Organic Chemistry Unit 5 Review: Stereochemistry at Tetrahedral Centers

Key Concepts

• Stereochemistry studies the three-dimensional arrangement of atoms in molecules and how it affects their properties
• Chirality is a fundamental concept in stereochemistry where molecules are non-superimposable on their mirror images
• Tetrahedral centers, also known as stereocenters or chiral centers, are carbon atoms bonded to four different substituents
  • The arrangement of these substituents in space determines the chirality of the molecule
• Enantiomers are pairs of stereoisomers that are mirror images of each other but are not superimposable
  • They have identical physical properties but can differ in their biological activity and interaction with plane-polarized light
• Diastereomers are stereoisomers that are not mirror images of each other and have different physical properties
• The absolute configuration of a stereocenter is determined using the Cahn-Ingold-Prelog (CIP) priority rules and is designated as either R or S
• Fischer projections are a convenient way to represent the three-dimensional structure of molecules in a two-dimensional format

Tetrahedral Centers and Chirality

• Tetrahedral centers occur when a carbon atom is bonded to four different substituents, creating a tetrahedral geometry
• The presence of a tetrahedral center is a necessary but not sufficient condition for chirality
  • A molecule must have at least one tetrahedral center to be chiral, but not all molecules with tetrahedral centers are chiral
• Chirality arises from the asymmetric arrangement of substituents around the tetrahedral center
• Chiral molecules are non-superimposable on their mirror images, meaning they cannot be overlapped perfectly
• The mirror images of chiral molecules are called enantiomers and have identical physical properties (melting point, boiling point, solubility) but can differ in their biological activity
• Molecules that are superimposable on their mirror images are achiral and do not exhibit chirality
• Certain molecules with tetrahedral centers can be achiral if they have a plane of symmetry (meso compounds) or an inversion center

Stereoisomers and Enantiomers

• Stereoisomers are compounds that have the same molecular formula and bonding sequence but differ in the three-dimensional arrangement of their atoms
• Enantiomers are a type of stereoisomer that are mirror images of each other but are not superimposable
  • They have identical physical properties (melting point, boiling point, solubility) but can differ in their biological activity and interaction with plane-polarized light
• Diastereomers are stereoisomers that are not mirror images of each other and have different physical properties
  • They can be formed when a molecule has multiple stereocenters or when there are geometric isomers (cis/trans) present
• The relationship between enantiomers is similar to that of left and right hands - they are mirror images but cannot be superimposed
• Enantiomers rotate plane-polarized light in equal but opposite directions, a property known as optical activity
  • The enantiomer that rotates plane-polarized light clockwise is called dextrorotatory (D or +), while the one that rotates it counterclockwise is called levorotatory (L or -)

R and S Configuration

• The absolute configuration of a stereocenter is determined using the Cahn-Ingold-Prelog (CIP) priority rules and is designated as either R or S
• The CIP rules assign priority to the substituents attached to the stereocenter based on their atomic number
  • Higher atomic number = higher priority
  • For isotopes, higher mass number = higher priority
• Double or triple bonds are treated as an equivalent number of single-bonded atoms for priority assignment (e.g., C=O is treated as C-O-O)
• If two substituents have the same atomic number, priority is determined by the atomic number of the next set of atoms until a difference is found
• Once priorities are assigned, the molecule is oriented with the lowest priority substituent pointing away from the viewer
• The remaining three substituents are then traced from highest to lowest priority
  • If the path follows a clockwise direction, the stereocenter is assigned an R (rectus) configuration
  • If the path follows a counterclockwise direction, the stereocenter is assigned an S (sinister) configuration

