Stereoisomerism and Conformational Analysis

Stereoisomerism

• Stereoisomerism is the existence of two or more compounds with the same molecular and structural formulae, but different spatial arrangements of atoms or groups.

Types of Isomerism

• Isomerism:
  • Structural Isomerism: Compounds with the same molecular formula but different structural formulae.
  • Stereoisomerism.

Stereoisomers

• Stereoisomers are divided into two groups:
  • Conformational isomers
  • Configurational isomers
• Stereochemistry refers to chemistry in three dimensions.

Isomer Classification

• Comparing two molecules:
  • Same formula?
    • No: Non-isomeric compounds
    • Yes: Isomers
      • Same connectivity?
        • No: Constitutional isomers (structural isomers)
          • Example: $CH<em>3Br$ and $CH</em>3OH$
        • Yes: Stereoisomers
          • Non-superimposable mirror images?
            • No: Diastereomers
              • More than one stereocenter, e.g.,
                • $(2S,3R)$
                • $(2S,3S)$
            • Yes: Enantiomers
              • $CH_3$ with R and S configurations
              • Example involving $CH_2OH$ groups.
          • Structures interconverted by rotation around σ-bonds?
            • Yes: Conformational isomers
              • Examples:
                • Ethane conformations: eclipsed, staggered, gauche.
                • Cyclic compounds: chair and boat conformations of cyclohexane.
                • Axial and equatorial substituents.
            • No: Configurational isomers
              • Cis/Trans isomers
                • Cyclic compounds with substituents on the same or opposite sides.
                • Alkenes with substituents on the same (Z) or opposite (E) sides of the double bond.

Conformations

• Conformations are different arrangements of atoms in a molecule with a definite structure that can be converted into one another by rotation about single carbon-carbon bonds.
• The cause of rotation is torsional strain.

Molecular Orbitals of Ethane

• $sp^3$ hybridized A.O. of carbon
• Sigma bond
• C-C bond length: $1.54 \text{ Å}$, energy: $88 \text{ kcal/mol}$
• C-H bond length: $1.10 \text{ Å}$, energy: $90 \text{ kcal/mol}$

Newman Projections

• Newman projections are created by sighting along one of the backbone bonds.
• Carbons are free to rotate around the single bond.

Staggered vs. Eclipsed Conformations

• Staggered conformation: H atoms on adjacent carbons are as far apart as possible.
• Eclipsed conformation: H atoms on adjacent carbons are as close as possible.

Torsional Energy

• The energy required to rotate the ethane molecule about the carbon-carbon bond is called torsional energy.

Dihedral Angle

• Dihedral angle: The angle between two specified groups in a Newman projection.
  • Staggered: Dihedral angle = $60^\circ$
  • Eclipsed: Dihedral angle = $0^\circ$
• The infinity of intermediate conformations are called skew conformations.

Energy Barrier to Rotation

• Rotation is not quite free; there is an energy barrier.
• The potential energy of the molecule is at a minimum for the staggered conformation, increases with rotation, and reaches a maximum at the eclipsed conformation.

Stability of Conformations

• Most ethane molecules exist in the most stable, staggered conformation.
• The two sets of orbitals in ethane tend to be as far apart as possible to be staggered.

Conformations of n-Butane

• Van der Waals repulsion.
• Due to the presence of the methyl groups, there are several different staggered conformations.
• Non-bonded interactions can be repulsive or attractive, leading to destabilization or stabilization of the conformation.

Butane Conformations

• Anti conformation (I)
• Gauche conformations (II and III)
• Two gauche conformations (II and III) in which the methyl groups are only $60^\circ$ apart.
• Conformations II and III are mirror images of each other, and are of the same stability; nevertheless, they are different.

Potential Energy Changes During Rotation

• Potential energy changes during rotation about the C(2)-C(3) bond of n-butane.
• Anti: 0 kcal
• Gauche: 0.8 kcal
• Eclipsed: 3.4 kcal
• Syn-periplanar: 4.4-6.1 kcal

Steric Strain

• The steric strain between two $CH<em>3$ groups is higher than for a $CH</em>3$ group and an H atom.
• Syn-periplanar: Severe steric + torsional strain ($16 \text{ kJ/mol}$)
• Anticlinal: Steric + torsional strain ($19 \text{ kJ/mol}$)
• Synclinal (gauche): Steric strain ($4 \text{ kJ/mol}$)
• Anti-periplanar: The C-C and C-H bonds are staggered and the two $CH_3$ groups are as far apart as possible (0 kJ/mol).

Stability

• The anti conformation is more stable (by $0.8 \text{ kcal/mol}$) than the gauche.
• Both are free of torsional strain.
• In a gauche conformation, the methyl groups are crowded together, and the molecule is less stable because of van der Waals strain (or steric strain).

