Chap. 3 Conformational Analysis and Molecular Mechanics

Conformation：One of several different spatial arrangements that a molecule can achieve by rotation about single bonds between atoms.

Notations：dihedral angle

θ= 0 ° eclipsed θ= 60 ° gauche(staggered)

(skew)

A B

H

HH H

ABH

HH H

B

H

H

A

H H

BH

H A

H H

AHH

BH H

AHB

HH H

θ= 120 ° eclipsed

θ= 240 ° eclipsed

θ= 180 ° anti(trans)

θ= 300 ° gauche(staggered)

(skew)

H

HCH3

CH3H

CH3

HCH3

H

CH3

CH3

H

H

CH3

HH

H

HCH3

HH

HH

CH3

ap

ap

+ sc - sc

+ sc - sc

syn- anti- periplanar- clinaldetermining substituent：1.If all three are diff. the one with highest priority2.If all three are identical, the one gives smallest θ3.If two are identical, the third one

H H

A

0°~30°30°~60°

60°~90°

90°~120°120°~150°150°~180°180°~210°210°~

240°2

40°~

270°

270°

~300° 3

00°~33

0° 330°~360°

- sp- sc

- sc

- ac

+sp

- ac- ap +ap

+ac

+ac

+sc

+sc

CH3H3C

H

HCH3H

CH3

H

HH3C

CH3

H

s-trans s-cis

s-cis

s-cis

s-cis

s-trans(Z) (Z)

cZc cZt

the C － N bond rotation is hindered and conformation isomer could be isolated.

N

CH3

O

IH2C

t-Bu

CH2CH3

N

CH3

O

CH2I

t-Bu

CH2CH3

m.p. 64~65℃ m.p. 105~106℃

H

Me

CO2CH3

H

CHO

H3C

H

H

HH3C

SnBu3

Pd-C/H2

O

O

O

H

H

Me

O

O

H

Me

O

H

H

Me

OMe

O

H

Me

H

O

H

Me

O

MeO

H

Me

H

O

H

Me

OMe

O

δ-

δ+

δ-

δ+

δ-

δ+

δ-

δ+

C

O

N

most stablized

major

1. Torsional Strain ( due to deviation from staggered bonds on adj. carbons)

E(φ) = 0.5V(1+cos 3φ )2. van der Waals strain ( repulsion due to overlap of electron clouds on non-bonded atoms)

H

CH3H

H

CH3

HCH3

HH

H

CH3

H

CH3H3C

HH

H3C

H

H

CH3

0.8 Kcal/mole 0.3 Kcal/mole

3.2 Kcal/mole

gauche antiΔG° = ΔH° - TΔS°

= - 0.8 Kcal/mol – ( - 0.00198 × 298× ln 2 ) = - 0.8+0.41= - 0.39 Kcal/mol

ΔG° = - RT ln K K = anti/gauche = 1.9 → 66% anti

a superimposition of torsional strain of ethane and van der waals strain

2.9 molkcal

CH3

H

H3C

H

HH

CH3

H

H3C

H

HH

CH3

CH3

H

H

HH

CH3

H

H

H3C

HH

CH3

H

CH3HHH

CH3

H3C

HHHH

CH3

H

HH3CHH

3.4 molkcal

0.8 molkcal

2.6 molkcal

6.0 molkcal

Barrier foldednessEthane and butane have a three-fold rotational profile.

Rotation around CH3-C6H5 has a six-fold profile.

