Organic Stereochemistry Essentials

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1. Stereochemistry Basics Definition: Study of 3D arrangement of atoms in space and its influence on chemical/physical properties. Stereoisomers: Compounds with similar structure and connectivity but different 3D arrangement. Stereoisomerism Types: Optical Isomerism Geometrical Isomerism Conformational Isomerism 2. Optical Isomerism 2.1. Plane Polarized Light Ordinary Light: Waves vibrate in all planes perpendicular to propagation. Plane Polarized Light: Vibrations restricted to a single plane after passing through a Nicol prism. Normal light Polariser Plane polarised light 2.2. Optical Activity Definition: Property of a substance to rotate the plane of polarized light. Optically Active Substances: Rotate plane polarized light (e.g., lactic acid, glucose). Dextrorotatory ($d$ or +): Rotates light to the right (clockwise). Laevorotatory ($l$ or -): Rotates light to the left (anticlockwise). Angle of Rotation ($\alpha$): Angle through which the plane is rotated. Polarimeter: Instrument used to measure direction and magnitude of rotation. 3. Chirality and Dissymmetry Chiral Molecules: Molecules that are non-superimposable on their mirror images (e.g., hands). Chirality / Dissymmetry: The property of non-superimposability of a structure on its mirror image. Achiral Molecules: Molecules that are superimposable on their mirror images (e.g., cup). Chiral Carbon Atom ($C^*$): A carbon atom bonded to four different atoms or groups. Examples of Chiral Molecules: 2-butanol: $CH_3CH(OH)CH_2CH_3$ Lactic acid: $CH_3CH(OH)COOH$ 2,3-dibromobutane: $CH_3CH(Br)CH(Br)CH_3$ 4. Symmetry Elements Plane of Symmetry: An imaginary plane that bisects a molecule such that two halves are mirror images. Chiral Molecules: Do NOT possess a plane of symmetry (dissymmetric). Achiral Molecules: Possess a plane of symmetry (symmetric). 5. Enantiomers Definition: Stereoisomers that are non-superimposable mirror images of each other. Characteristics: Identical physical properties (melting point, boiling point, density, solubility). Similar chemical properties. Rotate plane polarized light to the same extent but in opposite directions (same specific rotation, opposite sign). Can be dextrorotatory ($d$ or +) or laevorotatory ($l$ or -). Example: Enantiomers of 3-methylhexane. 6. Diastereomers Definition: Stereoisomers that are NOT mirror images of each other. Characteristics: Different physical properties (boiling points, solubilities, densities, refractive index). Different specific rotations (may have same or opposite signs, or be optically inactive). Example: In tartaric acid, structures I/II are enantiomers, and I/II are diastereomers of III/IV. 7. Meso Compounds Definition: Compounds with chiral centers that are superimposable on their mirror image and are optically inactive due to internal compensation. Possess a plane of symmetry despite having chiral centers. One half of the molecule rotates plane polarized light in one direction, and the other half rotates it in the opposite direction, canceling out overall rotation. Example: Certain forms of tartaric acid (III and IV). 8. Racemic Mixture Definition: An equimolar mixture of dextrorotatory and laevorotatory enantiomers ($dl$ or $\pm$). Optical Inactivity: Due to external compensation (rotations cancel each other out). Racemisation: Process of forming a racemic mixture from optically active $d$ or $l$ forms. 9. Total Number of Optical Isomers For compounds with $n$ asymmetric carbon atoms: Unsymmetrical Molecules: Total optical isomers = $2^n$. (Number of $d$ and $l$ isomers = $2^n$, meso isomers = 0). Symmetrical Molecules (n is even): Number of $d$ and $l$ forms = $2^{(n-1)}$ Number of meso isomers = $2^{(n/2 - 1)}$ Total = $2^{(n-1)} + 2^{(n/2 - 1)}$ Example: Tartaric acid ($n=2$) has $2^{(2-1)} = 2$ $d/l$ forms and $2^{(2/2-1)} = 1$ meso isomer, total 3. 10. Optical Isomerism without Asymmetric Carbon Atom Some compounds are optically active without a chiral carbon atom if the molecule as a whole is asymmetric (dissymmetric). Examples: Allenes: Compounds with general formula $>C=C=C Spiro Compounds (Spirans): Formed by replacing both bonds of allenes with rings. Two rings are perpendicular, leading to dissymmetry and optical activity. 