○ Number of structural isomers of alkanes based on carbon count: As the carbon content increases by 1, the number of structural isomers increases by approximately 2.36 times.

Chemical Formula	# of Structural Isomers
C₃H₈	1
C₄H₁₀	2
C₅H₁₂	3
C₆H₁₄	5
C₇H₁₆	9
C₈H₁₈	18
C₉H₂₀	35
C₁₀H₂₂	75
C₁₁H₂₄	159
C₁₂H₂₆	355
C₁₃H₂₈	802
C₁₄H₃₀	1,858
C₁₅H₃₂	4,347
C₁₆H₃₄	10,359
C₁₇H₃₆	24,894
C₁₈H₃₈	60,523
C₁₉H₄₀	148,284
C₂₀H₄₂	366,319
C₃₀H₆₂	4,111,846,763
C₄₀H₈₂	62,481,801,147,341

Table 1. Number of structural isomers of alkanes based on carbon count

○ Tip: Separate cases based on the carbon count of the main chain

○ Butane: 2 isomers. n -butane, isobutane. Nonisomorphic trees with 4 vertices

Figure 1. Structural isomers of butane

○ Pentane: 3 isomers. n -pentane, isopentane, neopentane. Nonisomorphic trees with 5 vertices

Figure 2. Structural isomers of pentane

○ Hexane: 5 isomers. Nonisomorphic trees with 6 vertices

Figure 3. Structural isomers of hexane

○ Heptane: 9 isomers. Nonisomorphic trees with 7 vertices

Figure 4. Structural isomers of heptane

○ Octane: 18 isomers. Nonisomorphic trees with 8 vertices

Figure 5. Structural isomers of octane

○ A Python code that depicts all of the structural isomers of alkanes according to the number of carbon atoms

④ Deuterium (D) and hydrogen (H) are treated as different entities → Not structural isomers

⑶ Stereoisomers

① Definition: Isomers with the same atomic bonding order but different spatial arrangement

○ Such stereoisomers are known as stereoselective products

② Type 1: Enantiomers (Optical Isomers, Enantiomorphs): Stereoisomers that do not overlap with their mirror images

③ Type 2: Diastereomers: All stereoisomers except enantiomers

④ Type 2-1: Geometrical Isomers: Stereoisomers within diastereomers with different spatial arrangements

○ Types

○ cis-Isomers: When two substituents are on the same side (e.g., cis-1,3-dimethylcyclobutane)

○ trans-Isomers: When two substituents are on opposite sides (e.g., trans-1-bromo-3-ethylcyclopentane)

○ Type 1: Fixed positions due to double bonds

Figure 6. Fixed positions due to double bonds

○ Type 2: Fixed positions due to rotational hindrance

○ Rotation might not be possible even with single bonds

○ Geometrical isomers can arise when two substituents on a cycloalkane are attached to different carbons

Figure 7. Fixed positions due to rotational hindrance

○ Type 3: Extension of the octet rule enables easy formation of geometrical isomers

○ cis, trans definitions still apply in this case

○ Example: Pt(NH₃)₂Cl₂, Pt(NH₃)₃Cl₃, PCl₂Br₃

⑤ Type 2-2: Epimers, Anomers

○ Epimer

○ Isomers with multiple chiral centers, differing in configuration at only one center

○ Used in monosaccharides, disaccharides

○ Anomer

○ Isomers in which the absolute configuration of the acetal or hemiacetal carbon differs

○ Used in monosaccharides, disaccharides

○ Anomeric Effect: The phenomenon where substituents next to a heteroatom in cyclohexane prefer an axial orientation.

