hap. 3 onformational Analysis and Molecular Mechanics onformation:ne of several different spatial arrangements that a molecule can achieve by rotation about single bonds between atoms. Notations: -sc -ac -sc B A B A A ap ap A B 0 ~30 3 3 3 dihedral angle A θ= 0 eclipsed θ= 60 gauche (staggered) (skew) θ= 120 eclipsed 30 ~60 120 ~150 150 ~180 180 ~210 210 ~240 240 ~270 -ac -sp 270 ~300 300 ~330 330 ~360 -ap +sp +ap 3 θ= 240 eclipsed 60 ~90 90 ~120 +sc +ac +sc +ac 3 3 3 B + sc - sc 3 + sc - sc A B A B θ= 180 anti (trans) 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 3 3 3 3 3 3 3
s-trans (Z) s-cis s-cis (Z) s-trans s-cis czc s-cis czt N the - N bond rotation is hindered and conformation isomer could be isolated. I 2 2 3 2 3 2 I N N t-bu 3 t-bu 3 m.p. 64~65 m.p. 105~106 3 3 2 3 Me δ + δ - δ - δ + Me Me δ + δ - δ - Me δ + Me SnBu 3 Pd-/ 2 most stablized Me Me Me Me Me Me major
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) 3 3 3 3 3 3 kcal 6.0 mol kcal 2.6 mol 3 3 kcal 0.8 mol 3 3 kcal 3.4 mol 3 a superimposition of torsional strain of ethane and van der waals strain 3 3 3 3.2 Kcal/mole 3 3 3 3 3 3 0.8 Kcal/mole 3 3 0.3 Kcal/mole gauche anti ΔG = Δ -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 3-65 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 3 anti 3 3 gauche 3 3 3 3 3 two gauche three gauche expected composition: 70:30 anti to gauche experimental composition: 1:2, = 0! geminal repulsion aggravate the vicinal repulsion in anti form and destabilize the anti form more than the gauche form A general case for R 2 R 2 molecules, nly gauche form -stabilizing London interaction, distance sum of van der Waals radii 3 1.75Å 3 l l gauche anti gauche is favored by 0.3 Kcal ± 0.3 intramolecular -bond
3. Angle Strain ( Bayer strain), ( deviation from standard bond angle.) Bayer s Theory based on planer geometry Angle Strain/ 2 total Angle Strain expt l Strain/2 cycloprapane Angle Strain 1 cyclobutane = (109.5-60 ) 2 cyclopentane = 24.75 cyclohexane 24 44 9 44 0 44-5 16 74 12 38 56 3 40-31 36 9.2 kcal/mol 6.55 1.3 0 cyclodecane -17 16-172 42 1.2 The discrepancy is due to non-planar geometry cyclopropane yclopropane - bond are short (1.51Å) than normal - bond (1.54Å) -- bond angle open up (115 ) than the value for -- (106 ) in the 2 of propane. - of cyclopropane are more acidic than normal alkanes. rehybridization, smaller -- bond angle, more p character is used. Then more s character for - bonds. Strain energy of cycloporpane 27.5 kcal/mole, may come from angle strain and also the eclipsing - bonds (eclipsing effect, a torsional strain) cyclobutane 35 1.45 kcal barrier Puckered Butterfly motion -- < 90 angle strain increase torsional strain decrease - bond length 1.55 Å, strain energy 26.5 kcal/mol -- = 90 higher torsional strain all - bonds eclipsed
cyclopentane envelope barrier <2kcal 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 van der Waal repulsion (distance 1.83Å Sum of -van de Walls radii 2.4Å) torsional strain by e - -diffraction -- 110 torsional angle 55.9 (slightly flattened) all staggered 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. substituted cyclohexane 3 equatorial 3 axial 1,3-diaxial interaction = gauche interaction in butane 3 3 2 (1 gauche ~ 0.8kcal) ~ 1.6kcal less stable gauche (exp t 1.74kcal)
equatorial preference = 1.74 kcal/mol A-value conformational free energy [ eq] 95 ΔG = -RTlnK K= = =19 [ ax] 5 useful locking gp. K 19 21 42 9432 -Δ(kcal) 1.75 1.60 1.52 entropy determines the trend ΔS(eu) -0.03 0.64 2.31 t-butyl is a locking gp. so that it dictates the conformation. if two substituents are non-interaction, the A-values are additive 3 2.87 1.74 ψ 3 ψ ΔG= -1.13
two interacting substituents cis 3 3 3 3 e,e e,a 3 3 3 a,a 3 trans-1,2-dimethylcyclohexane 3 3 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) a,e 3 ΔG = 2.7 kcal only e,e form 3 3 3 3 > cis 3 trans 3 3 trans > 3 Exception for favored equatorial preference may exist due to shape. cis 3 but Et Et Et Et Et Effect of dipole interaction van der Waals strain plus dipole interaction l l Br Br transdipole interaction 75% 25% 50% 50% l Br l Br effect of -bonding trans-diol diaxial incr.