An n-fold rotor and an m-fold rotor give a barrier with F = (nxm)/q

Where q is the number of eclipsing bond in the TS

H

C H3CH3

CH3

H

C H3

Tetraalkylethane

CH3

HCH3

CH3

H

C H3

two gauche three gauche

expected composition: 70:30 anti to gauche experimental composition: 1:2, ∆H = 0!geminal repulsion aggravate the vicinal repulsion in anti form and destabilize the anti form more than the gauche form

anti gauche

H

H

A general case for R2CHCHR2 molecules,

Only gauche form

gauche antigauche is favored by 0.3 Kcal ± 0.3

intramolecular H-bond

-stabilizing London interaction, distance≈ sum of van der Waals radii1.75Å

H

O HH

H

H

O HH

O HH

H O

H

H

H

C lH

H

C H3

HC l

HH

H

C H3

H

H

H

H

H

H

H

H

HH

H

H

H

H

H

H

H

H

H

H H

HH

H

H

3. Angle Strain ( Bayer strain), ( deviation from standard bond angle.)

Bayer’s Theory based on planer geometry

1.2-172° 42‘-17° 16‘cyclodecane

0-31° 36‘-5° 16‘cyclohexane

1.33° 40‘0° 44‘cyclopentane

6.5538° 56‘9° 44‘cyclobutane

9.2 kcal/mol74° 12‘24° 44‘cycloprapane

expt’lStrain/CH2total Angle StrainAngle Strain/CH2

The discrepancy is due to non-planar geometry

cyclopropane

all C-H bonds eclipsed

cyclobutane

C-C-C < 90°angle strain increase

torsional strain decrease

C-C-C = 90°higher torsional strain

1.45 kcalbarrier

PuckeredButterfly motion

35°

Angle Strain

= (109.5°-60°)

= 24.75 °21

Cyclopropane C-C bond are short (1.51Å) than normal C-C bond (1.54Å)H-C-H bond angle open up (115°) than the value for H-C-H (106°) in the CH2 of propane.C-H of cyclopropane are more acidic than normal alkanes.

rehybridization, smaller C-C-C bond angle, more p character is used. Then more s character for C-H bonds.Strain energy of cycloporpane 27.5 kcal/mole, may come from angle strain and also the eclipsing C-H bonds (eclipsing effect, a torsional strain)

H

H

H

HH

H

C-C bond length 1.55 Å, strain energy 26.5 kcal/mol

cyclopentane

H

H

H

H

H H

H

H

H H

H

H

HH

H

H

H

H

H

H

H

H

H

H

H H

H

H

H H

envelope Twist (half chair)Planar, all eclipsed

with high torsional strain, 5 kcal/mol above

the conformation is constantly changing →pseudo rotation, strain energy 6.2 kcal/mol, mostly due to torsional , some angle strain

cyclohexane

substituted cyclohexaneCH3

CH3H H

≣

H

H

H

HH

HH

CH3

H

H

H

HCH3

HH

H

equatorial axial1,3-diaxial interaction= gauche interaction in

butane

2 × (1 gauche ~ 0.8kcal)~ 1.6kcal

less stable(exp’t 1.74kcal)gauche

all staggered

by e--diffractionC-C-C 110°

torsional angle 55.9°(slightly flattened)

van der Waal repulsion (distance 1.83ÅSum of H-van de Walls radii 2.4Å)

torsional strain

release the flag pole van der Waal strain and torsional strain

the chair form and twist boat form are separated by a high energy barrier.

barrier <2kcal

equatorial preference = 1.74 kcal/mol →A-value conformational free energy

ΔG° = -RTlnK K= = =19 ][][

axeq

595

useful locking gp.→

→→→→

-ΔH(kcal)1.751.601.52

ΔS(eu)-0.030.642.31

K192142

9432entropy determines the trend

t-Butyl is a locking gp. so that it dictates the conformation.

HO

OH

if two substituents are non-interaction, the A-values are additive

H3C

H

Hψ CH3

HH

ψ

2.87 1.74

ΔG= -1.13

two interacting substituents

for trans the e,e form has one gauche interactionfor cis the e,a form= a,e form, has 2×1,3-diaxial+1 gauche inter

∴trans more stable by 2×1,3-diaxial ~1.8 kcal(expt’l 1.87)

CH3

CH3

H

CH3

CH3

H CH3

CH3

CH3

CH3

HCH3

H H

CH3

H

CH3

CH3

Ha,ae,e

e,a a,e

trans-1,2-dimethylcyclohexane

cis-1,2-dimethylcyclohexane

ΔG° = 2.7 kcalonly e,e form

H

H 3C

H

CH 3

H

CH 3

CH 3

CH 3

H

CH 3

HH 3C

H

H 3C

H

cis trans

trans cis

>

>

Exception for favored equatorial preference may exist due to shape.

