CHEM210 Lecture 10: Stereochemistry - Chiral Centers, Absolute Configuration, and Stereoisomers

Fundamentals of Chiral Carbons

• Definition of a Chiral Carbon: A chiral carbon (or stereocenter) is defined as a carbon atom that is bonded to four completely different groups.
• Hybridization Requirement:
  • A chiral carbon must be $sp^3$ hybridized.
  • Carbons involved in double bonds or triple bonds ($sp^2$ or $sp$ hybridized carbons) can never be chiral because they cannot be attached to four distinct groups.
• Criteria for Achiral Carbons:
  • Any carbon attached to two or more identical atoms or groups is achiral.
  • Examples include $-CH_2-$ groups (attached to two hydrogen atoms) and $-CH_3$ methyl groups (attached to three hydrogen atoms or possessing identical branch attachments).
• Groups vs. Atoms Distinction:
  • Chirality is evaluated based on attached groups of atoms, not merely the single directly bonded atom.
  • For example, if a carbon is attached to both an ethyl group ($-CH_2CH_3$) and a methyl group ($-CH_3$), both directly attached atoms are carbons, but the two attached groups are different, satisfying the four-different-groups rule.
• Evaluating Chirality in Cyclic Systems (Rings):
  • To determine if a carbon inside a ring is chiral, trace the pathway along the ring starting from that carbon in both directions (clockwise vs. counterclockwise).
  • If the two pathways around the ring are asymmetrical (e.g., encountering an $sp^2$ hybridized carbon, a substituent like an $-OH$ group, or a branch point along one side before the other), the two directions count as two distinct groups.
  • If an internal plane of symmetry exists across the ring such that both pathways are identical, the two pathways count as identical groups, making the ring carbon achiral.

Drawing Stereoisomers and Mirror Images

• Methods for Drawing Enantiomers (Non-Superimposable Mirror Images):
  • Method 1 (Inverting Stereocenters): Keep the carbon backbone fixed in the plane of the page and invert every stereochemical marker at the chiral centers (convert all wedges to dashes and all dashes to wedges).
  • Method 2 (Literal Mirror Reflection): Draw a complete physical reflection of the entire molecule across a vertical mirror plane.
• Common Error in Drawing Mirror Images:
  • Performing a physical reflection of the carbon chain and inverting the stereocenters ( wedges to dashes) simultaneously results in a double-inversion.
  • Doing both operations yields the exact same starting molecule (an identical, superimposable structure), rather than its mirror image.
• 3D Visualization:
  • Molecular model kits are highly recommended for stereochemistry to accurately visualize non-superimposable mirror images and rotation in three dimensions.

Molecular Chirality vs. Chiral Centers

• Chiral Atoms vs. Chiral Molecules:
  • A molecule can contain individual chiral carbons and still be an achiral molecule as a whole if internal symmetry is present.
  • The presence of a wedge and a dash in a structure merely indicates tetrahedral ($3D$) geometry; it does not automatically guarantee that the carbon or molecule is chiral.
• Impact of Symmetry on Enantiomer Formation:
  • An achiral molecule (a molecule possessing a plane of symmetry) has a mirror image that is completely identical and superimposable onto itself.
  • An enantiomer exists only when a molecule is chiral (lacking a plane of symmetry, resulting in a non-superimposable mirror image).
  • Symmetric geometric objects (such as a cube) yield identical superimposable mirror images upon reflection.

