PHYSICAL ORGANIC CHEMISTRY

Yu-Tai Tao (陶雨台）

Tel: (02)27898580E-mail: ytt@chem.sinica.edu.twWebsite:http://www.sinica.edu.tw/~ytt

Textbook:“Perspective on Structure and Mechanism in Organic Chemistry” by F. A. Corroll, 1998, Brooks/Cole Publishing Company

References:1. “Modern Physical Organic Chemistry” by E. V. Anslyn

and D. A. Dougherty, 2005, University Science Books.

Grading: One midterm (45%) one final exam (45%) and 4 quizzes (10%) homeworks

Review of Concepts in Organic Chemistry

§ Molecular dimensionsAtomic radiusionic radius, ri：size of electron cloud around an ion.covalent radius, rc：half of the distance between two atoms

of same element bond to each other.van der Waal radius, rvdw：the effective size of atomic cloud

around a covalently bonded atoms.

Cl- Cl2 CH3Cl

§ Quantum number and atomic orbitalsAtomic orbital wavefunctions are associated with four quantum numbers: principle q. n. (n=1,2,3), azimuthal q.n. (m=0,1,2,3 or s,p,d,f,..magnetic q. n. (for p, -1, 0, 1; for d, -2, -1, 0, 1, 2.electron spin q. n. =1/2, -1/2.

Chap.1

Bond length measures the distance between nucleus (or the local centers of electron density).

Bond angle measures the angle between lines connecting different nucleus.

Molecular volume and surface area can be the sum of atomic volume (or group volume) and surface area.

Principle of additivity (group increment)

Physical basis of additivity law: the forces between atoms in the same molecule or different molecules are very “short range”.

Theoretical determination of molecular size：depending on the boundary condition.

Boundary is a certain minimum value of electron density.

Molecular volume (1 au = 6.748e/Å3 ),

47.8044.1367.64C4H10

37.5742.7653.64C3H8

27.3431.1039.54C2H6

17.1219.5825.53CH4

expt’l0.02au0.001au

6 C(gr) ＋ 4 H2(g) ＋ O2(g) ΔHf°

＋ 7 O2(g) 6 CO2(g) ＋ 4 H2O(g)

ΔHcomb= -735.9 Kcal/mol

6 C(gr) ＋ 6 O2(g) 6 CO2(g)

ΔHcomb= -94.05 (Kcal/mol C) × 6

4 H2(g) ＋ O2(g) 4 H2O(g)

ΔHcomb= -68.32 (Kcal/mol H2)

ΔHsubl= 21.46 Kcal/mol

ΔHf°= 6 × (-94.05) ＋ 4 × (-68.32) ＋735.9 ＋21.46

= -80.22 (Kcal/mol)

§ Heats of formation and reactionHeat of formation：Difference in enthalpy between the compound and starting elements in their standard statesobtained indirectly from other components of known ΔHf°

correct for necessary phase change (such as vaporization, sublimation)correct for ΔH at different T by heat capacityexperimental measurement by calorimeter

　　m C(gr) ＋ n/2 H2 (g) 　　　CmHn 　　　　ΔHf°

To calculate the heat of formation of

O

O(g)

O

O(g)O

O(s)

O

O(s)

O

O(g)

Relative difference in heat of formation

The heat of hydrogenation is much smaller than the heat of combustion. Both will give the difference of the stability of the two isomers.

§ Bond increment calculation of heat of formationPrinciple of additivity：The property of a large molecule

can be approximated by adding the contribution of its component.

+ CF3COOH　　　　　　　　　∆H= -10.93 Kcal/mol

+ CF3COOH　　　　　　　　　∆H= -9.11 Kcal/mol

OCCF3

O

OCCF3

O

∆H= -1.82 Kcal/mol

CH3CH＝CHCH3 CH3CH2CH2CH3 ΔH=-28.6Kcal/molcis

CH3CH＝CHCH3 CH3CH2CH2CH3 ΔH=-27.6Kcal/moltrans

H2

H2

For butane

(-3.83) × 10 ＋ 3× (2.73) ＝ -30.11 Kcal/mol

HHH

H H

H H

HH

H

§ Group increment calculation of heat of formation

3 × (-10.08) ＋ 2 × (-4.95) ＋ 1 × (-1.90) ＝ -42.04 Kcal/mol (obs. -41.66)

4 × (-10.08) ＋ 2 × (-1.90) ＝ -44.12 Kcal/mol (obs. -42.49)

Further refinements correct for van der Waal strain, angle strain….

