Chap.
3
Conformational Analysis
Molecular Mechanics
and
Conformation：One of several different spatial arrangements
that a molecule can achieve by rotation about
single bonds between atoms.
Notations：
dihedral angle
A
A B
θ= 0 °
H
H
H
eclipsed
H
H
B
H
H
H
A
HA
H
H
H
θ= 120 ° eclipsed
B
H
H
H
H
B
A
- sp
21
°24
40
~2
0°
- ac
- ap
H
H
+sc
+ac
+ac
H
H
H
CH3
CH3
+ sc
H
CH3
H
CH3
- sc
H
ap
H
CH3
CH3
H
CH3
H3C
H
H
CH3
H
H3 C
H
H
θ= 300 ° gauche
(staggered)
(skew)
syn- anti- periplanar- clinal
determining substituent：
1.If all three are diff. the one with highest priority
2.If all three are identical, the one gives smallest θ
3.If two are identical, the third one
+sc
+ap
H
ap
H
+sp
360° 0°~30°
330°~
1
180° 80°~210°
150°~
H
B
H
0° 90°~12
60°~9
0° 1
2
0
°~
15
0°
- ac
θ= 240 ° eclipsed
H
H
°
60
°~
30
- sc
0° 270°~30
0°~27
0° 3
00
°~
33
0°
- sc
θ= 180 ° anti
(trans)
A
HA
H
B
θ= 60 ° gauche
(staggered)
(skew)
H
CH3
H
+ sc
CH3
H
H
H
H
CH3
- sc
CH3
H
H
CH3
s-trans
s-cis
s-cis
(Z)
s-cis
s-cis
cZc
O
C
cZt
the C － N bond rotation is hindered and
conformation isomer could be isolated.
N
IH2C
O
CH2CH3
CH2CH3
O
N
t-Bu
CH3
m.p. 105~106℃
H
δ-
H
H
+
δ
Me
O
O
+
H3C
Me
O
Me
OMe
+
+
δ
H
δ- H
H
H
O
CO2CH3
H
CH3
t-Bu
H
CHO
CH2I
N
m.p. 64~65℃
H3C
s-trans
(Z)
δ
δ
Me
H
-O
δ
δSnBu3
Pd-C/H2
H
H
H
most stablized
H
O
H
H
OMe
O
Me
O
major
O
MeO
Me
Me
O
O
Me
1. Torsional Strain ( due to deviation from staggered bonds
on adj. carbons)
kcal
2.9 mol
E(φ) = 0.5V(1+cos 3φ )
2. van der Waals strain ( repulsion due to overlap of electron
clouds on non-bonded atoms)
CH3
CH3
H3C H
H
H3C H
H
CH3
H
2.6
kcal
mol
HH
H
6.0
HH
H
CH3
H3C
a superimposition
of torsional strain
of ethane and van
der waals strain
H
H
kcal
mol
CH3
H
CH3
H
H
0.8
3.4
kcal
mol
H
H
CH3
H
H
kcal
mol
CH3
H
H
H
H3C
H
3.2 Kcal/mole
H
H3C
H
CH3
H
H
H
H
H
H
CH3
H3C
H3C H
CH3
CH3
H
0.8 Kcal/mole
H
H
CH3
H
H
H
CH3
H
CH3
0.3 Kcal/mole
gauche
anti
ΔG° = 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
Barrier foldedness
Ethane 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
Tetraalkylethane
gauche
anti
H
H
CH3
C H3
CH3
C H3
H
CH3
CH3
C H3
CH3
H
three gauche
two 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
A general case for R2CHCHR2 molecules,
Only gauche form
H
-stabilizing LondonH interaction, distance≈ sum of van der Waals radii
C H3
1.75Å
C H3
H
Cl
H
H
H
H
H
H
Cl
H
gauche
anti
gauche is favored by 0.3 Kcal ± 0.3
H
H
H
OH
H
H
OH
HO
H
OH
H
H
intramolecular H-bond
3. Angle Strain ( Bayer strain), ( deviation from standard
bond angle.)