Figure 8. Anomeric effect

⑷ Optical Resolution

① Structural and diastereomeric isomers exhibit different physical and chemical properties, enabling separation

② Enantiomers have identical physical and chemical properties except for the direction of specific rotation of plane-polarized light

③ Optical resolution: Special methods required to separate enantiomers

2. E-Z Nomenclature

⑴ Priority Rules (CIP rule, Cahn-Ingold-Prelog priority rule)

① Rule 1: Higher priority for atoms bonded directly to carbons with larger atomic numbers

② Rule 2: If two atoms have the same atomic number, priority goes to the one with the larger atomic number substituent

○ In the absence of double bonds, if any one of the three 2-layer atoms has a substituent with a higher atomic number, it takes priority

③ Rule 3: If 2-layer atoms can’t be compared, continue comparing with 3-layer, 4-layer, … until a difference is found.

○ Transition to (n+1)-layer atoms is possible after comparing all n-layer atoms.

④ Rule 4: Unshared electron pairs are considered the lowest priority

⑤ Rule 5: For multiple bonds, imagine replacing each multiple bond with single bonds. Then, treat each atom in the original bond as if it has the other atom as a substituent.

Figure 9. Priority rules for multiple bonds

⑵ E-Z Nomenclature

① Introduction: The cis/trans nomenclature is applicable only when there are exactly two of each substituent on an alkene

② Z Isomer: Higher-priority substituent is on the same side as cis, derived from the German word ‘zusammen’ meaning ‘together’

③ E Isomer: Higher-priority substituent is on the opposite side as trans, derived from the German word ‘entgegen’ meaning ‘opposite’

④ Imine (E) and (Z) can be determined, and unshared electron pairs are considered as the lowest priority

⑶ Re, Si Nomenclature

① Determine the priority of three substituents bonded to sp² hybridized carbons

② Re-face: The face where the order of the substituents is clockwise.

③ Si-face: The face where the order of the substituents is counterclockwise.

Figure 10. Re, Si Nomenclature

3. Mirror-Image Isomers

⑴ RS Nomenclature: A naming convention to distinguish mirror-image isomers. (Note: A problem to be solved extensively in organic chemistry)

① RS nomenclature is an absolute configuration naming convention

○ Absolute configuration

○ Relative configuration: The experimental relationship that designates whether two configurations are identical even if the absolute configuration is not known

② Basic principles

○ Priority rules are the same as E-Z isomers

○ With atom 4 placed in the rear, if the sequence of atoms 1, 2, 3 is clockwise, it’s labeled R; if counterclockwise, it’s labeled S.

○ R isomer: Derived from ‘rectus,’ meaning clockwise

○ S isomer: Derived from ‘sinister,’ meaning counterclockwise

③ Author’s suggested principle: Determining RS should take no more than 0.5 seconds.

○ Formula 1: If “Vector 1 × Vector 4 = Vector 2,” then it’s S

Figure 11. RS determination using Formula 1

As the cross product points outward, it’s R

○ Formula 2: If “Vector 1 × Vector 2 = Vector 3,” then it’s S

○ Formula 3: If “Vector 3 × Vector 4 = Vector 1,” then it’s S: Often seen in cases where methyl is on 3 and hydrogen is on 4

○ Explanation of Formula 1: Absolute configuration is S if the cross product direction of vector 1 and vector 4, with the central carbon as the origin, is 2

○ Memorize it as special since it’s S.

○ The cross product doesn’t perfectly align with the vertices of a regular tetrahedron due to the orthogonal vector nature

○ Proof of the author’s suggested principle

⑵ Chiral Molecules

① Chiral: Molecules capable of having mirror-image isomers

○ Chiral comes from the word ‘hand’

○ Achiral: Antonym of chiral

Figure 12. Examples of chiral molecules

② Presence of internal mirror planes (mirror plane, plane of symmetry): If no internal mirror plane exists, the molecule is chiral, otherwise achiral

③ Uniqueness of the mirror plane: Regardless of how the mirror plane is chosen, a molecule that can be superimposed onto its mirror image is eventually determined

④ Examples: Chiral pharmaceuticals are about 60% available in the market

○ (R)-Limonene is orange-scented ↔︎ (S)-Limonene is lemon-scented

○ (S)-Asp-(S)-PheOMe is very sweet, used in Coca-Cola ↔︎ (R)-Asp-(R)-PheOMe is used extensively