CH3

CH3

CH3

CH3

The electrostatic model for the stability of branched alkaneCharge on H：0.278× 10-10 esuCharge on C：neutralizing charge Branched more stableH H

H H

H H

H H

-2 -2-2 -2

+1

+1

+1+1+1

+1+1 +1 H H H H

-2 -2

+1 +1+1 +1

H HH

H+1

+1+1

+1

-3-1

JACS 1975, 97, 704.

e.g. CH3－H CH3． ＋ H． ΔH°r＝ +104 Kcal/mol

Cl－Cl Cl． ＋ Cl． ΔH°r＝ +58 Kcal/mol

Cl． ＋ CH3． CH3Cl ΔH°r＝ -84 Kcal/mol

＋） Cl． ＋ H． H－Cl ΔH°r＝ -103 Kcal/mol

CH3－H ＋ Cl－Cl CH3Cl ＋ HCl ΔH°r＝ -25 Kcal

Homolytic & Heterolytic Dissociation Energies

In gas phase：ΔH°het >ΔH°hom

In solution： solvation of ions can lower ΔH°het, so that heterolysis becomes favorable.

Use bond dissociation energy to calculate reaction ΔH°r

Hess Law：The difference in enthalpy between products and reactants is independent of the path of the reaction.

by heat of formationΔH°r＝ΣΔH°f(prd) －ΣΔH°f(pre)

= -23.7 Kcal/mol at 300℃

A－B(g) A． (g) ＋B． (g)

A+(g)＋B-

(g)

homolysis

heterolysis electron transfer

ΔH°hom：standard homolyticbond dissociation energy

ΔH°het：standard heterolytic bond dissociation energy

§ Bond length and bond energyBond length is nearly a constant property between

molecules.

§ PolarizabilityThe ability of electron cloud to distort in response to

external field, defined as the magnitude of dipole induced by one unit of field gradient.

Polarizability decreases across a row of the periodic table,. (C>N>O>F, CH4>NH3>H2O)

Polarizability increases along a column,(S>O, P>M, H2S>H2O)C-I bond is more polarizable than C-Cl

alkanes are more polarizable than alkenes, may due to Electronegativity. sp2 carbons are more electronegative thansp3 carbons.

+

§ Bonding ModelValence Bond Theory (VB) G.N. Lewis 1916Chemical bonds result from the sharing of electron pairs between two approaching atoms.

For complex molecules, hybridization and resonance are used to describe molecules in terms of orbitals which are mainly localized between two atoms.

means two bonding electrons in the region between two atom

The bond is localized.

H H H－HH：H

Cl Cl+ Cl Cl each achieve a filled shell

The region is orbital.

H Cl+ H Cl

σ bond from S and P σ bond by P and P

σ ：cylindrical symmetry

For carbon 1s22s22p2

the 2s, 2px, 2py, 2pz hybridize to form four equivalent sp3

4 bonds can be formed on carbonhighly directional sp3 orbital provide for more efficient overlap.

acetylene

ethene

methane CH4

HC≡CH, CO2, HCN, H2C=C=CH2

linearsp2

CH2=CH2, H2C=O, C6H6, CO3

=, CH3．Trigonalsp23

CH4, CCl4, CH3OH,Tetrahedral

sp34

GeometryHybrid

No. of ligand

C

+ 43s p sp3

H

HH

H

109.5° C

H

H H

H

H H o r H H

HHHH

1 2 0 °H H

H Ho r

π bond, plane sym.s + 2p → 3sp2

one p remaining

s + p → 2sptwo p remaining

H-C-C linear

Hybridization Theory：

Resonance Theory：

An extension of valence bond theory for molecules that more than one Lewis structure can be written. Useful in describing electron delocalization, in conjugate system and reactive intermediates.(a)If more than one Lewis structure can be written, which

has nuclear positions constant, but differ in assignment of electrons, the molecule is described by a combination of these structure (a hybrid of all).