Bayer’s Theory based on planer geometry
total Angle Strain
cycloprapane
24° 44‘
74° 12‘
cyclobutane
1
(109.5°-60°)
2
cyclopentane
9° 44‘
38° 56‘
6.55
0° 44‘
3° 40‘
1.3
cyclohexane
-5° 16‘
-31° 36‘
0
cyclodecane
-17° 16‘
-172° 42‘
1.2
Angle Strain
=
expt’l
Strain/CH2
Angle Strain/CH2
= 24.75 °
9.2 kcal/mol
The discrepancy is due to non-planar geometry
cyclopropane
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.
trehybridization, 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
H
cyclobutane
1.45 kcal
barrier
H
H
H
H
35°
H
H
H
H
H
H
Puckered
H
H
H
H
H
H
H
H
C-C-C
H
H
H
H
Butterfly motion
H
< 90°
angle strain increase
torsional strain decrease
H
H
all C-H bonds
eclipsed
H
C-C-C
= 90°
higher torsional strain
C-C bond length 1.55 Å, strain energy 26.5 kcal/mol
cyclopentane
H
H
H
H
H
H
H
H
H
barrier <2kcal
H
H
H
H
H
H
envelope
H
H
H H
H
H
H
H
H
H
H
H
H
H
H
Planar, all eclipsed
Twist (half chair)
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
van der Waal repulsion (distance 1.83Å
Sum of H-van de Walls radii 2.4Å)
torsional strain
by e--diffraction
C-C-C 110°
torsional angle
55.9°
(slightly flattened)
release the flag pole
van der Waal strain
and torsional strain
all staggered
the chair form and twist boat form are separated
by a high energy barrier.
substituted cyclohexane
≣
CH3
H
equatorial
H
H
H
H
H
H
H
CH3
H
H
H
H
axial
CH3
H
2 × (1 gauche ~ 0.8kcal)
~ 1.6kcal
less stable
H
(exp’t 1.74kcal)
gauche
H
H
CH3
1,3-diaxial interaction
= gauche interaction in
butane
equatorial preference = 1.74 kcal/mol →A-value conformational free energy
95
[eq]
ΔG° = -RTlnK
K=
=
=19
5
[ax]
K -ΔH(kcal) ΔS(eu)
→ 19
1.75
-0.03
→ 21
1.60
0.64
→ 42
1.52
2.31
→ 9432
useful
locking gp.→
entropy
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
2.87
H
H3C
H
ψ
1.74
CH3
H
ΔG= -1.13
H
ψ
two interacting substituents
ΔG° = 2.7 kcal
only e,e form
H
CH3
CH3
CH3
CH3
e,e
CH3
a,a
H
H
CH3
trans-1,2-dimethylcyclohexane
CH3
CH3
CH3
H
CH3
e,a
cis
CH3
CH3
a,e
H
H
H
cis-1,2-dimethylcyclohexane
for trans the e,e form has one gauche interaction
for 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)
H
H
H 3C
CH
CH
H
>
3
cis
CH
H
3
trans
H
CH
H 3C
H
3
>
3
H 3C
H
cis
trans
CH
3
Exception for favored equatorial preference may exist due to shape.
but
Et
Et
Et
Effect of dipole interaction
Cl
dipole i
nteracti
on
Et
Et
Cl
effect of H-bonding
Cl
transvan der Waals
strain plus dipole
interaction
75%
25%
Br
Br
50%
O
trans-diol
Br
50%
O
Cl
diaxial incr
Br
.
H
H
For larger rings, more conformations are possible due to the
flexibility, but the strain may increase.
cycloheptane
twist-chair
most stable
chair
boat
twist-boat
cyclooctane
boat-chair
most stable
boat-boat
crown
cyclodecane
H
H
H
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.
Cycloalkene
The 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.
Table 3.3 Rotational Energy Barriers of
Compounds of the Type CH3-X
HH
Barrier height
(kcal/mol)
Compound
Alkanes
C-C
1. CH3-CH3
2.88
1.54Å
2. CH3-CH2CH3
3.4
3. CH3-CH(CH3)2
3.9
4. CH3-C(CH3)3
4.7
5. CH3-SiH3
1.7
Si-C
Haloethanes
1.87Å
6. CH3-CH2F
3.3
vdw
inc.
7. CH3-CH2Cl
3.7
bond
length
inc.