Et

EtEt

EtEtbut

Effect of dipole interaction

OO H

Htrans-diol

ClCl

Cl

Cl

BrBr

Br

Br

trans-

dipole interaction

75% 25%

50% 50%

effect of H-bonding

van der Waals strain plus dipole

interaction

cis

diaxial incr.

For larger rings, more conformations are possible due to the flexibility, but the strain may increase.

cycloheptane

twist-chairmost stable

chair boat twist-boat

boat-chairmost stable

boat-boat crown

cyclooctane

cyclodecane

H

HH

H

H

H

boat-chair-boat

van der Waals repulsion, release of this repulsion by twisting will introduce torsional strain.

angle & torsional

torsional strain

cross-ring vdw strain

For simple bicyclic system, the strain is close to the sum of individual rings.e.g. for bicyclo[3,1,0]heptane 6.2+27.5 = 33.7 (expt’l 33.9)Exception for smaller rings due to extra strain by fusion.

CycloalkeneThe trans-double bond introduces strain in a cyclic system. The smaller the ring is,the higher the strain is.

Bredt’s rule: For bicyclo[a,b,c], the smallest number S=a+b+c that can accommodate a bridgehead double bond.The stability of bridgehead olefins follow the stability pattern of trans cyclic olefins.

H

H

H

H H

H

HH H

H

H CH3

H

H

H

CH3

H3C CH3

H

H

H

H

H3C CH3

1-Alkene

H3C

HH

H

CH2H

HCH3

H

CH2H

H3CH

H

CH2H

HCH3

H

CH2

A B C D

eclipsed bisected

more stable, and B is slightly more stable than A (by 0.15kcal)increase the size of group at C-3increase the preference for B

by M.O. interpretation

eclipsed formbisected form

3.29. CH3-CH2I3.78. CH3-CH2Br3.77. CH3-CH2Cl3.36. CH3-CH2F

Heteroatom substitution

Haloethanes

Alkanes

Table 3.3 Rotational Energy Barriers of Compounds of the Type CH3-X

2.713. CH3-OCH3

1.0712. CH3-OH3.6211. CH3-NHCH3

1.9810. CH3-NH2

1.75. CH3-SiH3

4.74. CH3-C(CH3)3

3.93. CH3-CH(CH3)2

3.42. CH3-CH2CH3

2.881. CH3-CH3

Barrier height (kcal/mol)Compound

C-C 1.54Å

Si-C 1.87Å

vdw inc.bond length inc.

0.50.5

1.6, more sensitive

1.6, due to shorter bond

no. of eclipsed bonds

0.8

Major repulsive interaction between filled methyl and filled π

Ethane 2.88

H3C

HH

H

OH

HCH3

H

O

H3C

H3C

O

CH3

HH3C

H3CO

CH3

H

For carbonyl cpds.

more stable by 0.9 kcal, (may due to non-bonded interaction between the C-H of the methyl and oxygen. C…H…O hydrogen bonding)

if CH3 become t-Bu, the H-eclipsed becomes favored

R'

HH

R

OH

HR'

