Isomerism and Stereochemistry

Isomers are different compounds that have the same molecular formula but a different arrangement of atoms. Structural (constitutional) isomerism is divided into three categories:

• Chain isomerism: carbon atoms are connected differently (linear vs branched chain). Example: C₅H₁₂ has three isomers: n-pentane (linear), isopentane (branched), neopentane (highly branched). The number of isomers grows rapidly: C₆H₁₄ has 5 isomers, C₁₀H₂₂ has 75.
• Position isomerism: same atoms and same chain, but a functional group or substituent occupies a different position. Example: C₃H₈O can be 1-propanol (CH₃CH₂CH₂OH) or 2-propanol (CH₃CH(OH)CH₃).
• Functional group isomerism: same atoms but different functional group. Example: C₂H₆O can be ethanol (CH₃CH₂OH, alcohol) or dimethyl ether (CH₃OCH₃, ether). Compounds with the same formula but different functions have radically different chemical and physical properties (ethanol boils at 78°C, dimethyl ether at −24°C).

Real-world applications: functional group isomerism is exploited in pharmaceuticals to modify bioavailability: prodrugs are administered in one form and metabolically converted to the active one.

Stereoisomers have the same connectivity between atoms but a different spatial arrangement. Geometric (cis-trans) isomerism occurs when rotation around a bond is prevented:

• C=C double bonds: the $pi$ bond prevents rotation. If the two substituents on each carbon of the double bond are different, two isomers exist: cis (same side) and trans (opposite sides). Example: maleic acid (cis) and fumaric acid (trans), with very different properties (melting point, solubility, reactivity).
• Cycloalkanes: in rings, rotation around C—C bonds is prevented. Substituents can be on the same side of the ring plane (cis) or on opposite sides (trans).

The E/Z system (more general) assigns priorities to substituents according to the Cahn-Ingold-Prelog (CIP) rules: higher atomic number → higher priority. Z (zusammen, together) when the higher priority groups are on the same side; E (entgegen, opposite) when they are on opposite sides.

The CIP rules for assigning priority:

1. Compare the atomic numbers of the atoms directly bonded to the double-bond carbon. Higher Z → higher priority.
2. If the first atoms are identical, proceed along the chains to the first point of difference.
3. Atoms with multiple bonds are counted as duplicated or triplicated atoms (e.g., C=O counts as C bonded to O, O, C).

Real-world applications: oleic acid (cis-9-octadecenoic acid, a fatty acid) is liquid at room temperature, while its trans isomer (elaidic acid) is solid. Artificial trans fats (partial hydrogenation) are harmful to health because they alter the fluidity of cell membranes.

An object is chiral if it is not superimposable on its mirror image (like the right and left hands). In organic chemistry, the most common chirality is due to a stereogenic center (asymmetric carbon): a carbon atom bonded to four different substituents.

Two enantiomers are non-superimposable mirror images:

• Same molecular formula, same connectivity, but different absolute configuration
• Same physical properties in an achiral environment (melting point, boiling point, solubility)
• Different interaction with plane-polarized light: one rotates the plane of polarization clockwise (dextrorotatory, +), the other counterclockwise (levorotatory, −). A 1:1 mixture is racemic and shows no optical activity.
• Different interaction with other chiral compounds (e.g., enzymes, biological receptors): often one enantiomer is therapeutically active, the other inactive or toxic.

The maximum number of stereoisomers for a molecule with $n$ stereogenic centers is $2^n$, but it can be lower if internal symmetry planes exist (meso compounds). Diastereomers are stereoisomers that are not enantiomers (not mirror images): they have different physical properties and can be separated by crystallization or chromatography.

Real-world applications: thalidomide — one enantiomer was an effective sedative, the other caused severe fetal malformations. Today, the FDA requires stereochemical characterization of every new chiral drug. The pharmaceutical industry increasingly produces enantiomerically pure drugs (e.g., omeprazole, escitalopram).

Fischer projections represent chiral molecules in 2D, standard for carbohydrates and amino acids:

• The carbon chain is vertical, with the most oxidized carbon at the top (for sugars: CHO at top for aldoses)
• Horizontal bonds are coming toward the viewer (out of the plane)
• Vertical bonds are behind the plane (away from the viewer)
• A 180° rotation of the projection in the plane leaves the configuration unchanged; a 90° rotation inverts it

Absolute configuration R/S is assigned using the Cahn-Ingold-Prelog rules:

1. Assign priorities to the four substituents based on atomic number (1 = highest priority, 4 = lowest)
2. Orient the molecule so that the substituent with priority 4 is pointing away from the viewer (at the top in a Fischer projection)
3. Observe the order 1 → 2 → 3: if clockwise → R (rectus), if counterclockwise → S (sinister)

Optical activity is measured with a polarimeter: the specific rotation $[alpha]$ at a given temperature and wavelength (usually the sodium D line, 589 nm) is: $$[alpha]^T_lambda = dfrac{alpha}{l,c}$$ where $alpha$ is the observed rotation (degrees), $l$ the cell length (dm), $c$ the concentration (g/mL). A racemic mixture shows $[alpha] = 0$. Enantiomeric excess (ee%) measures optical purity: ee% = $|R-S|/(R+S) imes 100$.

Real-world applications: specific rotation is a fast, non-destructive method for evaluating the enantiomeric purity of a sample. Chiral stationary phase chromatography (chiral HPLC) separates enantiomers by exploiting their different interaction with a chiral selector.