Comprehensive Organic Spectroscopy, Stereochemistry, and Alkyl Halide Reactivity

Infrared Spectroscopy (IR)

• Fundamental Principle: Molecular absorption of infrared radiation corresponds to quantized vibrational energy transitions of covalent bonds. Photon energy is governed by $E = h\nu = \frac{hc}{\lambda}$.

• Vibrational Frequency Determinants: Bond stretching frequency increases with bond strength (bond energy) and decreases with increasing reduced mass of the bonded atoms ($\bar{\nu} \propto \sqrt{\frac{k}{\mu}}$).

• IR Selection Rule: A molecular vibration is IR-active only if it produces a net change in dipole moment. Symmetrical nonpolar bonds (such as the $N \equiv N$ stretch in $N_2$) do not absorb IR radiation and are IR-inactive.

• Spectral Regions:

  • Functional Group Region ($1600 - 3500\,\text{cm}^{-1}$): Contains distinct, predictable stretching vibrations diagnostic of specific functional groups.

  • Fingerprint Region ($600 - 1400\,\text{cm}^{-1}$): Contains complex bending, rocking, and skeletal vibrational modes characteristic of the molecule as a whole.

• Key Functional Group IR Absorptions:

  • Hydroxyl ($O-H$): Alcohols display a strong, smooth, broad absorption at $3200 - 3600\,\text{cm}^{-1}$. Carboxylic acids exhibit an extremely broad absorption at $2500 - 3500\,\text{cm}^{-1}$ overlapping alkyl $C-H$ modes.

  • Amine/Amide ($N-H$): Medium intensity, sharp or spiked bands at $3200 - 3500\,\text{cm}^{-1}$.

  • Aliphatic and Unsaturated $C-H$ Stretches:

  • $sp^3$ $C-H$: $2800 - 3000\,\text{cm}^{-1}$ (just below $3000\,\text{cm}^{-1}$).

  • $sp^2$ $=C-H$: $3000 - 3100\,\text{cm}^{-1}$ (just above $3000\,\text{cm}^{-1}$).

  • $sp$ $\equiv C-H$: $\sim 3300\,\text{cm}^{-1}$ (sharp, strong).

  • Triple Bonds: Alkynes ($C \equiv C$) absorb weakly at $\sim 2150 - 2200\,\text{cm}^{-1}$; nitriles ($C \equiv N$) yield a prominent, sharp peak at $\sim 2250\,\text{cm}^{-1}$.

  • Carbonyls ($C=O$): Very strong band centered near $1710\,\text{cm}^{-1}$.

  • Ketones and carboxylic acids: $\sim 1710 - 1718\,\text{cm}^{-1}$.

  • Aldehydes: $\sim 1725\,\text{cm}^{-1}$, accompanied by characteristic $C-H$ doublet stretches at $2720\,\text{cm}^{-1}$ and $2820\,\text{cm}^{-1}$.

  • Esters: $\sim 1735\,\text{cm}^{-1}$.

  • Amides: Lowered to $1630 - 1660\,\text{cm}^{-1}$.

  • Conjugation effect: Conjugation with an alkene or aromatic ring decreases the $C=O$ stretching frequency below $1700\,\text{cm}^{-1}$.

  • Alkenes ($C=C$): Isolated alkenes absorb at $1640 - 1680\,\text{cm}^{-1}$; conjugated dienes absorb at $1620 - 1640\,\text{cm}^{-1}$; aromatic rings absorb near $1600\,\text{cm}^{-1}$.

Mass Spectrometry (MS)

• Operating Principle: Neutral molecules are ionized via electron impact (bombardment with high-energy electrons) to eject an electron, generating an unstable radical cation ($M^{+\bullet}$). Positively charged fragments are accelerated and deflected by a magnetic field based on mass-to-charge ratio ($m/z$).

• Key Spectral Peaks:

  • Molecular Ion Peak ($M^{+\bullet}$): Corresponds to the intact radical cation giving the molecular weight.

  • Base Peak: The most abundant ion detected, defined as $100\%$ relative abundance.

• Isotope Signatures:

  • Carbon-13 ($^{13}C$): Contributes an $M+1$ peak of approximately $1.1\%$ intensity per carbon atom.