(b)The most favorable (lowest energy) resonance structure makes the greatest contribution to the true structure.determining energy：maximum number of covalent bond, minimum separation of unlike charge, placement of negative charge on most electronegative atom (vice versa).

(c)Those with delocalized electrons are usually more stable than single localized structure.

H 3 CC CH 2

H 2 C

H 3 CC CH 2

H 2 C

H 3 CC O

H 2 C

H 3 CC O

H 2 C

H CCH

CH

H

H

H CCH

CH

H

H

HH

HH

HC

HC

CH

O

H

HC

HC

CH

O

H

HC

HC

CH

O

H

more stable

major minorsignificant

two equivalent structurecharge located equally on two C’sthe allyl cation is planar for maximum p interaction

restricted rotation around single bond

§ Dipole moment：the vector quantity that measures the separation of charges.

bond dipole = q × d = 0.1× (4.8× 10-10esu) × 1.5× 10-8 cm= 0.72× 10-18esu．cm= 0.72 D (1 Debye = 10-18esu．Cm)

Molecular dipole is the vector sum of various “bond dipoles”.It provides information about molecular structure and bonding.

From trigonometry, the calculated angles between two bond “dipole moment” are 89° , 122° , 180°.

support the concept that benzene is planar.

The dipole moment results from unequal sharing of the electron. due to different attraction for electron

electronegativity

Polar bond = [covalent bond] +λ [ionic bond]

λ= weighing factor

% ionic character = × 100 %

HCl +0.17 electron charge on H．

- 0.17 electron charge on Cl． λ = 0.45

λ2

(1 +λ2)

e.g. CH3F μ= 1.81 DH

CHH

F

1.385Å

Cl

μ= 1.61 D

For dichlorobenzene μ= 2.30, 1.55, 0

Cl Cl ClCl

ClCl

q = = 0.27 e-1.81× 10-18

1.385× 4.8× 10-10

+q -q 1 electron charge = 4.8x10-10 esu0.1 e 0.1e

d = 1.5x10-8cm

§ Electronegativity & Bond PolarityElectronegativity：The power of an atom in a molecule to attract electrons to itself. Pauline 1932

χp：based on the difference in bond energy of AB

and other scale of electronegativity,

more related to atomic properties.

χM = I：ionization potential of atom

A：e- affinity of atom

χspec：based on the average I.P.of all of the valence P and S electrons.

χα：based on atomic polarizability

VX：no. of valence electron /covalent radii

A-A + B-B2

I + A2

Mulliken1934

Allen 1989Nagle 1990

Benson 1988

Third Dimension of Periodic Table J. Am. Chem. Soc. 1989, 111, 9004.

In complex molecules with many polar bonds involved, electrostatic potential surfaces (from quantum mechanic calculation) are used to view the charge distribution in the whole molecule.

red ----negative potentialblue --- positive potentialgreen---neutral

Fδ

δ

δ

δ

δ

0.36

-0.17

0.09

-0.24

Molecular Orbital Method

Electrons are distributed among a set of molecular orbitals of discrete energies. The orbitals extend over the entire molecule.

First Approximation：the MO is a linear combination of contributing atomic orb.

Ψ = c1ψ1 + c2 ψ2 + ‥‥‥ + cn ψn

ψ’S are basis set

c’S coefficient, reflect contribution

The no. of MO’s (bonding + non-bonding +antibonding) = total no. of a.o.’s

1s

σ*

σ

1s

For H2, 2e- For HHe+, 2e-

He 1s

1s

For CO, 10e-

2Px,2Py,2Pz

σ’*

2Px,2Py,2Pz

σ’

π x*, π

y*

π x, π y

σ’*

σC O

2s2s

MO for methane

First approach

ψsp31＝ (C2s ＋ C2px

＋ C2py＋ C2pz

)

ψsp32＝ (C2s ＋ C2px

－ C2py－ C2pz

)

ψsp33＝ (C2s － C2px

＋ C2py－ C2pz

)

ψsp34＝ (C2s － C2px

－ C2py＋ C2pz

)

1212

12

12

each sp3 overlap with a 1s of H to form CH4

bond angle 109.5°

This implies identical bonds for the bonding electrons.