Absolute Configuration: The Cahn-Ingold-Prelog ($R$/$S$) System

• Configuration vs. Conformation:
  • Conformation: The spatial arrangements of a molecule that interconvert freely via single-bond rotations or ring flips (e.g., chair conversions or Newman projections) without breaking bonds.
  • Configuration: The specific 3D spatial arrangement of substituents around a chiral center. Changing configuration requires breaking and reforming bonds, creating a distinct stereoisomer.
• Cahn-Ingold-Prelog Priority Rules:
  • Rule 1 (Atomic Number): Assign priorities $1, 2, 3, 4$ to the four attached groups based on the atomic number ($Z$) of the atom directly attached to the chiral center. Higher atomic number receives higher priority ($1$ = highest, $4$ = lowest).
  • Rule 2 (Chain Tracing): If there is a tie between directly attached atoms, proceed atom-by-atom along the parallel chain pathways until the first point of difference is identified.
  • Rule 3 (Multiple Bonds): Treat double and triple bonds as equivalent numbers of single bonds to that same atom:
  • A carbonyl group ($C=O$) is treated as a carbon bonded to two separate oxygen atoms ($(O, O)$).
  • A carboxylic acid carbon ($-COOH$) is treated as a carbon bonded to three oxygen atoms ($(O, O, O)$).
  • A nitrile group (-C \n\nequi N) is treated as a carbon bonded to three separate nitrogen atoms ($(N, N, N)$).
  • An alkene group ($-CH=CH_2$) is treated as a carbon bonded to two carbon atoms ($(C, C)$).
• Determining Absolute Configuration ($R$ vs. $S$):
  • Orient the molecule so that the lowest priority group (Priority $4$, commonly Hydrogen) is directed away from the viewer on a dashed bond.
  • Trace a circular arrow from Priority $1 \rightarrow 2 \rightarrow 3$:
  • $R$ Configuration (Rectus): Clockwise path ($1 \rightarrow 2 \rightarrow 3$).
  • $S$ Configuration (Sinister): Counterclockwise path ($1 \rightarrow 2 \rightarrow 3$).
• Rule Inversion for Wedged Lowest Priority Group:
  • If Priority $4$ is pointing towards the viewer on a wedged bond, determine the apparent direction ($1 \rightarrow 2 \rightarrow 3$) and invert the result:
  • Apparent Clockwise path = $S$ Configuration.
  • Apparent Counterclockwise path = $R$ Configuration.
• Hand Trick for Configuration Verification:
  • Point the thumb of your hand in the direction of Priority $4$ (thumb pointing away/down for a dash; thumb pointing towards/up for a wedge).
  • Curl fingers in the direction of $1 \rightarrow 2 \rightarrow 3$:
  • Matching right hand = $R$ Configuration.
  • Matching left hand = $S$ Configuration.

Worked Examples of $R$/$S$ Configuration

• Example 1: Amino Acid Systems (e.g., Alanine):
  • Chiral center bound to $-NH_2$, $-COOH$, $-CH_3$, and $-H$ (dashed):
  • Priority $1$: $-NH_2$ (Nitrogen, $Z = 7$).
  • Priority $2$: $-COOH$ (Carbon attached to $(O, O, O)$).
  • Priority $3$: $-CH_3$ (Carbon attached to $(H, H, H)$).
  • Priority $4$: $-H$ (Hydrogen, $Z = 1$, on a dash).
  • Tracing $1 \rightarrow 2 \rightarrow 3$ yields a counterclockwise path, establishing an $S$ Configuration.
• Example 2: Haloalkenes with Wedged Hydrogen:
  • Chiral center bound to $-Br$, $-CH=CH_2$, $-CH_2CH_3$, and $-H$ (wedged):
  • Priority $1$: $-Br$ (Bromine, $Z = 35$).
  • Priority $2$: $-CH=CH_2$ (Carbon treated as attached to $(C, C, H)$).
  • Priority $3$: $-CH_2CH_3$ (Carbon attached to $(C, H, H)$).
  • Priority $4$: $-H$ (Hydrogen pointing towards viewer on a wedge).
  • Path $1 \rightarrow 2 \rightarrow 3$ appears counterclockwise, but because Priority $4$ is on a wedge, the result is inverted to establish an $R$ Configuration.

Stereoisomeric Relationships and the Max Stereoisomers Formula

• Classification of Stereoisomers:
  • Enantiomers: Non-superimposable mirror images in which every chiral center in the molecule is inverted (all $R$ centers become $S$, and all $S$ centers become $R$).
  • Diastereomers: Stereoisomers that are not mirror images of one another. These occur when at least one chiral center is inverted while at least one other chiral center remains unchanged.
• Calculating Maximum Stereoisomers ($2^n$ Rule):
  • The maximum number of possible stereoisomers for a given compound is calculated using the formula:     $\text{Maximum Stereoisomers} = 2^n$     where $n$ equals the total number of chiral carbons (stereocenters) in the molecule.
  • For $n = 1$ chiral center: $\text{Max Stereoisomers} = 2^1 = 2$ ($1$ pair of enantiomers).
  • For $n = 2$ chiral centers: $\text{Max Stereoisomers} = 2^2 = 4$
  • For $n = 3$ chiral centers: $\text{Max Stereoisomers} = 2^3 = 8$
• Exceptions to the $2^n$ Rule (Meso Compounds):
  • Meso Compounds: Molecules that contain two or more stereocenters but also possess an internal plane of symmetry.
  • An internal plane of symmetry makes the entire molecule achiral and superimposable on its mirror image, reducing the actual number of stereoisomers below the maximum predicted by $2^n$.