8. CH3-CH2Br
3.7
9. CH3-CH2I
3.2
Heteroatom substitution
no. of eclipsed 1.98
Ethane 2.8810. CH3-NH2
11. CH3-NHCH3 bonds
3.62
12. CH3-OH
1.07
13. CH3-OCH3
2.7
H
H
H
H
0.5
0.5
HH
0.8
H
CH3
H
H
H
H
H
CH3
H3C
H
H CH3
1.6, more sensitive
H
CH3
H3C
H
1.6, due to shorter bond
1-Alkene
CH2
CH2
H3C
CH2
H
H
H
H
H
H
H
H
A
CH2
CH3
eclipsed
H3C
B
H
H
H
C
bisected
more stable, and B is slightly more stable than A (by 0.15kcal)
increase the size of group at C-3
increase the preference for B
by M.O. interpretation
bisected form
eclipsed form
Major repulsive interaction between filled methyl and filled π
H
CH3
D
For carbonyl cpds.
O
O
H3C
H
H
H
H
H
H
CH3
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
anti
O
O
R'
H
R
H
H
diene
R
H
gauche
R'
even more stable
H
H
H
H
H
H
H
H
H
H
CH2
H
S-trans
more stable
CH2
H
H
S-cis
skew
less πoverlap
maximize πoverlap
H
O
H
H
H
H
H
O
H
H
S-trans
only
H
O
H
H
CH3
H
CH3
H
O
H
S-trans
73%
H
H3C
H3C
S-cis
27%
H
H3C
O
CH3
CH3
S-trans
28%
H3C
O
S-cis
82%
ΔG┿ 10.8kcal
CH2
reduced torsional (sp2-sp2)
strain in ring inversion
CH2
7.7kcal
reduced steric requirement
for =CH2 ,
O
O
O
ΔG┿ 4.9kcal
1,3-diaxial
O
O
eclipsed, favored
reduced 1,3-diaxial
ΔG°= -1.3~1.4
O
O
α-haloketone effect
O
smaller than that for cyclohexane
Cl
O
Cl
dipole smaller
favored in CCl4
4. allylic strain
dipole larger
favored in methanol
CH3
CH3
CH3
CH3
CH3
CH3
equatorial preference is smaller
ΔG°= -2.6kcal
Anomeric Effects
CH2OH
O
H
HO
CH2OH
H
H
HO
OH
H
OH
HO
OH
OH
32%
α-D-Glucopyranose
64%
β-D-Glucopyranose
CH2OH
O
H
HO
CH2OH
OH
H
H
O
OH
HO
HO
H
( By A of 0.87
90% exp’ted )
O
HO
OH
HO
H
OH
68%
α-D-Mannose
32%
β-D-Mannose
O
O
CH3
CH3
32:1
Cl
Cl
Suggested interpretations
1. dipolar interaction
μO
μCO
O
μO
O
O
μCO
destabilized Some anomeric effect are
2. Molecular orbital interaction
n
σ*
O
O
solvent dependent
longer C-X bond
stabilized
≣
X
shorter O-C bond
X-ray data agrees
O
V-B term
X
Special Conformations
X
X
H
X
H
H
H
H
H
H
X
H
ΔEt-g
-0.6 gauche
1.2
1.7 anti favored
2.6
X
F
Cl
Br
I
the gauche form increases with
more electronegative atoms
X
H+
O
X
O
O
cis
trans
ΔEt-g
0.3
1.1
1.25
0.63
X
F
Cl
Br
OMe
O
gauche incr. for electronegative atoms
bent-bond interpretation：With more electronegative atom X
Small H-C-X angle expected
bent
H
F
C
H
H
F
F
C
anti
C
F
C
F
C-C bond length
longer by 0.01Å
(By ab initio calc.)
C
gauche
better overlap
bond length shorter
§ Molecular Mechanics
use 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
bond
E(θ)：energy of distorting a bond angle from ideal value
E(Φ)：torsional strain (due to non-staggered bonds)
E( d )：non-bonded interaction, van der Waals force
E( r ) = 0.5kr × (Δr)2 × ( 1+CS ×Δr)
kr ：force constant
Δr：deformation of bond length
CS：cubic stretching constant
E(θ) = 0.5kθ × (Δθ)2 × ( 1+SF ×Δθ4)
stretching-bending ESB strain energy may be added.
E(Φ) = 0.5V0 × ( 1+ cos 3Φ)
more General term
E(Φ) = 0.5V1 × ( 1+ cosΦ) + 0.5V2 × ( 1- cos 2Φ)
+ 0.5V3 × ( 1+ cos 3Φ)
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 and
iterative 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
trans-
cisHO
OH
Rel. rate of oxidation
3.23
：
Rel. rate of acetylation
1
：
1
3.7
the rate is determined by the transition state energy
OH
O
> 0.7kcal
O
C
O
C
CH3
CH3
cis
trans
0.7kcal
cis-acetate
trans-acetate
energy difference in T.S. increases due to larger gp.