But ESCA data of methane shows

The M.O. formed above is symmetry incorrect.

each of these has a shape of , pointing to the corner of a tetrahedron

1s

290eV 23.0eV 12.7eV

The symmetry of the M.O. must conform to the symmetry of the molecule in such a way that the M.O.’s are either symmetric or antisymmetric to all the symmetry elements of the molecule.Solution：form the delocalized methane M.O. directly form unhybridized orbitals：1C2s, 3C2p’s, 4H1s

ψ1 ＝ 0.545 C2s ＋ 0.272 (H1 ＋ H2 ＋ H3 ＋ H4)

ψ 2 ＝ 0.545 C2px＋ 0.272 (H1 ＋ H2 － H3 － H4)

ψ3 ＝ 0.545 C2py＋ 0.272 (H1 － H2 ＋ H3 － H4)

ψ4 ＝ 0.545 C2pz＋ 0.272 (H1 － H2 － H3 ＋ H4)

The energy of on M.O. increase with the no. of nodes in the M.O.

ψ1

ψ2 ψ3 ψ4

+-

+

+

++

+

+

+

+

++

ψ1

+

--

-

--

++

Group orbitals from qualitative molecular orbital theory(QMOT)planar methyl

pyramidal methyl Walsh diagram

Building larger molecule from group orbitals

Valence Shell Electron Pair Repulsion Theory (VSEPR)

In predicting the shape of molecules, bonds are treated asrepulsive points and the repulsive points made as far apart as possible.

－ counting the number of electron groups：unshared pair is a group, each bond is a group, whether single or multiple.

－ 2 groups linear

3 groups trigonal

4 groups tetrahedral

－ non-bonding electron pair more repulsive

－ bonding pair to electronegative groups less repulsive

CH

HH

H109.5°

CH

HH

C

H

HH

∠H-C-H =109.5° ∠H-C-H = 109.3°

NH

HH

∠H-N-H = 107°

OH H

∠H-O-H = 104.5°

Cl

CH

H H

Cl

CH

H H

∠H-C-H = 110°52'∠H-C-Cl = 108°0'

predicted ∠H-C-H = 109.5°　　　　 ∠H-C-Cl = 109.5°

Bonding electron polarized toward Cl, 1.76Å

1.09Å

1.781Å

1.096Å

Effect of lone pair on bond angleRepulsion：lone pair occupies larger domainlone pair：lone pair＞lone pair：bond pair＞bond pair：bond pair

Effect of lone pair on bond lengthThe closer and larger domain of lone pair prevents a

bonding pair getting closer. The adjacent bond longer

Effect of electronegativity on bond angle

98.2OSBr2101.0PBr3

96.2OSCl2100.3PCl3

92.3OSF297.8PF3

∠XSX(° )OSX2∠XPX(° )PX3

Increasing electronegativity, the bonding pair shifts further away from the central atom. angle decreases

PF

FF

120.2° > 109.5°

96.9° < 109.5°

BrF

F

F

FF

1.79Å

1.68Å

SO O

H3CO OCH3

Multiple bond domain ≣ > ＝ > －

SO O

SO O

SO O＞ ＞

H

B

H

H

HB

H

H

122°

109°

98°122°

122°

97°

Multi-center bond occupies less domain than a single bondMulti-center bond

Trigonal bipyramidal molecules

5 points are non-equivalent

(1) the axial bond is longer than eq. bond rax/req = 1~1.4

(2) larger domain electron pair (lone pair, multiple bond) occupies equatorial position