R

Oanti

gaucheeven more stablediene

H

HH

HH

HH

H

H

HH

H

H

CH2

CH2

S-transmore stable

S-cis skewless πoverlap

maximize πoverlap

H

H

O

H

H

H

HO

HH

S-transonly

H

H

O

CH3

H

H

HO

CH3H

S-trans73%

S-cis27%

S-trans28%

S-cis82%

ΔG┿ 10.8kcal

CH2

CH27.7kcal

O

O

ΔG┿ 4.9kcal

O

Oeclipsed, favored

1,3-diaxial

O

O

reduced 1,3-diaxial ΔG°= -1.3~1.4

smaller than that for cyclohexaneα-haloketone effect

4. allylic strain

CH3

CH3

CH3

CH3

CH3

CH3

ΔG°= -2.6kcal

reduced torsional (sp2-sp2) strain in ring inversion

reduced steric requirement for =CH2 , O

O

OCl

Cl

dipole smallerfavored in CCl4

dipole largerfavored in methanol

equatorial preference is smaller

Anomeric EffectsO

H

HO

HO

H

H

OHOH

H

CH2OH

OHO

HOOH

OH

CH2OH

32%α-D-Glucopyranose

64%β-D-Glucopyranose

( By A of 0.87 90% exp’ted )

OH

HO

HO

H

OH

HOH

H

CH2OH

OHO

HOH

OH

CH2OH

OH

68%α-D-Mannose

32%β-D-Mannose

Suggested interpretations

1. dipolar interaction

2. Molecular orbital interaction

O

O O

OμO

μCO

μCO

μO

destabilized

O

X

O

X

stabilized

n

σ*

V-B term

≣

longer C-X bond

shorter O-C bond

X-ray data agrees

O

CH3

Cl

O

CH3 Cl32:1

Some anomeric effect are solvent dependent

X

H H

H

X

H

H

XH

H

X

H

Special Conformations

2.6I1.7Br1.2Cl-0.6FΔEt-gX

gauche

anti favored

the gauche form increases with more electronegative atoms

O

O

XO

OXH+

cis trans

0.63OMe1.25Br1.1Cl0.3F

ΔEt-gX

gauche incr. for electronegative atoms

bent-bond interpretation：With more electronegative atom X Small H-C-X angle expected

C F

H

H

H

C C

F

F

C C

F F

bent

anti

C-C bond length longer by 0.01Å

(By ab initio calc.)

gauche

better overlap bond length shorter

§ Molecular Mechanicsuse classical mechanics, atoms and bonds are treated as mass and springs, to calculate the total energy of a conformation.

MM1, MM2, MM3, UFF, N.L. Allinger

MM2 Total steric energy Esteric =E( r ) +E(θ) +E(Φ) +E( d )E( r )：the energy of stretching or compressing an individual

bondE(θ)：energy of distorting a bond angle from ideal valueE(Φ)：torsional strain (due to non-staggered bonds)E( d )：non-bonded interaction, van der Waals force

stretching-bending ESB strain energy may be added.E(Φ) = 0.5V0 × ( 1+ cos 3Φ)

more General termE(Φ) = 0.5V1 × ( 1+ cosΦ) + 0.5V2 × ( 1- cos 2Φ)

+ 0.5V3 × ( 1+ cos 3Φ)

E( r ) = 0.5kr × (Δr)2 × ( 1+CS ×Δr)kr ：force constantΔr：deformation of bond lengthCS：cubic stretching constant

E(θ) = 0.5kθ × (Δθ)2 × ( 1+SF ×Δθ4)

E(d) depends on extent and pattern of substitution. The interaction is attractive as the distance decreases, then repulsive at small distance.Other terms include electrostatic interactions, hydrogen bonding…

To calculate the strain, an initial conformation is assigned anditerative minimization of total strain energy is carried out.

→a minimum in total energy may contain components that is not the lowest among all conformers

→the calculation approaches local minimum, which may not be a global minimum, so that initial assignment of conformation is important.

Cyclohexane case

Conformational effects on reactivity

O C

OH

CH3

O C

O

CH3

O Cr+O

O-

OH

H

O Cr+O

O-

OH

H

Rel. rate of oxidation3.23 ： 1

Rel. rate of acetylation1 ： 3.7

the rate is determined by the transition state energy

energy difference in T.S. increases due to larger gp.

