Structure Determination: Mass Spectrometry and Infrared Spectroscopy

Overview of Structure Determination

• Structure determination is primarily achieved through two analytical techniques: Mass Spectrometry ($MS$) and Infrared ($IR$) Spectroscopy.
• Mass Spectrometry ($MS$) is used to determine molecular weight and molecular formula by measuring the mass of a molecule.
• Infrared ($IR$) Spectroscopy is used to identify specific functional groups within a molecule.
• Organic molecules absorb energy from electromagnetic radiation at specific frequencies, which allows for identification.

Mass Spectrometry ($MS$) of Small Molecules

• Fundamental Principle: Mass spectrometry measures the mass of a molecule by converting it into ions.
• Process of Ionization:
  • A small amount of sample is vaporized.
  • Vaporized molecules undergo ionization, often via radio frequency ($rf$) ionization, to form cation radicals.
  • These cation radicals are represented as $M^{+\cdot}$.
• Fragmentation:
  • The amount of energy transferred during ionization is often sufficient to cause cation radicals to fragment into smaller positive and neutral pieces.
  • Only the positive fragments are analyzed by the mass spectrometer.
• Magnetic-Sector Instruments:
  • Fragments pass through a strong magnetic field inside a curved pipe.
  • The magnetic field segregates ions according to their mass-to-charge ratio ($m/z$).
  • Because the charge ($z$) is typically $+1$, the $m/z$ value effectively represents the mass of the ion.
• Detection and Analysis:
  • Sorted positive fragments hit a detector and are recorded as peaks on a spectrum.
  • Modern instruments can analyze masses up to $2500\,amu$ (atomic mass units).

Understanding and Interpreting the Mass Spectrum

• The Mass Spectrum Plot:
  • X-axis: Mass-to-charge ratio ($m/z$).
  • Y-axis: Intensity of the signal (relative abundance), which corresponds to the number of ions detected.
• Key Peaks:
  • Base Peak: The tallest peak in the spectrum, assigned an intensity of $100\%$.
  • Molecular Ion ($M^+$) or Parent Peak: The peak that corresponds to the unfragmented radical cation. Its $m/z$ value provides the molecular weight of the compound.
• Fingerprint Pattern: The way a molecular ion breaks down produces characteristic fragment patterns that assist in structural identification.
• Soft Ionization Methods: Used for compounds that do not show a molecular ion peak due to excessive fragmentation under electron bombardment. These methods minimize fragmentation to ensure the molecular weight can be determined.

Fragmentations in Specific Compounds

• Hexane ($C_6H_{14}$, MW = $86$):
  • Parent ion ($M^+$) at $m/z = 86$.
  • Significant fragment peaks at $m/z = 71$, $57$, $43$, and $29$.
  • The base peak occurs at $m/z = 57$.
• 2,2-Dimethylpropane ($C_5H_{12}$, MW = $72$):
  • Commonly exhibits no molecular ion peak when electron-impact ionization is used.
  • A major peak is observed at $m/z = 57$, representing the loss of a methyl group ($CH_3$), resulting in a tertiary butyl cation ($(CH_3)_3C^+$).

Worked Example: Distinguishing Isomers by MS

• Scenario: Distinguishing between methylcyclohexane and ethylcyclopentane (both $C_7H_{14}$, MW = $98$).
• Observations:
  • Both show $M^+ = 98$.
  • Sample A: Base peak is at $m/z = 69$. This represents the loss of an ethyl group ($CH_2CH_3$), which has a mass of $29\,amu$ ($98 - 29 = 69$). Sample A is ethylcyclopentane.
  • Sample B: Base peak is at $m/z = 83$. This represents the loss of a methyl group ($CH_3$), which has a mass of $15\,amu$ ($98 - 15 = 83$). Sample B is methylcyclohexane.

Mass Spectrometry of Common Functional Groups

• Alcohols:
  • Fragment via two primary pathways:
  1. Alpha ($\alpha$) Cleavage: The $C-C$ bond nearest the hydroxyl group breaks, yielding alkyl radicals and a resonance-stabilized oxygen-containing cation.
  2. Dehydration: An $E2$-type elimination of water ($H_2O$), resulting in a loss of $18\,amu$.
  • Example: 2-Pentanol ($C_5H_{12}O$, MW = $88.15$) shows fragments like $m/z = 73$ (loss of methyl) and $m/z = 70$ (dehydration).
• Amines:
  • Nitrogen Rule: A compound with an odd number of nitrogen atoms has an odd-numbered molecular weight.
  • Like alcohols, amines undergo $\alpha$-cleavage to produce alkyl radicals and resonance-stabilized nitrogen-containing cations.
  • Example: Triethylamine (MW = $101$) shows a major fragment at $m/z = 86$.
• Halides:
  • Elements with common isotopes produce distinctive mass spectra patterns.
  • Chlorine: Exists as $^{35}Cl$ and $^{37}Cl$ in a roughly $3:1$ ratio. This results in an $M$ peak and an $M+2$ peak (2 units higher) in a $3:1$ height ratio.
  • Bromine: Exists as $^{79}Br$ and $^{81}Br$ in a roughly $1:1$ ratio. This results in an $M$ peak and an $M+2$ peak of nearly equal intensity.
• Carbonyl Compounds:
  • Alpha ($\alpha$) Cleavage: Generates alkyl radicals and resonance-stabilized oxygen-containing cations.
  • McLafferty Rearrangement: Occurs in aliphatic aldehydes and ketones with hydrogens on the gamma ($\gamma$) carbon.
  • Example: Butyrophenone ($M^+ = 148$):
  • $\alpha$-cleavage of the propyl substituent: Loss of $C_3H_7$ ($43\,amu$) to give $m/z = 105$.
  • McLafferty rearrangement: Loss of ethylene ($C_2H_4$, $28\,amu$) to give $m/z = 120$.

