Stereochemistry: Isomerism, Chirality, and Optical Activity

Chapter 5: Stereoisomerism

5.1 Isomers – Overview

Isomers are compounds with the same molecular formula but different arrangements of atoms. Understanding the types of isomers is fundamental in organic chemistry.

• Constitutional Isomers: Same molecular formula, different connectivity (order of atom attachment).

• Stereoisomers: Same molecular formula and connectivity, but different spatial arrangement of atoms.

Example: Cis/trans isomers in cycloalkanes and alkenes. Cis: groups on the same side; Trans: groups on opposite sides.

5.2 Stereoisomers – Chirality and Enantiomers

Stereoisomers include cis/trans isomers and other relationships such as chirality. Chirality is a property where an object is not superimposable on its mirror image.

• Chiral Molecule: A molecule that is asymmetric and not identical to its mirror image.

• Chiral Center: Typically a carbon atom bonded to four different groups.

• Enantiomers: Stereoisomers that are mirror images but not superimposable.

Example: 2-bromobutane has a chiral center; its mirror image is its enantiomer.

Practice: Identify chiral centers in molecules and determine the number of chiral centers.

5.3 Assigning R and S Configuration (Cahn-Ingold-Prelog System)

Enantiomers differ in configuration at chiral centers. The Cahn-Ingold-Prelog (CIP) system assigns each chiral center as "R" (rectus) or "S" (sinister).

1. Step 1: Prioritize the four groups attached to the chiral center by atomic number (highest = 1).

2. Step 2: Orient the molecule so the lowest priority group (4) is pointing away.

3. Step 3: Trace the sequence from 1 → 2 → 3. Clockwise = R; Counterclockwise = S.

4. Step 4: For ties, compare atoms one layer at a time until a difference is found.

5. Step 5: Double bonds are treated as two single bonds for priority purposes.

Useful Trick: Switching two groups on a chiral center inverts its configuration.

Example: Assigning (R) or (S) to 2-bromobutane.

In IUPAC Nomenclature: The (R) or (S) configuration is included in the compound's name.

5.4 Optical Activity

Enantiomers have identical physical properties except for their interaction with chiral environments and their optical activity.

• Plane-Polarized Light: Chiral compounds rotate the plane of polarized light; this property is called optical activity.

• Polarimeter: Instrument used to measure optical rotation.

• Specific Rotation: Standardized measurement of optical rotation, dependent on concentration, pathlength, temperature, and wavelength.

$[\alpha] = \frac{\alpha_{obs}}{l \cdot c}$ where $[\alpha]$ is specific rotation, $\alpha_{obs}$ is observed rotation, $l$ is pathlength (dm), $c$ is concentration (g/mL).

• Dextrorotary (+): Rotates light clockwise.

• Levorotary (−): Rotates light counterclockwise.

• Racemic Mixture: 50/50 mixture of enantiomers; optical rotation is zero.

• Enantiomeric Excess (% ee): Measures the excess of one enantiomer over the other.

$\%\ ee = \frac{|R - S|}{R + S} \times 100$

Example: If a mixture of (R) and (S) 2-bromobutane has a specific rotation of −4.6°, % ee can be calculated.

5.5 Diastereomers

Stereoisomers that are not mirror images are called diastereomers. They have different physical properties and can be separated by conventional methods.

• Enantiomers: Mirror images, not superimposable.

• Diastereomers: Not mirror images.

Example: Cis- and trans-2-butene are diastereomers.

Number of Stereoisomers: For n chiral centers, maximum number is $2^n$.

5.6 Symmetry and Chirality

Symmetry plays a crucial role in determining chirality. A molecule with a plane of symmetry is achiral.

• Meso Compounds: Molecules with chiral centers but a plane of symmetry; they are achiral.

• Achiral Compounds: Superimposable on their mirror image, often due to symmetry.

Example: Cis-1,2-dimethylcyclohexane is achiral (meso), while trans is chiral.

Summary: Plane of symmetry = achiral; absence of plane of symmetry usually = chiral, but exceptions exist (e.g., inversion center).

5.7 Fischer Projections

Fischer projections are a 2D representation of molecules with chiral centers, especially useful for sugars and amino acids.

• Horizontal lines: Groups coming out of the page.

• Vertical lines: Groups going back into the page.

Application: Quickly assess stereoisomeric relationships (enantiomers vs diastereomers).

5.8 Conformationally Mobile Compounds

Single bonds allow free rotation, leading to different conformations. Some conformations may be chiral, but if they interconvert rapidly, the molecule is not chiral overall.

• Example: Butane's gauche conformations are chiral, but butane itself is achiral.

• Chair conformations: Cis-1,2-dimethylcyclohexane conformations are enantiomeric but interconvert, making the compound achiral.

5.9 Chirality without Chiral Centers

Some molecules are chiral even without traditional chiral centers.

• Atropisomers: Stereoisomers due to hindered rotation around a bond (e.g., BINAP).

• Allenes: Compounds with two adjacent C=C bonds; can be chiral if substituents on each end are different.

5.10 Resolution of Enantiomers

Enantiomers have identical physical properties, making separation challenging. Special methods are required.

• Pasteur Method: Manual separation of enantiomeric crystals (historical).

• Resolving Agent: Use of a chiral compound to form diastereomers, which can be separated.

• Affinity Chromatography: Chiral adsorbents allow separation based on differential interaction.

5.11 E and Z Designations for Alkenes

For alkenes with different groups on each carbon, E/Z notation is used instead of cis/trans.

1. Step 1: Prioritize groups attached to the C=C bond by atomic number.

2. Step 2: If top priority groups are on the same side, it is Z (zussamen = together); if on opposite sides, it is E (entgegen = opposite).

Summary Table: Types of Isomers

Type	Definition	Example
Constitutional Isomers	Same formula, different connectivity	Butane vs. Isobutane
Stereoisomers	Same formula and connectivity, different spatial arrangement	Cis/trans alkenes
Enantiomers	Mirror images, not superimposable	(R)- and (S)-2-bromobutane
Diastereomers	Not mirror images	Cis- and trans-2-butene
Meso Compounds	Chiral centers, but achiral due to symmetry	Cis-1,2-dimethylcyclohexane

Summary Table: Optical Activity

Compound Type	Optical Activity	Physical Properties
Enantiomers	Equal magnitude, opposite direction	Identical except for optical activity
Diastereomers	Different	Different
Racemic Mixture	Zero	Mixture of enantiomers

Additional info: The notes include references to SkillBuilder exercises for practice, which are not reproduced here. Students are encouraged to use molecular models for visualizing chirality and stereochemistry.