Conformation of Cyclic Aliphatic Compounds

• Angle strain, torsional strain, and van der Waals repulsion, working together or opposing each other, determine the net stability of a conformation.

Baeyer Strain Theory

• According to Baeyer theory, when carbon is bonded to four other atoms, the angle between any pair of bonds is the tetrahedral angle $109.5^\circ$.
• Any deviations from the "normal" bond angles are accompanied by angle strain, so in cyclic compounds simultaneously coexist:
  • angle strain
  • torsional strain
  • van der Waals repulsion

Cyclic Compounds

• Cyclopropane: plane, angle is $60^\circ$.
• Cyclobutane: rapid transformation between equivalent non-planar "folded" conformations.
• Cyclopropanes are highly strained because of torsional strain (eclipsed C-H bonds on adjacent carbons) and angle strain (bond angle compressed from $109.5^\circ$ to $60^\circ$).

Cyclopentane

• Planar cyclopentane: much torsional strain.
• The molecule is actually puckered, as an "envelope".

Cyclohexane

• Chair form
• Boat form

Conformations of Cyclohexane

• Chairs and Chair Flips

Energy Diagram of Cyclohexane Conformations

• Chair (0 kJ/mol)
• Twist-boat (22 kJ/mol)
• Boat (28 kJ/mol)
• Half-chair (50.6 kJ/mol)

Angle Strain, Torsional Strain, and Van der Waals Repulsion

• These factors determine the net stability of a conformation.

Cyclohexane Conformations

• Chair conformation
• Boat conformation
• Twist-boat conformation
• Conformations of cyclohexane that are free of angle strain ($\sim 110.8^\circ$).

Axial vs. Equatorial Positions

• Equatorial positions are "outward facing" in green.
• Axial positions are perpendicular to the ring plane.

Chair Conformation

• The most stable conformation of cyclohexane.

Equatorial and Axial Bonds in Cyclohexane

• The bonds holding the hydrogens that are in the plane of the ring lie in a belt about the "equator" of the ring and are called equatorial bonds.
• The bonds holding the hydrogen atoms that are above and below the plane are pointed along an axis perpendicular to the plane and are called axial bonds.
• Chair cyclohexane:
  • Six equatorial C-H bonds: equatorial bonds are parallel to C-C bonds in the ring.
  • Six axial C-H bonds: an alternating arrangement of bonds pointing up and down.

Stability of Chair Conformation

• The chair conformation is a good deal more stable than the boat conformation.
• Staggered cyclohexane; chair:
  • If we sight along each of the carbon-carbon bonds in turn, we see in every case perfectly staggered bonds.

Newman Projections of Methylcyclohexane

• Anti and Gauche interactions in chair conformations.

1,3-Diaxial Interactions

• Steric repulsion between axial substituents and other groups in the axial positions on the same side of the ring.
• Axial substituents increase the energy of the molecule.

Ring-Flip

• Two conformations of 1-methylcyclohexane: one with $CH<em>3$ axial, one with $CH</em>3$ equatorial.
• These two conformations can be converted to each other through a cyclohexane "chair flip".

Boat Conformation

• considerable torsional strain: as much as in two ethane molecules. Eclipsed cyclohexane ethane Boat
• In addition, there is van der Waals strain due to crowding between the "flagpole" hydrogens.

Isomer Types

• Cis- and trans- isomers
  *Optical isomers

Configurational Isomerism

• Configurational isomerism includes two types of isomerism:
  • Optical Isomerism: The necessary structural feature of such type of compounds is the presence of asymmetric carbon atom (chiral centre).
  • Geometrical Isomerism (cis-trans isomerism): due to difference in spatial arrangements of the groups (atoms) about the doubly bonded carbon atoms (π-diastereomers)

Geometrical Isomerism

• cis-2-Butene
• trans-2-Butene

Enzyme Catalysis

• Most biochemical reactions are catalyzed by enzymes.
• The enzyme fumarase, for example, catalyzes the hydration of fumaric acid to malic acid in apples and other fruits, Krebs cycle.

Chirality

• In geometry, an object that is not superposable on its mirror image is said to be dissymmetric.
• In chemistry, the word that corresponds to dissymetric is chiral, as in a chiral molecule.
• A molecule that has any element of symmetry, such as a plane, axe or a center of symmetry, is superposable on its mirror image, is achiral.

Molecular Chirality

• Optical Isomerism.
• The stereogenic (chiral) center(s)

Enantiomers

• Enantiomers are non-superimposable mirror images.

Glyceraldehyde Enantiomers

• L-glyceraldehyde
• D-glyceraldehyde

2n Rule

• The two mirror-image forms are enantiomers of one another and are not superposable.
• $2^n$ rule for the number of existing isomeric structures will apply.