○ (S)-Thalidomide is used for morning sickness ↔︎ (R)-Thalidomide induces deformities

○ (S)-Ketamine is an anesthetic ↔︎ (R)-Ketamine is a hallucinogen

○ (S)-Penicillamine is used for rheumatoid arthritis ↔︎ (R)-Penicillamine induces mutations

⑶ Stereogenic Center: The atom that becomes a stereoisomer when its two substituents are interchanged

① Chiral Center: The atom that becomes a mirror-image isomer when its two substituents are interchanged

○ Principle: The central atom must have different substituents (e.g., C, N, O, P, S, Si)

○ Chiral centers are typically sp³ hybridized.

○ Unshared electron pairs are also considered as substituents

② Chiral centers can create chirality but not all compounds with chiral centers are chiral compounds

○ Example: Mesocompounds, amine inversion, etc.

③ Stereogenic center refers to both chiral centers and geometric centers

⑷ Criteria for Chirality Determination

① No stereogenic centers: Achiral (Exception: ⑹)

② One stereogenic center: Chiral

③ Two or more stereogenic centers: Chiral determination based on internal symmetry planes

⑸ Chirality of Heteroatoms

① Natural occurrence noise: 80 kJ/mol

② Nitrogen inversion in amines: 25 kJ/mol

○ In the case of secondary and tertiary amines, chiral analysis can include non-shared electron pairs, similar to a chiral center.

○ Nitrogen inversion occurs very easily at room temperature and does not exhibit chirality.

○ Chirality arises when there is an increase in energy difference due to torsional strain, angle strain, etc., in nitrogen inversion.

Figure 13. Nitrogen inversion

○ Counterexample: 1,2,2-trimethylaziridine (18.5 kcal/mol)

○ In this case, it exhibits optical activity.

○ Reason: Due to the ring strain of cyclopropane, the energy instability is significant.

○ Nitrogen inversion occurs in heterocyclic amine compounds with rings other than three-membered rings, such as four-membered and five-membered rings.

③ Sulfides, sulfoniums, phosphines, phosphine oxides

○ Consider electron transfer from P=O, S=O, to form P⁺-O^-, S⁺-O^-.

○ Chirality arises due to large energy barriers.

⑹ Chirality in compounds without a chiral center

① Allen

○ Example: H(CH₃)C=C=C(CH₃)H, 4-chloropenta-2,3-dien-2-ol

② Cycloalkenes

○ Planar chirality

○ Example: trans-cyclooctene

③ Helicenes

○ Example: phenanthro[3,4-c]phenanthrene

④ Atropisomers

○ Chirality arises due to steric repulsion.

○ Rotation can occur in high-temperature environments.

○ Example: BINAP

Figure 14. Examples of atropisomers

⑤ Spiro compounds

○ Example: Fecht acid

⑺ (+) / (-) Nomenclature

① Definition: If a (+) polarization is observed in a polarization experiment, the isomer is a (+) isomer. If a (-) polarization is observed, the isomer is a (-) isomer.

② Explanation: (+) polarization indicates dextrorotary or right-handed rotation, while (-) polarization indicates laevorotary or left-handed rotation.

③ Note: The (+) isomer is also referred to as the d-isomer, and the (-) isomer as the l-isomer, but the d/l nomenclature is no longer in use (ref).

④ Important: The (+) / (-) nomenclature provides no information about the RS nomenclature.

○ Example: (S)-(+)-lactic acid, (S)-(-)-lactate

⑻ DL Nomenclature: Commonly Used in Biology

① DL Nomenclature for Carbohydrates

○ In glucose, the D and L forms are determined based on the stereochemistry of the carbon furthest from the aldehyde group (CHO) in the Fischer projection.

○ In the standard Fischer projection, if the -OH group attached to the carbon furthest from CHO is on the right side (R-form), it is classified as the D-form; if not, it is classified as the L-form.

○ This nomenclature represents the absolute configuration of only one carbon and has no correlation with positive or negative optical rotation.

○ In living organisms, carbohydrates like monosaccharides exist in the D-form isomer.