  • Chlorine: Exhibits an $M+2$ peak approximately one-third the intensity of the $M^+$ peak ($^{35}Cl : {}^{37}Cl \approx 3:1$ ratio; $75.5\%$ to $24.5\%$).

  • Bromine: Exhibits an $M+2$ peak nearly equal in height to the $M^+$ peak ($^{79}Br : {}^{81}Br \approx 1:1$ ratio; $50.5\%$ to $49.5\%$).

  • Nitrogen Rule: Organic molecules containing an odd number of nitrogen atoms possess an odd nominal molecular mass ($M^+$); molecules with zero or an even number of nitrogens have an even molecular mass.

• Fragmentation Patterns:

  • Molecular ions fragment homolytically or heterolytically into a detectable cation and an undetected neutral radical ($[M]^{+\bullet} \rightarrow R^+ + R^{\prime \bullet}$).

  • Cleavages favor the generation of more stable carbocations (tertiary, allylic, benzylic, and resonance-stabilized oxonium or iminium ions).

  • Alcohols readily undergo dehydration ($M - 18$ via loss of $H_2O$) or $\alpha$-cleavage adjacent to the hydroxyl group.

Proton Nuclear Magnetic Resonance (¹H NMR)

• Physical Principle: Nuclei with odd mass numbers or odd atomic numbers possess nuclear spin. In an applied magnetic field ($B_0$), nuclear spins align either with the field ($\alpha$ spin, lower energy) or against the field ($\beta$ spin, higher energy). Radiofrequency (RF) irradiation induces spin flips; relaxation back to equilibrium generates NMR signals.

• Four Structural Features of ¹H NMR:

  • Number of Signals: Identifies the number of chemically non-equivalent sets of protons. Chemically equivalent protons (due to symmetry or rapid rotation) yield one signal.

  • Chemical Shift ($\delta$, ppm): Measures resonance frequency relative to tetramethylsilane ($\text{TMS} = 0\,\text{ppm}$).

  • Shielded (Upfield, Right): High surrounding electron density creates an induced magnetic field opposing $B_0$.

  • Deshielded (Downfield, Left): Proximity to electronegative groups ($O, N, X$) or magnetic anisotropy withdraws electron density, exposing the nucleus to a higher effective magnetic field.

  • Characteristic Ranges:

    • Alkyl $sp^3$ $C-H$: $\delta = 0.9 - 2.0\,\text{ppm}$ ($\text{R-CH}_3 \sim 0.9$, $\text{R}_2\text{CH}_2 \sim 1.3$, $\text{R}_3\text{CH} \sim 1.7$).

    • Benzylic, allylic, and $\alpha$-to-carbonyl ($Z-C-H$, $Z=C=C, C=O$): $\delta = 1.5 - 2.5\,\text{ppm}$.

    • Terminal alkyne ($\equiv C-H$): $\delta \sim 2.5\,\text{ppm}$ (shielded along the cylinder axis of the $\pi$ system).

    • Protons on carbon adjacent to heteroatoms ($Z-C-H$, $Z=O, N, X$): $\delta = 2.5 - 4.5\,\text{ppm}$.

    • Vinylic ($=C-H$): $\delta = 4.5 - 6.0\,\text{ppm}$.

    • Aromatic ring protons: $\delta = 6.5 - 8.0\,\text{ppm}$ (strongly deshielded by the induced ring current of delocalized $\pi$ electrons).

    • Aldehyde ($R-CHO$): $\delta = 9.0 - 10.0\,\text{ppm}$.

    • Carboxylic acid ($R-COOH$): $\delta = 10.0 - 12.0\,\text{ppm}$.

  • Integration: The area beneath an NMR signal is directly proportional to the relative number of protons producing that signal.

  • Spin-Spin Splitting (Multiplicity): Occurs through magnetic coupling across up to three $\sigma$ bonds. Governed by the $N + 1$ rule, where $N$ chemically equivalent neighboring protons split a resonance into $N + 1$ peaks with Pascal's triangle intensity ratios.

• Coupling Constants ($J$): Distance in Hz between multiplet peaks, independent of $B_0$. Alkene stereoisomers display characteristic coupling constants: $J_{\text{trans}} = 11 - 18\,\text{Hz}$, $J_{\text{cis}} = 5 - 10\,\text{Hz}$, and $J_{\text{geminal}} = 0 - 3\,\text{Hz}$.

