Stereochemistry at Tetrahedral Centers: Chirality, Enantiomers, and Optical Activity

Stereochemistry at Tetrahedral Centers

Enantiomers

Stereochemistry examines the three-dimensional arrangement of atoms in molecules. Enantiomers are a type of stereoisomer that are non-superimposable mirror images of each other, much like left and right hands.

• Molecular Handedness: Molecules such as CH(3)X and CH(2)XY are superimposable on their mirror images and thus are not chiral. In contrast, CHXYZ molecules (where X, Y, and Z are different groups) are not superimposable on their mirror images and are chiral.

• Definition: Enantiomers occur when a tetrahedral carbon atom is bonded to four different substituents.

• Properties: Enantiomers cannot be superimposed, even if some groups align, because the remaining groups will not match.

• Example: Lactic acid (with H, OH, CH3, and CO2H attached to the central carbon) exists as two enantiomers: (+)-lactic acid and (−)-lactic acid. Both are found in sour milk, but only (+)-lactic acid is present in muscle tissue.

Chirality

Definition and Identification

A molecule is chiral if it is not identical to its mirror image. Chirality is a key concept in organic chemistry, as it affects molecular behavior and interactions.

• Chiral Molecule: Not superimposable on its mirror image.

• Achiral Molecule: Has a plane of symmetry, making it superimposable on its mirror image.

• Plane of Symmetry: Divides an object so that one half is a mirror image of the other. For example, a coffee mug has a plane of symmetry, but a hand does not.

• Examples: Propanoic acid is achiral (has a symmetry plane), while lactic acid is chiral (no symmetry plane in any conformation).

• Chirality Centers: The most common cause of chirality is a tetrahedral carbon bonded to four different groups. Such carbons are called chirality centers, stereocenters, asymmetric centers, or stereogenic centers.

• Chirality vs. Chirality Center: Chirality describes the entire molecule, while a chirality center is the source of chirality.

• Complex Cases: Determining chirality centers can be challenging if differences in substituents are distant from the center (e.g., 5-bromodecane is chiral because carbon 5 is bonded to H, Br, a butyl group, and a pentyl group).

• Non-Chiral Centers: Carbons in CH2, CH3, C=O, C=C, and C≡C groups cannot be chirality centers.

Optical Activity

Interaction with Plane-Polarized Light

Chiral molecules can rotate plane-polarized light, a property known as optical activity. This phenomenon is measured using a polarimeter.

• Plane-Polarized Light: Ordinary light oscillates in many planes; a polarizer restricts oscillation to one plane.

• Optically Active Compounds: Rotate plane-polarized light. Discovered by Jean-Baptiste Biot in substances like sugar and camphor.

• Measurement: The angle of rotation is measured with a polarimeter, where light passes through a sample and an analyzer.

• Direction of Rotation:

  • Levorotatory (−): Rotates light to the left (counterclockwise).

  • Dextrorotatory (+): Rotates light to the right (clockwise).

  • Examples: (−)-morphine is levorotatory; (+)-sucrose is dextrorotatory.

• Factors Affecting Observed Rotation: Concentration, pathlength, and wavelength of light. Doubling concentration or pathlength doubles the observed rotation.

• Specific Rotation [α]D: Standardizes rotation at 589.6 nm (sodium D line), 1 dm pathlength, and 1 g/cm³ concentration.

Formula for Specific Rotation:

$[\alpha]_D = \frac{\alpha}{l \times c}$

• Where:

  • $[\alpha]_D$ = specific rotation

  • $\alpha$ = observed rotation (degrees)

  • $l$ = pathlength (dm)

  • $c$ = concentration (g/cm³)

• Specific rotation is a physical constant for each optically active compound.

• Example: (+)-lactic acid has $[\alpha]_D = +3.82$, (−)-lactic acid has $[\alpha]_D = −3.82$.

Table: Examples of Specific Rotations

Compound	Specific Rotation $[\alpha]_D$
Penicillin V	+221
Sucrose	+66.5
Camphor	+44.3
Cholesterol	−31.5
Morphine	−132
Cocaine	−15.6
Chloroform	0 (achiral)
Acetic acid	0 (achiral)
Additional info: Values inferred for illustration; actual values may vary.

Pasteur’s Discovery of Enantiomers

Historical Perspective

Louis Pasteur's work in 1848 on tartaric acid salts was foundational in the understanding of enantiomers.

• Pasteur observed two types of sodium ammonium tartrate crystals, which were non-superimposable mirror images.

• He separated the crystals into right-handed and left-handed forms, each optically active but with opposite specific rotations.

• The original mixture (racemic mixture) was optically inactive, but the separated forms were optically active.

• Pasteur concluded that the molecules themselves had asymmetric arrangements, a concept later confirmed by structural theory.

• Enantiomers (optical isomers) have identical physical properties except for the direction in which they rotate plane-polarized light.

Sequence Rules for Specifying Configuration

Cahn–Ingold–Prelog (CIP) Priority Rules

To unambiguously describe the three-dimensional arrangement of groups around a chirality center, the Cahn–Ingold–Prelog sequence rules are used to assign R (rectus, right) or S (sinister, left) configuration.

• Rule 1: Rank the four atoms directly attached to the chirality center by atomic number. The highest atomic number gets the highest priority (1), the lowest (usually hydrogen) gets the lowest (4). For isotopes, the heavier isotope ranks higher.

• Rule 2: If the first atoms are identical, compare the next set of atoms along each substituent until a difference is found. For example, ethyl (–CH2CH3) outranks methyl (–CH3) because ethyl's second atom is carbon, while methyl's is hydrogen.

• Rule 3: Multiple bonds are treated as if the atom is bonded to an equivalent number of single-bonded atoms. For example, a carbonyl group (C=O) is treated as if the carbon is bonded to two oxygens.

Assigning R and S Configuration

• Orient the molecule so that the lowest-priority group (4) points away from you.

• Trace a path from priority 1 → 2 → 3. If the path is clockwise, the configuration is R; if counterclockwise, it is S.

• Example: In (−)-lactic acid, −OH is 1, −CO2H is 2, −CH3 is 3, and −H is 4. With −H away from the observer, the path 1 → 2 → 3 is clockwise, so the configuration is R.

• Note: The sign of optical rotation (+ or −) does not correlate with R or S configuration. For example, (S)-glyceraldehyde is levorotatory (−), while (S)-alanine is dextrorotatory (+).

Absolute Configuration

• Absolute configuration refers to the actual spatial arrangement of atoms at a chirality center.

• There is no direct correlation between R/S configuration and the direction of optical rotation.

• Absolute configurations were confirmed by X-ray diffraction methods in 1951.

Summary Table: Assigning R/S Configuration

Step	Description
1	Assign priorities to the four groups attached to the chirality center using atomic number.
2	If necessary, use the next set of atoms to break ties.
3	Treat multiple bonds as equivalent single bonds for ranking purposes.
4	Orient the molecule so the lowest-priority group is away from you.
5	Trace the path from 1 → 2 → 3; clockwise = R, counterclockwise = S.

Additional info: The above notes expand on the original content with definitions, examples, and tables for clarity and completeness.