemical electrocyclic react.

h

HOMO exitet state (= LUMO ground state)

Disrotatory

No. of electrons 4n 4n + 2

Reactions in the ground state (termal) Conrotatory Disrotatory

Reactions in exited state (Photochem.) Disrotatory Conrotatory

Cycloadditions (i.e. Diels Alder) Suprafacial cycloadd.

[4+2]

LUMO - diene

HOMO - Diene

LUMO - dienophile

HOMO - dienophile

[4+2] A

C

B

D

A C B

D

Stereospesific react.

endo - exo selectivity O O

O

O O

O

O

O

Endo O

O

O

O

Exo

HOMO - Diene

HOMO - Diene

Primary interact., bond formation

O

O

Secondary interact., extra TS# stabil.

O

O

O

O

LUMO - dienophile

Normal electron demand DA - Electron poor dienophile (Michael accept.) Michael accept. LUMO -alkene Lower LUMO

Ethene etc, very low react. LUMO -alkene

EWG HOMO - LUMO gap

EWG

HOMO-alkene

HOMO-alkene

[2+2] Cycloadditions Antarafacial cycloadd. (termal cond.)

Suprafacial cycloadd. HOMO - Diene

HOMO-alkene

h

Suprafacial cycloadd. (photochem. cond.) HOMO-alkene exited state

LUMO -alkene LUMO -alkene

LUMO -alkene

Geometrical constrains Difficult to make small rings by antrafacial cycloadd

No. of electrons 4n 4n + 2

Reactions in the ground state (termal) Antarafacial Suprafacial

Reactions in exited state (Photochem.) Suprafacial Antarafacial

Carbene Cycloadditions Singlet Carbene Empty p-orb LUMO of carbene R C

sp2 hybr orbital with lone pair HOMO of carbene

R

Empty p-orb LUMO of carbene R

R

R

R

R

R

HOMO of carbene C

C R

R

HOMO alkene

LUMO alkene

Sigmatropic Rearrangements [3,3] Rearrangements; Claisen rearrang. etc. Claisen rearrangement O

Allyl-vinyl ether or Allyl aryl ether

-bond to be broken

1 2 O

3

1 2 O

1

3

1

2

O

O

3

-bond to be formed

3

2

taut H

HO

Cope rearrangement 1 R 1

2

2

1

3

R 1

3

2

2

3 3

Oxy-Cope rearrangement 1 HO 1

2

2

3 3

1 HO 1

2

2

3 3

taut

1 O 1

2

2

3 3

Suprafacial

[1,5] Rearrangement (H-shift) H

-bond to be broken

1 H 1

5

1

4

No. of electrons 4n

H 1

3

2

5

2

H

4 3

Reactions in the ground state (termal) Antarafacial Suprafacial

4n + 2

H

Suprafacial

Reactions in exited state (Photochem.) Suprafacial Antarafacial

[1,3] Rearrangement (H-shift) h H

H

Antarafacial

Too strained TS#

Suprafacial

H

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