Optical Activity

• Optical activity is the ability of a chiral molecule to rotate plane-polarized light
• Enantiomers rotate plane-polarized light in equal but opposite directions
  • The enantiomer that rotates plane-polarized light clockwise is called dextrorotatory (D or +)
  • The enantiomer that rotates plane-polarized light counterclockwise is called levorotatory (L or -)
• The degree of rotation is measured using a polarimeter and is expressed as the specific rotation $[\alpha]$
  • $[\alpha] = \frac{\alpha}{l \times c}$, where $\alpha$ is the observed rotation, $l$ is the path length in decimeters, and $c$ is the concentration in g/mL
• The sign of the specific rotation (+ or -) does not necessarily correlate with the absolute configuration (R or S) of the molecule
• A racemic mixture, which contains equal amounts of both enantiomers, does not exhibit optical activity as the rotations cancel each other out
• Optical activity is important in the pharmaceutical industry, as enantiomers can have different biological activities and side effects

Fischer Projections

• Fischer projections are a convenient way to represent the three-dimensional structure of molecules in a two-dimensional format
• In a Fischer projection, the carbon chain is drawn vertically, with the carbon atoms represented by the intersection of horizontal and vertical lines
  • The substituents are then drawn on either side of the vertical line, with the horizontal lines representing bonds coming out of the plane and the vertical lines representing bonds going into the plane
• By convention, the most oxidized carbon (e.g., aldehyde or carboxylic acid) is placed at the top of the Fischer projection
• To determine the absolute configuration (R or S) of a stereocenter in a Fischer projection:
  1. Assign priorities to the substituents using the CIP rules
  2. If the two highest-priority substituents are on the same side (left or right) of the vertical line, the stereocenter has the opposite configuration (right = S, left = R)
  3. If the two highest-priority substituents are on opposite sides of the vertical line, the stereocenter has the same configuration as the side of the highest-priority substituent (right = R, left = S)

Molecules with Multiple Stereocenters

• Molecules with multiple stereocenters can have several stereoisomers, depending on the number of stereocenters and their relative configurations
• For n stereocenters, there are a maximum of $2^n$ stereoisomers
  • However, the actual number of stereoisomers may be less due to the presence of meso compounds or other symmetry elements
• Diastereomers are stereoisomers that are not mirror images of each other and have different physical properties
  • They can be formed when a molecule has multiple stereocenters with different relative configurations
• To determine the stereochemistry of molecules with multiple stereocenters:
  1. Assign the absolute configuration (R or S) to each stereocenter using the CIP rules
  2. Compare the relative configurations of the stereocenters to identify diastereomers and enantiomers
• Molecules with multiple stereocenters can have a combination of R and S configurations (e.g., RR, RS, SR, SS)
  • Enantiomers have opposite configurations at all stereocenters (e.g., RR and SS)
  • Diastereomers have at least one stereocenter with the same configuration and at least one with the opposite configuration (e.g., RS and SR)

Applications in Organic Synthesis

• Understanding stereochemistry is crucial for the synthesis of complex organic molecules, particularly in the pharmaceutical industry
• Many biologically active compounds, such as drugs and natural products, are chiral and require the synthesis of specific enantiomers or diastereomers
  • Thalidomide is a well-known example of a drug where one enantiomer had the desired therapeutic effect, while the other caused severe birth defects
• Stereoselective synthesis involves the creation of new stereocenters with a specific absolute configuration (R or S)
  • This can be achieved through the use of chiral auxiliaries, chiral catalysts, or substrate control
• Stereospecific reactions are those in which the stereochemistry of the starting material determines the stereochemistry of the product
  • Examples include SN2 reactions, which proceed with inversion of configuration, and E2 eliminations, which are anti-stereospecific
• Enantiomeric excess (ee) is a measure of the purity of a chiral compound, expressed as the difference between the percentage of the major and minor enantiomers
  • $ee = \frac{[major] - [minor]}{[major] + [minor]} \times 100\%$
• Diastereomeric excess (de) is a similar concept applied to diastereomers
• Chiral resolution techniques, such as chiral chromatography or recrystallization of diastereomeric salts, can be used to separate enantiomers or diastereomers