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 cyclodecane boat-boat crown 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. ycloalkene 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 ompounds of the Type 3 -X ompound 1-Alkene Barrier height (kcal/mol) Alkanes - 1. 3-3 1.54Å 2.88 2. 3-2 3 3.4 3. 3 -( 3 ) 2 3.9 4. 3 -( 3 ) 3 4.7 5. 3 -Si 3 Si- 1.7 aloethanes 1.87Å 6. 3-2 F 3.3 7. 3-2 l vdw inc. 3.7 8. 3-2 Br bond length inc. 3.7 9. 3-2 I 3.2 eteroatom substitution 10. 3 -N 2 no. of eclipsed Ethane 2.88 1.98 11. 3 -N 3 bonds 3.62 12. 3-1.07 13. 3-3 2.7 0.5 0.5 0.8 3 3 3 3 1.6, more sensitive 3 3 1.6, due to shorter bond 3 2 2 3 3 2 2 3 A B D eclipsed bisected more stable, and B is slightly more stable than A (by 0.15kcal) increase the size of group at -3 increase the preference for B by M.. interpretation bisected form eclipsed form Major repulsive interaction between filled methyl and filled π
For carbonyl cpds. 3 more stable by 0.9 kcal, (may due to non-bonded interaction between the - of the methyl and oxygen. hydrogen bonding) diene 3 if 3 become t-bu, the -eclipsed becomes favored R' anti R even more stable S-trans more stable S-cis maximize πoverlap R' R gauche 2 2 skew less πoverlap S-trans only 3 3 3 S-trans 73% 3 S-trans 28% 3 3 3 S-cis 27% 3 S-cis 82%
ΔG 10.8kcal 2 7.7kcal 2 reduced torsional (sp 2 -sp 2 ) strain in ring inversion reduced steric requirement for =2, ΔG 4.9kcal 1,3-diaxial eclipsed, favored reduced 1,3-diaxial ΔG = -1.3~1.4 α-haloketone effect l dipole smaller favored in l 4 smaller than that for cyclohexane l dipole larger favored in methanol 4. allylic strain 3 3 3 3 3 ΔG = -2.6kcal 3 equatorial preference is smaller
Anomeric Effects 2 32% α-d-glucopyranose 2 68% α-d-mannose 2 64% β-d-glucopyranose 2 32% β-d-mannose ( By A of 0.87 90% exp ted ) 3 32:1 l Suggested interpretations 1. dipolar interaction μ μ 2. Molecular orbital interaction n 3 μ destabilized l μ Some anomeric effect are solvent dependent X σ * stabilized longer -X bond shorter - bond X-ray data agrees V-B term X
Special onformations X X X X X F l Br I ΔE t-g -0.6 1.2 1.7 2.6 gauche anti favored the gauche form increases with more electronegative atoms X + X cis trans X F l Br Me ΔE t-g 0.3 1.1 1.25 0.63 gauche incr. for electronegative atoms bent-bond interpretation:with more electronegative atom X Small --X angle expected bent F F F F anti F gauche - bond length longer by 0.01Å (By ab initio calc.) 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 E steric =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 ) = 0.5k r (Δr) 2 ( 1+S Δr) k r :force constant Δr:deformation of bond length S:cubic stretching constant E(θ) = 0.5k θ (Δθ) 2 ( 1+SF Δθ 4 ) stretching-bending E SB strain energy may be added. E(Φ) = 0.5V 0 ( 1+ cos 3Φ) more General term E(Φ) = 0.5V 1 ( 1+ cosφ) + 0.5V 2 ( 1- cos 2Φ) + 0.5V 3 ( 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. ther 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. yclohexane case