• Stereochemical Nonequivalence:

  • Enantiotopic Protons: Substitution of either proton generates a pair of enantiomers; they are chemically equivalent and exhibit identical chemical shifts in achiral environments.

  • Diastereotopic Protons: Substitution generates diastereomers (common in molecules containing an existing stereogenic center or on rigid rings/alkenes); they are chemically non-equivalent, display distinct chemical shifts, and split each other.

• Proton Exchange: Labile hydroxyl ($O-H$) and amine ($N-H$) protons undergo rapid intermolecular exchange, collapsing spin-spin splitting into broad singlets; treating with $D_2O$ eliminates these peaks via deuterium exchange.

Carbon-13 Nuclear Magnetic Resonance (¹³C NMR)

• General Principles: Only the $^{13}C$ isotope ($1.1\%$ natural abundance) is NMR active ($^{12}C$ has spin $I=0$). Due to low abundance, homonuclear $^{13}C-^{13}C$ coupling is negligible. Broadband proton spin decoupling removes $^{1}H-^{13}C$ splitting, collapsing all resonances into sharp singlets.

• Quantitative Limitation: Peak integration does not reliably correlate to carbon counts due to unequal nuclear Overhauser effect (NOE) enhancements and long relaxation times.

• Chemical Shift Scale ($0 - 220\,\text{ppm}$):

  • Alkyl $sp^3$ carbons: $\delta = 5 - 45\,\text{ppm}$.

  • Carbons bonded to heteroatoms ($C-O, C-N, C-X$): $\delta = 30 - 80\,\text{ppm}$.

  • Alkyne $sp$ carbons: $\delta = 65 - 100\,\text{ppm}$.

  • Alkene $sp^2$ carbons: $\delta = 100 - 140\,\text{ppm}$.

  • Aromatic carbons: $\delta = 120 - 150\,\text{ppm}$.

  • Carbonyl carbons ($C=O$): $\delta = 160 - 210\,\text{ppm}$.

• DEPT Experiments (Distortionless Enhancement by Polarization Transfer):

  • DEPT-90: Displays exclusively methine ($CH$) carbons as positive peaks.

  • DEPT-135: Displays methyl ($CH_3$) and methine ($CH$) carbons pointing up (positive), methylene ($CH_2$) carbons pointing down (inverted/negative), and excludes quaternary carbons.

Stereochemistry: Principles and Chirality

• Isomer Classification: Constitutional isomers have different atomic bonding connectivity, while stereoisomers share the same connectivity but differ strictly in three-dimensional orientation.

• Chirality and Symmetry:

  • A chiral molecule lacks an internal mirror plane ($\sigma$) and cannot be superimposed onto its mirror image.

  • Molecules possessing an internal mirror plane ($\sigma$) of symmetry are achiral and optically inactive.

• Stereogenic Centers: Typically a tetrahedral $sp^3$ carbon bonded to four distinct groups (chiral carbon).

  • A molecule with exactly one chiral center is always chiral.

  • Maximum possible stereoisomers is governed by the $2^n$ rule, where $n$ is the number of tetrahedral stereogenic centers.

• Meso Compounds: Achiral molecules that possess two or more stereogenic centers alongside an internal plane of symmetry, reducing the total stereoisomer count to fewer than $2^n$.

• Chirality Without Asymmetric Carbon Atoms:

  • Atropisomerism: Chiral restricted-rotation biaryl systems (e.g., BINAP).

  • Chiral Allenes: Allenes ($C=C=C$) with non-identical substituents on each terminal $sp^2$ carbon, creating perpendicular dissymmetric systems.

• Cahn-Ingold-Prelog (CIP) Rules for $R/S$ Assignment:

  • Assign priority ($1 > 2 > 3 > 4$) based on decreasing atomic number of directly attached atoms ($I > Br > Cl > S > P > F > O > N > C > H$).

  • Resolve ties by comparing atoms attached along the substituent chain at the first point of difference.

  • Multiple bonds are treated by adding duplicated phantom atoms (e.g., $-CH=O$ counts as carbon bonded to two oxygens).