11. Geometrical Isomerism (cis-trans isomerism) Definition: Stereoisomers that have the same structural formula but differ in the spatial arrangement of atoms or groups around a double bond. Arises due to hindered rotation around the carbon-carbon double bond. Conditions: Molecule must have a double bond. Different atoms or groups must be attached to the same carbon atom of the double bond. Cis isomer: Bulky groups are on the same side of the double bond. Less stable. Trans isomer: Bulky groups are on opposite sides of the double bond. More stable. Characteristics: Geometrical isomers are diastereomers and have different physical properties. Examples: cis-1,2-dichloroethene vs. trans-1,2-dichloroethene Maleic acid (cis) vs. Fumaric acid (trans) 12. E-Z Nomenclature (for compounds where cis-trans fails) Used when three or four different groups are attached to the carbon atoms of a double bond. Based on Cahn-Ingold-Prelog (CIP) sequence rules for assigning priorities: Atom with higher atomic number gets higher priority (e.g., $I > Br > Cl > F$). For isotopes, higher mass isotope gets higher priority (e.g., $D > H$). If first atoms are identical, compare next atoms (e.g., ethyl > methyl). Double/triple-bonded groups are treated as duplicated/triplicated for priority assignment. Z (Zusammen - together): Higher priority groups are on the same side of the double bond. E (Entgegen - opposite): Higher priority groups are on opposite sides of the double bond. 13. Absolute Configuration (R/S System) Defines arrangement of atoms around a chiral center using CIP sequence rules. Steps: Assign priorities (1, 2, 3, 4) to ligands around the chiral center (1 = highest, 4 = lowest). View the molecule from the side farthest away from the lowest priority ligand (4). Determine the direction of decreasing precedence of ligands 1 $\to$ 2 $\to$ 3. R (Rectus - right): Clockwise direction. S (Sinister - left): Anticlockwise direction. For Fischer Projections: If lowest priority group (4) is not at the bottom, perform an even number of exchanges to move it there. Odd exchanges invert the configuration. 14. Conformational Isomerism in Hydrocarbons Arises from rotation about carbon-carbon single bonds (sigma bonds have cylindrical symmetry). Different spatial arrangements are called conformations . 14.1. Conformations of Ethane ($CH_3-CH_3$) Infinite number of conformations due to rotation around C-C bond. Staggered Conformation: Hydrogens on two carbons are maximally distant. Repulsion is minimum, energy is lowest, most stable. Dihedral angle = $60^\circ$. Eclipsed Conformation: Hydrogens on the second carbon are directly behind those on the first. Repulsion is maximum, energy is highest, least stable. Dihedral angle = $0^\circ$. Skew Conformations: Intermediate conformations between staggered and eclipsed. Relative Stabilities: Staggered > Skew > Eclipsed. Energy difference is small ($\approx 3 \text{ kcal/mol}$), so rapid interconversion occurs. Representations: Sawhorse projections, Newman projections. 14.2. Conformations for Butane ($CH_3CH_2CH_2CH_3$) Focus on rotation around the $C_2-C_3$ bond and relative positions of methyl groups. Syn Eclipsed (I): Both methyl groups aligned, maximum steric repulsion, highest energy. Gauche Staggered (II, VI): Methyl groups separated by $60^\circ$ dihedral angle. Lower energy than eclipsed. Eclipsed (III): One methyl group aligned with a hydrogen. Anti Staggered (IV): Methyl groups are $180^\circ$ apart. Minimum steric repulsion, lowest energy, most stable. Relative Stabilities: Anti Staggered > Gauche Staggered > Eclipsed (III) > Syn Eclipsed. Anti-conformation is more stable than gauche by $\approx 0.8 \text{ kcal/mol}$. 14.3. Conformations of Cyclohexane Cyclohexane is non-planar to avoid strain and maintain tetrahedral bond angles ($109^\circ 28'$). Chair Conformation: More stable. Adjacent hydrogen atoms are staggered, minimizing repulsion. Has six axial ($a$) and six equatorial ($e$) hydrogen atoms. Boat Conformation: Less stable. Adjacent hydrogen atoms ($C_2-C_3$ and $C_5-C_6$) are eclipsed. "Flagpole" hydrogens on $C_1$ and $C_4$ repel each other. Cyclohexane exists mainly in the chair form.