(3) more electronegative atom occupies axial position

eg. PF3Cl2, PF2Cl3PCl5

Limitations：－ not applicable to ionic comp’d－ for localized bonding/non-bonding pair, not for

delocalized－ for sufficiently large ligands, steric interaction prevails

90°

120°

√2 r

√3 r

C l

PC l

C l

C l

C lF

S

FF

FF

S

FF

FO

F

Kr

F

F

Xe

F

OO

O

F

PF

Cl

F

FF

PCl

Cl

F

FF

PCl

Cl

F

ClF

PCl

Cl

Cl

Cl

1.2

1.05

1.01

0.91

0.96

0.9

§ Variable Hybridization and Molecular GeometryFor carbon bonded to different atom, different

hybridizations are proposed.For CH4, CCl4：sp3 hybridization % S = 25

% P = 75

For spn, define λ 2 = n ,λ：hybridization parameter

% S = , % P =

sum of P-fraction Σ = n,

sum of S-fraction Σ = 1

Interorbital angle θab , 1+ λa λb cosθab = 0if a = b,1+ λa

2 cosθaa = 0, cosθaa =

λ2

(1 +λ2)1

(1 +λ2)

-1λa

2

hybridization index

sp3 → θaa = 109.5 °sp2 → θaa = 120 °sp → θaa = 180 °

3sin2 θab = 2 (1- cosθaa )from θab = 108° , θaa = 110.5 °from θaa = 110.5° , λa

2 = 2.86∴sp2.86 for C－H

from 3 ( ) + = 1, λb2 = 3.51

1 +λb2

11 + 2.86

the S character↑ , λ↓

λi2

(1 +λi2)i

i1

(1 +λi2)

C

a b

Cl

CH

H

H

b

aa

a

θab

108°

110.5°

sp3.5

sp2.86

more S-character

more P

For CA3B

For CH2Cl2 λCl

2 = = 2.69

∴sp2.69 for C－Cl

from 2 ( ) + 2 ( ) = 1

λH2 = 3.37, sp3.37 for C－H

-1cos111°47

′

11 +λH

21

1 + 2.69

from cosθHH = , θHH = 107° ≠-1λH

2 112 ° (expt’l)

λHH2 = 2.67,

λCl2 = 3.39,

θClCl = 107°

the inter-orbital bond angle smaller than the inter nuclear bond angle

H

C

Cl

ClH

111.47°112°

1.082Å 1.772Å

Cl

CH

HH

F

CH

H

H

F

C

HH

H

108.0°

110.52°

108.9°

109.54°

106.7°

(by inter nuclear)bent bond

H

C

Cl

ClH

Experimental support of variable hybridization:NMR coupling constants J13C-1H:: cyclopropane 161, cyclobutane 134, cyclopentane 128, cyclohexane 124, cycloheptane 123, cyclooctane 122

Cyclopropane

bent bond from sp3 hybridization (or variable hybridization)

H

H

H

H

H

H

115 ° 1

H

H

Sp3.94

sp2.36

Walsh orbital：from sp2 hybridization

θcc=105°

H

CHHC

H

H

HC

HC

HCH C

Prediction of Physical Properties with diff. Bonding model1. Alkene Geometry

C－C ethane ethene ethyne

bond length 1.54Å 1.34Å 1.20Å

by σ,πformulation：

sp3 hybrid. % S = 25

in ethene sp2 hybrid. % S = 33.3 S↑bond legth dec.addition π bond, shorter bond

in ethyne sp hybrid. % S = 50, no quantitative prediction

by bent bond formulation：

C－C distance 1.32Å

C－C distance 1.18Å

2. Acidity

ethane 10-42 sp3

ethene 10-36.5 sp2

ethyne 10-25 sp

bent bond formulation

HC

H HC

H

CH C H

1.54Å

1.54Å

1.54Å

only sp3

hybridization

S character increase greater e--pulling power for the orbital better stabilization of the anion

decreased repulsionfurther decrease in repulsion

conformation of propene

σ,π-formation predicts Ⅱ to be more stable, because more repulsion between double bond and the C－H bond in IBent bond formulation：

The bent bond (Ω bond ) is agreed in cyclopropaneproposed or shown to more suitable than σ,π description in CF2＝CF2, CO2, CO, benzene

Conclusion

H

H

H

CH2 H CH2H

H

H

H3C C

CH2

H

H

H CH2

H

H

HH CH2

H

H

more stable by 2Kcal/mole

more stable

IIIII