  • Orient the lowest-priority substituent ($4$) away from the observer: clockwise priority sequence ($1 \rightarrow 2 \rightarrow 3$) corresponds to $R$, while counterclockwise corresponds to $S$.

Optical Activity and Stereoisomeric Relationships

• Enantiomers vs. Diastereomers:

  • Enantiomers: Non-superimposable mirror images with opposite stereochemical configurations at all chiral centers. They have identical physical properties (boiling point, melting point, density) except for the sign of optical rotation and interactions with other chiral entities.

  • Diastereomers: Non-mirror-image stereoisomers with identical configuration at one or more chiral centers and opposite configuration at others (e.g., cis/trans isomers, carbohydrate epimers). They exhibit different physical and chemical properties.

• Polarimetry and Specific Rotation: Optically active substances rotate plane-polarized light. Dextrorotatory ($d$ or $(+)$) corresponds to clockwise rotation; levorotatory ($l$ or $(-)$) corresponds to counterclockwise rotation.

  • Specific rotation is calculated as:   $[\alpha] = \frac{\alpha}{c \cdot l}$   where $\alpha$ is observed rotation ($^\circ$), $c$ is concentration in $\text{g/mL}$, and $l$ is path length in $\text{dm}$ ($1\,\text{dm} = 10\,\text{cm}$).

• Mixtures of Enantiomers:

  • Racemic Mixture: A $1:1$ ($50:50$) mixture of enantiomers; optically inactive ($[\alpha] = 0^\circ$).

  • Optical Purity (o.p.) and Enantiomeric Excess (e.e.):   $\text{o.p.} = \frac{\alpha_{\text{observed}}}{\alpha_{\text{pure}}} \times 100$   $\%\,\text{ee} = \%\,\text{Major enantiomer} - \%\,\text{Minor enantiomer}$

• Biological Impact of Chirality:

  • Thalidomide: $(R)$-enantiomer is an effective sedative/anti-nausea agent; $(S)$-enantiomer is a teratogen causing severe birth defects.

  • Naproxen: $(S)$-naproxen is an anti-inflammatory drug; $(R)$-naproxen acts as a liver toxin.

  • Pheromones: $(R)$-japonilure is the female sex pheromone of the Japanese beetle (Popillia japonica); $(S)$-japonilure is the pheromone of the scarab beetle (Anomala osakana).

• Resolution of Enantiomers: Racemic mixtures are separated by reacting them with an enantiomerically pure resolving agent to yield diastereomers (which possess distinct physical properties and can be separated by crystallization or chromatography) followed by cleavage.

• Fischer Projections: 2D cross representations where vertical lines project away from the viewer (dashes) and horizontal lines project toward the viewer (wedges). Rotating a projection by $180^\circ$ maintains the molecular identity; rotating by $90^\circ$ inverts the configuration to the enantiomer.

Alkyl Halides: Properties and Synthesis

• Structure and Nomenclature: Alkyl halides are classified by substitution at the carbon bearing the halogen ($X$): methyl, primary ($1^\circ$), secondary ($2^\circ$), or tertiary ($3^\circ$). Geminal dihalides have two halogens on the same carbon; vicinal dihalides bear halogens on adjacent carbons. Halogen substituents are ranked lowest in functional group IUPAC naming priority.

• Carbon-Halogen Bond Metrics:

  • Bond Length: $C-F (1.38\,\text{\AA}) < C-Cl (1.78\,\text{\AA}) < C-Br (1.94\,\text{\AA}) < C-I (2.14\,\text{\AA})$.

  • Dipole Moment: $C-I (1.29\,\text{D}) < C-Br (1.48\,\text{D}) < C-F (1.51\,\text{D}) < C-Cl (1.56\,\text{D})$.

• Physical Property Trends:

  • Boiling points increase with increasing halogen surface area and polarizability ($CH_3Cl \; [-24\,^\circ\text{C}] < CH_2Cl_2 \; [40\,^\circ\text{C}] < CHCl_3 \; [61\,^\circ\text{C}] < CCl_4 \; [77\,^\circ\text{C}]$).