Physics of Spectroscopy and the Electromagnetic Spectrum

• Nature of Radiation:
  • Electromagnetic radiation exhibits dual behavior as both a photon (particle) and an energy wave.
  • Waves are characterized by wavelength ($\lambda$), frequency ($\nu$), and amplitude.
  • Wavelength ($\lambda$): Distance between successive wave maxima.
  • Amplitude: Height of the wave from the center.
• Mathematical Relationships:
  • $\text{Wavelength} \times \text{Frequency} = \text{Speed of Light}$
  • $\lambda(m) \times \nu(s^{-1}) = c(m/s)$
  • Speed of light ($c$) is approximately $3.00 \times 10^8\,m/s$.
  • Energy ($E$) of a photon: $E = h\nu = \frac{hc}{\lambda}$
  • Molar energy calculation (using Avogadro\'s number $N_A$):
  • $E = \frac{1.20 \times 10^4\,kJ/mol}{\lambda(\mu m)}$
  • Or, relating $\lambda$ in meters: $E = \frac{1.20 \times 10^{-4}\,kJ/mol}{\lambda(m)}$
• Energy Comparisons:
  • Higher frequency radiation (e.g., visible light at $5 \times 10^{14}\,Hz$) is higher in energy than lower frequency radiation (e.g., FM radio at $1.015 \times 10^8\,Hz$).
  • Gamma rays ($\gamma$) are at the high-frequency/high-energy end; radio waves are at the low-frequency/low-energy end.

Infrared Spectroscopy ($IR$) Principles

• Mechanism of Absorption:
  • The $IR$ region is lower energy than visible light.
  • Absorption of $IR$ radiation causes covalent bonds to stretch and bend more vigorously.
  • A molecule absorbs energy only if the radiation frequency matches the vibration frequency of the bond.
• Units and Measurement:
  • Wavenumber (\nu^{~}): Defined as the reciprocal of wavelength.
  • $\nu^{~}(cm^{-1}) = \frac{1}{\lambda(cm)}$
  • The standard $IR$ spectrum ranges from $4000\,cm^{-1}$ to $400\,cm^{-1}$.
• The IR Spectrum Appearance:
  • Transmittance: A value of $100\%$ means all energy passes through.
  • Absorption: Downward spikes (peaks) represent energy absorption at specific wavenumbers.
• Interpreting Regions:
  • 4000 to 2500 $cm^{-1}$: Single-bond stretching motions (especially bonds to Hydrogen).
  • 2500 to 2000 $cm^{-1}$: Triple-bond stretching motions.
  • 2000 to 1500 $cm^{-1}$: Double-bond stretching motions.
  • 1500 to 400 $cm^{-1}$: The Fingerprint Region. Complex patterns unique to specific molecules; difficult to interpret fully but useful for identification via comparison.

Characteristic Infrared Absorptions

Detailed IR Behavior of Functional Groups

• Alkanes: Only $C-H$ and $C-C$ bonds. Simple spectrum.
• Alkenes: Vinylic $=C-H$ above $3000\,cm^{-1}$. Out-of-plane bending occurs between $700-1000\,cm^{-1}$.
• Alkynes: Terminal alkynes show a characteristically sharp $\equiv C-H$ stretch at $3300\,cm^{-1}$.
• Alcohols: $O-H$ stretch is typically very broad due to hydrogen bonding.
• Amines: $N-H$ stretch is sharper and less intense than alcohol $O-H$.
• Carbonyls ($C=O$):
  • Position depends on the specific environment.
  • Aldehydes: $1730\,cm^{-1}$ in saturated versions. Drops to $1705\,cm^{-1}$ if conjugated with a double bond or aromatic ring due to resonance delocalization.
  • Ketones: Saturated open-chain ketones are at $1715\,cm^{-1}$.
  • Ring Strain: Decreasing ring size increases the $C=O$ frequency ($5$-membered at $1750\,cm^{-1}$, $4$-membered at $1780\,cm^{-1}$).
  • Esters: Saturated at $1735\,cm^{-1}$; two strong $C-O$ bands between $1300-1000\,cm^{-1}$. Conjugation lowers the $C=O$ stretch to $1715\,cm^{-1}$.

IR Worked Examples

• Isomer Discrimination (Ethanol vs. Dimethyl Ether):
  • Ethanol ($CH_3CH_2OH$) has a strong $O-H$ bond at $3400-3640\,cm^{-1}$.
  • Dimethyl ether ($CH_3OCH_3$) lacks this band.
• Isomer Discrimination (Acetone vs. 2-propen-1-ol):
  • Acetone ($CH_3COCH_3$): Strong $C=O$ at $1715\,cm^{-1}$.
  • 2-propen-1-ol ($H_2C=CHCH_2OH$): $O-H$ at $3500\,cm^{-1}$ and $C=C$ at $1660\,cm^{-1}$.
• Unknown Compound ($C_8H_8O$):
  • Spectrum details: Intense absorption at $1725\,cm^{-1}$ (carbonyl), weak aromatic peaks $1800-2000\,cm^{-1}$, and aromatic $C-H$ at $3030\,cm^{-1}$.
  • Conclusion: The compound is phenylacetaldehyde.