onformational effects on reactivity cis- trans- Rel. rate of oxidation 3.23 : 1 Rel. rate of acetylation 1 : 3.7 the rate is determined by the transition state energy > 0.7kcal 3 3 energy difference in T.S. increases due to larger gp. cis trans 0.7kcal cis-acetate trans-acetate r + - r + - cis trans In transition state, the diaxial interaction is released by going from sp 3 sp 2
Effect of angle strain on reactivity Smaller rings are more strained and more reactive. 3 3 Br 2 3 3 3 2 Br + Br 2 ( 3 ) 2 + Br 2 2 3 Br Br Br ~60% 20% 20% l 2 2 2 l 2 + l l + l 2 l 45% 4% 41% + 2 l 3 3 3 l I 3 3 3 I 2 + ( 3 ) 2 2 I 2 3 I oplanarity of double bond substituents can only exists transiently. trans-cyloalkene, with ring size 11, the trans-isomers become more stable
Bridge head double bond Bred t rule:the existence of = or =N bonds (1924) at a bridgehead position in a polycyclic system is not possible, unless for large rings. Effect of Ring Size and Ring losure 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 losure as a Function of Ring Size Relative rate Reaction Ring size = 3 4 5 6 7 1. Br( 2 ) x 2 - lactone 2. Br( 2 ) x N 2 cyclic amine Ph( 2 ) x 3. nucleophilic participation in solvolysis - 4. cyclic ether ( 2 ) x Br formation 8.3 10-4 0.07 - - 0.31 0.001 0.37-90 100 36-1 1 1 1 0.005 2 0.002 0.13 0.01 8 6 10-5 - - 4 10-4 5. ArS 2 N( 2 ) x l cyclization 17 33-1 - - Small ring disfavored by enthalpy Large ring disfavored by entropy
Baldwin s Rule Table 3.11 lassification of Ring-losure Types Exocyclic bonds Endocyclic bonds sp sp 2 sp 3 sp sp 2 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 sp 3 ( tetrahedral) X + X - Nu - exo-tet Nu - X + X exo-trig 2 2 2 exo-dig R R Z R 2 2 Nu - 5-endo-trig unfavored Z Nu - R Z Nu M LUM much deviate from planar geometry for 5-membered ring R Z Nu - 5-endo-dig Z Nu favored
( 3 ) 2 Ph 3 3 Ph ( 3 ) 2 Ph 3 Na 3 3 Ph Effect of torsional strain reactivity NaB 4 rel. rate 23 : NaB 4 1 The rxn converts a sp 2 carbon to sp 3 carbon in 6-membered ring, all staggered bonds in 5-membered ring, eclipsing interaction increases acetolysis Ts 3 Ts acetolysis 3 faster In transition state, a sp 3 is converted to sp 2, eclipsing effect in 5-membered ring released.
Nu axial attack Nu Bulky reagents attack from the equatorial direction (steric control ) Smaller nucleophiles attack from axial direction Nu Nu - - axial attack Nu equational attack Nu or σ π * σ * π Stereo electronic effect distorted π * exo : endo exo : endo B 2 6 99.5 0.5 22 78 ydroboration R 3 99.5 0.5 12 88 Epoxidation 2, Pd 90 10 10 90 hydrogenation