  • Density increases with halogen mass and degree of halogenation ($CH_3CH_2F \; [0.72\,\text{g/mL}] < CH_3CH_2Cl \; [0.90\,\text{g/mL}] < CH_3CH_2Br \; [1.46\,\text{g/mL}] < CH_3CH_2I \; [1.94\,\text{g/mL}]$). Alkyl bromides and iodides are denser than water.

• Free-Radical Halogenation:

  • Mechanism: Photochemical initiation ($X_2 \xrightarrow{h\nu} 2X^\bullet$), propagation (hydrogen abstraction by $X^\bullet$ to form an alkyl radical, followed by halogen atom abstraction from $X_2$), and termination (radical recombination).

• Regioselectivity: Radical stability follows $3^\circ > 2^\circ > 1^\circ > \text{methyl}$. Bromination is endothermic in the hydrogen-abstraction step, highly selective for the most substituted radical ($3^\circ$ carbon); chlorination is exothermic, highly reactive, and unselective.

• Allylic Halogenation: Due to resonance stabilization of allylic radicals, allylic $C-H$ bonds possess significantly reduced bond dissociation energies, undergoing selective radical functionalization.

Nucleophilic Substitution: S_N2 vs S_N1 Mechanisms

• $S_N2$ Mechanism (Bimolecular Nucleophilic Substitution):

  • Kinetics & Concerted Pathway: One-step concerted mechanism with simultaneous bond-breaking and bond-forming via a trigonal bipyramidal transition state. Rate law is second-order: $\text{Rate} = k[\text{electrophile}][\text{nucleophile}]$.

  • Stereochemical Inversion: Backside attack of the nucleophile into the $\sigma^*$ orbital of the $C-LG$ bond causes complete Walden inversion of configuration at the reacting center.

  • Substrate Steric Constraints: Governed by steric congestion: $\text{methyl} > 1^\circ > 2^\circ \gg 3^\circ$ (tertiary halides cannot react via $S_N2$; neopentyl halides react extremely slowly due to severe steric clash).

  • Nucleophile Dependency: Requires strong, reactive nucleophiles ($HO^-, RO^-, RS^-, N_3^-, CN^-, R-C \equiv C^-$).

  • Nucleophilicity decreases across a period ($CH_3^- > NH_2^- > OH^- > F^-$).

  • Nucleophilicity increases down a column in protic solvents due to polarizability ($I^- > Br^- > Cl^- > F^-$).

  • Sterically hindered nucleophiles struggle with substitution.

  • Solvent Effects: Polar aprotic solvents (DMF, DMSO, acetonitrile, acetone) maximize $S_N2$ reaction rates by solvating counter-cations while leaving nucleophilic anions naked and reactive. Polar protic solvents drastically decrease nucleophilicity via hydrogen-bonding networks.

• $S_N1$ Mechanism (Unimolecular Nucleophilic Substitution):

  • Kinetics & Stepwise Pathway: Two-step mechanism initiated by rate-determining heterolytic dissociation of the leaving group to form a planar carbocation intermediate, followed by nucleophilic capture. Rate law is first-order: $\text{Rate} = k[\text{electrophile}]$.

  • Stereochemistry: Stereoablative process; because the intermediate $sp^2$ carbocation is planar and achiral, nucleophilic attack occurs with equal probability from either face, causing racemization.

  • Substrate Electronic Requirements: Governed by carbocation stability: $3^\circ > 2^\circ \gg 1^\circ > \text{methyl}$ (stabilized by hyperconjugation and inductive effects; allylic and benzylic substrates react rapidly due to resonance).

  • Nucleophile Dependency: Accommodates weak, neutral nucleophiles ($H_2O, ROH$).

  • Solvent Effects: Polar protic solvents ($H_2O, ROH$, carboxylic acids) accelerate $S_N1$ ionization by stabilizing both the carbocation and departing halide anion via dipole and hydrogen-bonding solvation spheres.

  • Carbocation Rearrangements: Intermediate carbocations are subject to spontaneous 1,2-hydride or 1,2-alkyl shifts whenever migration generates a more stable secondary-to-tertiary or resonance-delocalized carbocation.

• Leaving Group Trends: Good leaving groups are weak conjugate bases of strong acids ($I^- > Br^- > Cl^- \gg F^-$; sulfonate esters such as tosylate, mesylate, and triflate).