O
Cr+ OH
O
OH
H
O
O
cis
+
Cr OH
O
trans
-
In transition state, the diaxial interaction is released
by going from sp3→sp2
Effect of angle strain on reactivity
Smaller rings are more strained and more reactive.
CH3
CH3
CH3
Br2
CH3CH
CH3
Cl2
CHCH2Br
+
Br
Br
~60%
20%
H2C CHCH2CHCl2
+
BrCH2CHCH(CH3)2
+ Cl
Br
Cl
45%
BrCH2CCH2CH3
20%
Cl
+
CH2Cl
4%
41%
CH2Cl
+
Cl
CH3
I
H3C
CH3
CH3
H3C
I2
+
(CH3)2C
CCH2CHI2
H3C
H3C
I
H
H
Coplanarity of double bond substituents can only
exists transiently.
H
trans-cyloalkene,
with ring size ≧ 11, the trans-isomers become more stable
Bridge head double bond
Bred’t rule：the existence of C=C or C=N bonds
(1924) at a bridgehead position in a polycyclic
system is not possible, unless for large
rings.
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
Scheme 3.4 Relative Rates of Ring Closure as a Function of Ring Size
Reaction
Ring size =
Relative rate
5
6
3
4
8.3×10-4
0.31
90
0.07
0.001
→ nucleophilic
participation in
solvolysis
－
→ cyclic ether
formation
5. ArSO2N(CH2)xCl → cyclization
1. Br(CH2)xCO2- → lactone
2. Br(CH2)xNH2 → cyclic amine
3.
PhC(CH2)xC
O
O-
4.
O(CH2)xBr
7
8
1
0.005
2
6×10-5
100
1
0.002
－
0.37
36
1
0.13
－
－
－
－
1
0.01
4×10-4
17
33
－
1
－
－
Small ring disfavored by enthalpy
Large ring disfavored by entropy
Baldwin’s Rule
Table 3.11 Classification of Ring-Closure Types
Exocyclic bonds
Endocyclic bonds
sp
sp2
sp3
sp
sp2
Ring size
(dig)
(trig)
(tet)
(dig)
(trig)
3
unfav
fav
fav
fav
fav
4
unfav
fav
fav
fav
unfav
5
fav
fav
fav
fav
unfav
6
fav
fav
fav
fav
fav
7
fav
fav
fav
fav
fav
sp3 ( tetrahedral)
C
C
X
Nu-
+
X-
+
HX
Nu-
exo-tet
O
C
O
X
O
H
C
exo-trig
O
H
R
HOCH2CH2CH2C
R
C
O
C
exo-dig
Z
R
O
HOMO
Z
Z
Nu
H2C
H2C
O
H
Nu-
Nu-
5-endo-trig
unfavored
R
C
C
Z
much deviate from
planar geometry
for 5-membered
LUMO ring
H
R
Z
Nu
-
Nu
5-endo-dig
favored
O
O
H3C
(CH3)2CCCH CHPh
OH
Ph
O
H3C
O
O
(CH3)2C C C
H3C
C Ph
CH3ONa
OH
Effect of torsional strain
reactivity
NaBH4
O
Ph
O
H3C
rel. rate
OH
23
H
：
NaBH4
OH
1
O
H
The rxn converts a sp2 carbon to sp3 carbon
in 6-membered ring, all staggered bonds
in 5-membered ring, eclipsing interaction increases
H
acetolysis
OTs
H
CH3
O
C
O
H
OTs
acetolysis
H
CH3
O
C
O
In transition state, a sp3 is converted to sp2,
eclipsing effect in 5-membered ring released.
faster
Nu
H
O
O
H
H
Nu
axial attack
H
Bulky reagents attack from the equatorial direction (steric control )
Smaller nucleophiles attack from axial direction
Nu
Nu
H
O-
OH
O
axial
attack
H
σ
Nu
Nu
H
π*
H
equational
attack
H
π
σ*
O
O
or
Stereo electronic effect
O
distorted π*
exo : endo
B2H6
Hydroboration
RCO3H
Epoxidation
H2, Pd
hydrogenation
exo : endo
99.5 0.5
22
78
99.5 0.5
12
88
90
10
90
10