② DL Nomenclature for Amino Acids

Figure 15. Nomenclature of amino acids and LD

○ The DL nomenclature for amino acids is determined by the spatial arrangement of the substituents around the central carbon, including the hydrogen atom, carboxyl group, amino group, and functional group, as illustrated above.

○ In living organisms, amino acids exist in the L-form isomer.

4. Optical activity (chirality)

⑴ Enantiomers related by a mirror plane have identical physical and chemical properties (melting point, boiling point, solubility, etc.).

⑵ Plane-polarized light

① Light vibrates in all directions perpendicular to its propagation direction, but only in one direction in plane-polarized light.

② Passing through a polarizing prism (Nicol prism) aligns the vibrations in the same direction.

⑶ Polarimeter: Device that allows plane-polarized light to pass through a sample containing organic compounds.

Figure 16. Polarimeter

⑷ Optical activity

① Achiral molecules do not rotate plane-polarized light.

② Chiral molecules rotate plane-polarized light, resulting in optical activity.

③ Enantiomers rotate plane-polarized light in opposite directions.

⑸ Specific rotation: The inherent property of each chiral molecule

① Usually measured at 25°C.

② α: Specific rotation measured using a polarimeter, αD indicates the use of the D line of Na lamp.

③ λ: Wavelength of light, typically using the D line of sodium vapor lamp (589.3 nm).

④ l: Length of the sample tube (unit: dm = 10 cm).

⑤ c: Concentration of chiral sample (g/ml).

⑥ (+) / (-) Isomers

○ If the compound is dextrorotatory, it is denoted as (+); if it is levorotatory, it is denoted as (-).

○ (+) Isomer: An isomer that rotates the plane of polarized light to the right.

○ (-) Isomer: An isomer that rotates the plane of polarized light to the left.

5. Mesocompounds and racemic mixtures

⑴ Maximum number of stereoisomers for a chiral center with n substituents is N.

⑵ Mesocompound

① Definition: A compound with more than two substituents having a molecular internal symmetry plane, making it identical to its mirror image.

② Depending on the context, mesocompound can refer to a compound with more than two chiral centers.

③ Tip: (R, S) is possible for mesocompounds, but (R, R) and (S, S) are not.

Figure 17. Example of mesocompound determination

○ (A) ≠ (B) ≠ (C) ≠ (D), but (a) = (d) ≠ (b) ≠ (c) holds true.

○ Relationship of (A), (B), (C), (D): Optical enantiomers.

○ Relationship of (b), (c): Optical enantiomers.

○ Relationship of (a), (d): Mesocompound.

③ Tip: If a compound has an odd number of chiral centers greater than 2, it’s not a mesocompound because it must have chirality.

○ Note that although the third carbon in 2,3,4-tribromo-pentane is a chiral center, it’s not a chiral center due to mesocompound rules.

⑶ Racemic mixture: The origin of this word is the Latin “racemus,” meaning “cluster of grapes.”

① Definition: A mixture of enantiomers in a 1:1 ratio.

② Optical activity: Equal amounts of enantiomers cancel out, resulting in an optical purity of 0.

③ Difference from mesocompounds: Mesocompounds consist of a single substance, while racemic mixtures are mixtures.

④ Natural and laboratory settings

○ In nature, enzymes yield only one enantiomer of a chiral molecule.

○ Example: Lactic dehydrogenase converts (+) lactic acid exclusively to pyruvic acid.

○ Example: Fumarase allows water molecules to approach from only one side.

○ Administering mirror-image enantiomers of natural chiral molecules to organisms can be risky.

○ Certain reactions in the laboratory produce racemic mixtures, reducing purity and increasing harm potential.

⑤ Racemization: Reaction producing racemic mixture

○ Reaction where a non-chiral molecule (reactant) reacts to form a chiral molecule (product)

○ Reaction producing chiral molecules through an achiral intermediate

○ Multistep reactions can lead to racemization if condition 2) is met, even if the reactant is chiral.