Fischer Projections

• Fischer Projections of Sugar Molecules
• Fischer projection of a glyceraldehyde enantiomer.
• A projection of the chiral carbon onto the page is a cross. It is customary to orient molecules with several carbons so that the carbon chain is vertical, the more oxidized carbon on the top.

L and D Notation

• The assignment of L and D and (R) and (S) notation for glyceraldehyde. Two systems are in common use today: the so-called D,L system and the (R,S) system.

Physical Properties of Enantiomers

• The usual physical properties are identical for both enantiomers of a chiral compound, but the direction of rotation of polarized light plane (equal numerically but opposite).

Chiral Recognition

• The term chiral recognition has been coined to refer to the process whereby some receptors, enzyme or reagent interacts selectively with one of the enantiomers of a chiral molecule. Very high levels of chiral recognition are common in biological processes.

Optical Activity

• Optical activity is a physical property of a substance, just as melting point, boiling point, density, and solubility are and is measured by using an instrument called a polarimeter.
• A substance which causes the plane of polarized light to undergo a rotation is said to be optically active.

Rotation of Polarized Light

• When the substance is chiral and one enantiomer is present in excess of the other, then the plane of polarization is rotated through some angle $\alpha$.
  • $\lambda$: wavelength
  • c: concentration of solution (g/dm^3)
  • l: cell of length (dm)
  • Positive rotation

Racemic Mixtures

• Mixtures containing equal quantities of enantiomers are called racemic mixtures and are optically inactive.
• All achiral substances are optically inactive.

Dextrorotatory and Levorotatory

• Rotation of the plane of polarized light in the clockwise sense is taken as positive (+), or dextrorotatory (d); rotation in the anticlockwise sense is taken as a negative (-) rotation or levorotatory (l).
• The enantiomers of 2-butanol were called:
  • The dextrorotatory form: d-2-butanol
  • The levorotatory form: l-2-butanol
  • A racemic mixture: dl-2-butanol
• Current custom favors using algebraic signs instead, as in (+)-2-butanol, (-)-2-butanol, and (±)-2-butanol, respectively.
• The sign and the magnitude of rotation could be determined only experimentally.

Absolute and Relative Configuration

• The precise arrangement of substituents at a chiral center is its absolute configuration.
• Neither the sign nor the magnitude of rotation by itself provides any information concerning the absolute configuration of a substance.

Molecular Shape

• Molecular shape is critical to the proper functioning of biological molecules.
• The tiniest difference in shape can cause two compounds to behave differently or to have different physiological effects in the body.

Relative Configurations

• Of all the compounds had experimentally determined, compare with the absolute configuration of
  • A salt of (+)-tartaric acid
  • D- and L- glyceraldehyde`s configurations, which were previously determined.

Molecules with Multiple Stereogenic Centers

• Many naturally occurring compounds contain several stereogenic centers. The maximum number of stereoisomers for a particular constitution is $2^n$, where n is equal to the number of stereogenic centers.
• The best examples of substances with multiple stereogenic centers are the carbohydrates.

Stereoisomers of Threose and Erythrose

• D-threose
• L-threose
• D-erythrose
• L-erythrose
• Enantiomers and diastereomers.

Isomers with Multiple Chiral Carbons

• For compounds with more than one chiral carbon, the quantity of isomers are fewer than the maximum number of stereoisomers if there are elements of symmetry.
• Isomers I and II are nonsuperposable mirror images of one another; i.e., they are enantiomers, but Isomers III and IV are identical (plane of symmetry). Note: there are only 3 stereoisomers for tartaric acid.

Meso Compounds

• A compound such as this unique isomer of tartaric acid is called a meso compound.
• Meso compounds are characterized by:
  • An internal reflection plane, that is, one-half of the molecule reflects the other.
  • Each chiral carbon has the same set of four different substituents.
  • The number of stereoisomers is then less than $2^n$.
• For meso-tartaric acid this set is -H, -OH, —COOH, and –CHOH-COOH.

Optical Activity

• Chiral center (asymmetric carbon) containing compounds reveal optical activity if there is NO any element of symmetry in the structure ( plane, axis or center).

Diastereomers

• Stereoisomers that are not related as an object and its mirror image are called diastereomers and are not enantiomers.
• Enantiomers must have equal and opposite specific rotations.
• Diastereomeric substances can have different rotations, with respect to both sign and magnitude.

Erythro and Threo Diastereomers

• When the carbon chain is vertical and like substituents are on the same side of the Fischer projection, the molecule is described as the erythro diastereomer.
• When like substituents are on opposite sides of the Fischer projection, the molecule is described as the threo diastereomer.

Hexoses

• Since there are four stereogenic centers and there is no possibility of meso forms, there are $2^4$, or 16, stereoisomeric hexoses.
• All 16 are known, having been isolated either as natural products or as the products of chemical synthesis.

Examples of Hexoses

• D-glucose
• D-mannose
• D-fructose
• Epimers