Hydrogen Deficiency Index (HDI) and Degrees of Unsaturation

Definition and Calculation

The Hydrogen Deficiency Index (HDI), also known as the degree of unsaturation, is a tool used to determine the number of rings and/or pi bonds present in an organic molecule based on its molecular formula.

• HDI Formula: For a compound with formula CnHm:

• Each ring or pi bond increases the HDI by 1.

• Halogens (X): Count as hydrogens (add to m).

• Nitrogen (N): Subtract one hydrogen for each nitrogen.

• Oxygen (O): Ignore in HDI calculation.

Example: C4H6 has HDI = (2×4 + 2 – 6)/2 = 2. This could be two double bonds, a triple bond, or a ring and a double bond.

Nuclear Magnetic Resonance (NMR) Spectroscopy

1H NMR: Chemical Shift, Splitting, and Signal Counting

1H NMR is a powerful technique for determining the structure of organic molecules by analyzing the environment of hydrogen atoms.

• Chemical Shift (δ): Indicates the electronic environment of a proton. Downfield (higher δ) = deshielded (near electronegative atoms or pi systems).

• Splitting Pattern (Multiplicity): Determined by the number of neighboring (vicinal) protons (n). Follows the n+1 rule:

• Integration: Area under each signal corresponds to the number of protons represented.

• Number of Signals: Each set of equivalent protons gives one signal. Non-equivalent protons give separate signals.

• Carbon NMR: Same principle applies; equivalent carbons give one signal.

Example: In ethyl acetate, the methyl protons adjacent to the carbonyl appear as a singlet, while the methyl and methylene protons on the ethoxy group show triplet and quartet patterns, respectively.

Structure Elucidation Using 1H NMR

• Given a molecular formula and a 1H NMR spectrum (chemical shifts, multiplicity, integration), deduce the structure by:

  • Calculating HDI to narrow down possible structures.

  • Assigning signals to specific protons based on chemical shift and splitting.

  • Matching integration values to the number of protons.

Example: A compound with C3H8O and a triplet (3H), quartet (2H), and singlet (1H) suggests isopropanol.

DEPT and 13C NMR: Identifying Carbon Types

DEPT (Distortionless Enhancement by Polarization Transfer) is a 13C NMR technique that distinguishes between CH3, CH2, and CH carbons.

• DEPT-90: Shows only CH carbons.

• DEPT-135: CH3 and CH appear positive; CH2 appear negative.

• Quaternary carbons (C with no H) do not appear in DEPT spectra.

Application: Combine molecular formula, 13C NMR, and DEPT data to deduce the structure of small molecules (less than 5 carbons).

Conjugated Systems: Nomenclature and Preparation

Naming Conjugated Systems

Conjugated systems contain alternating single and multiple bonds. When naming, consider the presence of alkyl, hydroxyl (OH), or halide substituents.

• Number the chain to give the lowest possible numbers to the double bonds and substituents.

• Indicate the position of each double bond and substituent.

• Use prefixes such as "dien-", "trien-" for multiple double bonds.

Example: 2,4-hexadiene, 3-chloro-1,3-butadiene.

Preparation of Dienes

• Elimination reactions (E2 or E1) of dihalides or alcohols can generate conjugated dienes.

• Dehydrohalogenation of allylic halides is a common method.

Example: 1,3-butadiene can be prepared by dehydrohalogenation of 1,4-dibromobutane.

Reactions of Conjugated Dienes

Electrophilic Addition: 1,2- and 1,4-Adducts

Conjugated dienes react with electrophiles (e.g., HX) to give two types of products:

• 1,2-Adduct: Addition occurs at adjacent carbons (positions 1 and 2).

• 1,4-Adduct: Addition occurs at terminal carbons (positions 1 and 4).

• Both products can form; their ratio depends on temperature (kinetic vs. thermodynamic control).

Mechanism: Involves carbocation intermediates. Arrow-pushing shows protonation, resonance stabilization, and nucleophilic attack.

Example: 1,3-butadiene + HBr yields 3-bromo-1-butene (1,2-adduct) and 1-bromo-2-butene (1,4-adduct).

Pericyclic Reactions

Cycloaddition Reactions

• [4+2] Cycloaddition (Diels-Alder Reaction): A conjugated diene reacts with a dienophile to form a six-membered ring.

• [2+2] Cycloaddition: Two alkenes (or a diene with itself) combine to form a four-membered ring. Typically requires photochemical activation.

• Regioselectivity: Orientation of substituents in the product.

• Stereoselectivity: Preference for formation of specific stereoisomers.

• Stereospecificity: Stereochemistry of reactants determines stereochemistry of products.

Example: Diels-Alder reaction between 1,3-butadiene and ethene forms cyclohexene.

Electrocyclic Reactions

Electrocyclic reactions involve the concerted making and breaking of sigma and pi bonds in a conjugated system, resulting in ring closure or opening.

• 4 π Electron System: (e.g., butadiene) Under thermal conditions, proceeds via conrotatory motion; under photochemical conditions, disrotatory.

• 6 π Electron System: (e.g., hexatriene) Under thermal conditions, disrotatory; under photochemical, conrotatory.

• Woodward-Hoffmann Rules: Predict the stereochemical outcome based on conservation of orbital symmetry.

Example: Thermal ring closure of 1,3-butadiene to cyclobutene is conrotatory.

Additional info: The HOMO (highest occupied molecular orbital) changes symmetry upon excitation (light), affecting the allowed pathway.

Sigmatropic Rearrangements

Sigmatropic rearrangements are pericyclic reactions where a sigma bond migrates across a pi system.

• (3,3) Sigmatropic Rearrangement: Both ends of the migrating sigma bond are three atoms away from the pi system. Example: Cope rearrangement.

• (1,5) Sigmatropic Rearrangement: The sigma bond migrates from position 1 to 5. Example: Cope rearrangement.

• Claisen Rearrangement: A (3,3) rearrangement involving an allyl vinyl ether, resulting in a carbonyl compound.

Example: The Claisen rearrangement of allyl phenyl ether yields o-allylphenol.

Summary Table: Types of Pericyclic Reactions