In transition state, the diaxial interaction is released by going from sp3→sp2

0.7kcalcis

trans

> 0.7kcal

cis-acetate

trans-acetate

cis

trans

HO

OH

cis- trans-

Effect of angle strain on reactivity

Smaller rings are more strained and more reactive.

I2+ (CH3)2C CCH2CHI2

H3C

CH3

H3C

H3C

I CH3

H3CI H

CH3

H

H

CH3

CH3

Br2CH3CH

Br

CH3

CHCH2Br + BrCH2CHCH(CH3)2

Br

BrCH2CCH2CH3

Br

+

CH3

~60% 20% 20%

Cl2+ +H2C CHCH2CHCl2 Cl Cl

Cl CH2Cl

+

Cl

CH2Cl

45% 4% 41%

Coplanarity of double bond substituents can only exists transiently.

trans-cyloalkene,

with ring size ≧ 11, the trans-isomers become more stable

Bridge head double bond

Effect of Ring Size and Ring Closure facility

Roughly the rate of ring closure for a particular rxn

5 > 6 > 3 > 7 > 4 > 8~10

Small ring disfavored by enthalpy

Large ring disfavored by entropy

Bred’t rule：the existence of C=C or C=N bonds at a bridgehead position in a polycyclic system is not possible, unless for large rings.

(1924)

Scheme 3.4 Relative Rates of Ring Closure as a Function of Ring SizeRelative rate

1

1

1

1

1

6

－

0.01

0.13

0.002

0.0052

7

－－33175. ArSO2N(CH2)xCl → cyclization

4×10-4－－－4. → cyclic ether

formation

－360.37－3. → nucleophilic

participation in solvolysis

－1000.0010.07 2. Br(CH2)xNH2 → cyclic amine

6×10-5900.318.3×10-41. Br(CH2)xCO2- → lactone

8543Ring size =Reaction

PhC(CH2)xC

O

O-

O(CH2)xBr

Baldwin’s Rule

sp3 ( tetrahedral)

C X

Nu-

C+ X-

Nu-

exo-tet

C X

O

CO

+ HX

OH

Oexo-trig

Z

H2C

R

H

H2C Nu-

Z

Nu-

ZNu

5-endo-trigunfavored

HOMO

LUMO

C CR

ZNu-

H R

Z Nu

5-endo-dig favored

much deviate from planar geometry for 5-membered ring

favfavfavfavfav7favfavfavfavfav6

unfavfavfavfavfav5unfavfavfavfavunfav4favfavfavfavunfav3

(trig)(dig)(tet)(trig)(dig)Ring sizesp2spsp3sp2sp

Endocyclic bondsExocyclic bondsTable 3.11 Classification of Ring-Closure Types

HOCH2CH2CH2C CC

O

RO

H

O

R

exo-dig

(CH3)2CCCH

OH

O

CHPh

O

O

H3C

H3CPh

(CH3)2C

OH

O

C

O

O

H3C

H3CPh

C C PhCH3ONa

H

H

OTs

OTs

acetolysis

acetolysis

H

H

O

O

C

O

CH3

C

O

CH3

Effect of torsional strain reactivity

O

O

NaBH4

NaBH4

OH

OH

H

H

rel. rate

23

：

1

The rxn converts a sp2 carbon to sp3 carbonin 6-membered ring, all staggered bondsin 5-membered ring, eclipsing interaction increases

faster

In transition state, a sp3 is converted to sp2, eclipsing effect in 5-membered ring released.

O OH

HH

H

Nu

Nuaxial attack

Bulky reagents attack from the equatorial direction (steric control )Smaller nucleophiles attack from axial direction

Nu

O-

H

H

Nu

O

H

H

O-

NuH

H

Nu

axialattack

equationalattack

orO

O

Oσσ*π* π

distorted π*

Stereo electronic effect

B2H6 99.5 0.5 22 78 HydroborationRCO3H 99.5 0.5 12 88EpoxidationH2, Pd 90 10 10 90hydrogenation

exo : endo exo : endo