⑥ Enantiomer excess (ee)

○ Enantiomer excess ee(%) = Percentage of enantiomer A - Percentage of enantiomer B

○ Mixture optical rotation = Inherent optical rotation × Enantiomer excess (%)

○ If A is 60% and B is 40%, ee(%) = 60 - 40 = 20% ee, indicating that A exists 20% more than B.

⑦ Optical purity

○ Definition: Ratio of pure enantiomer’s optical rotation to mixture’s optical rotation

○ Optical purity = Inherent optical rotation × Optical isomer ee%

○ A racemic mixture of equal amounts of A and B has an optical purity of 0.

⑧ Separation of racemic mixtures

○ 1^st. Chiral-specific acid/base reactions, enzymatic reactions create chiral molecules as (R, R) or (R, S) forms.

○ 2^nd. Liquid chromatography (LC), recrystallization, fractional distillation for separation.

○ Examples

○ Treating acetic anhydride with (R)-alanine and (S)-alanine produces (R)-N-acetylanaline and (S)-N-acetylanaline, respectively.

○ Subsequent treatment with acylase results in hydrolysis of (S)-N-acetylanaline’s amide bond, while ( R )-N-acetylanaline remains, allowing separation based on functional group differences.

6. Coordination Isomers

⑴ Type 1. Geometric isomers: cis / trans isomers, fac / mer isomers, etc.

⑵ Type 1-1. cis / trans isomers: cis if two substituents are on the same side, trans if they are on opposite sides.

⑶ Type 1-2. fac / mer isomers

① fac isomers

○ When three substituents are mutually orthogonal.

○ “Fac” comes from “facial,” and it refers to a plane where three substituents are all positioned orthogonally to each other.

② mer isomers

○ When a pair of substituents is across from each other.

○ “Mer” comes from “meridional,” indicating that a pair of opposite substituents forms a line along the equator.

⑷ Type 2. Optical isomers (enantiomers)

⑸ Example 1. FeCl₃(H₂O)₃ (ferric chloride) exists as fac/mer isomers. Since there’s a molecular symmetry plane, there are no optical enantiomers.

Figure 18. Stereoisomers of FeCl₃(H₂O)₃

⑹ Example 2. Co(en)₂Cl₂⁺ has two cis-Co(en)₂Cl₂⁺ and one trans-Co(en)₂Cl₂⁺ enantiomers related by a mirror relationship.

Figure 19. Stereoisomers of Co(en)₂Cl₂⁺

⑺ Example 3. Co(en)₂BrCl⁺ has two cis-Co(en)₂BrCl⁺ and one trans-Co(en)₂BrCl⁺ enantiomers related by a mirror relationship.

① It becomes evident when turned slowly.

Figure 20. Stereoisomers of Co(en)₂BrCl⁺

⑻ Example 4. [Co(en)₃]³⁺ with symmetric ligands has two stereoisomers due to mirror relationships.

Figure 21. Stereoisomers of [Co(en)₃]³⁺

⑼ Example 5. [Co((R)-pn)₃]³⁺ has four stereoisomers: Λ-fac, Δ-fac, Λ-mer, Δ-mer.

Figure 22. Stereoisomers of [Co((R)-pn)₃]³⁺

⑽ Example 6. [Fe(gly)₃]^3- with three bidentate (N,O) chelating ligand glys yields four stereoisomers similar to Example 5.

7. Bürgi–Dunitz trajectory

⑴ Bürgi–Dunitz angle: The angle at which a nucleophile’s HOMO approaches the antibonding orbital (LUMO) of a carbonyl group.

Figure 23. Comparison of reduction reaction rate by NaBH₄

⑵ According to the Bürgi–Dunitz trajectory angle, BH₄^- attacks the carbonyl carbon’s π* at an angle of approximately 107 degrees.

⑶ Since the two phenyl groups are not on the same plane, BH₄^- experiences significant repulsion when approaching via this pathway.

Figure 24. Actual structure of benzophenon

Input: 2019.01.09 02:03

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Chapter 4. Stereochemistry

1. Isomers