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