IR Spectroscopy Cheatsheet

Cheatsheet Content

### Instrumentation Techniques #### FTIR (Fourier Transform Infrared Spectroscopy) - Uses a Michelson Interferometer instead of dispersive elements. - Light passes through the sample, collected as an interferogram (energy vs. time). - A Fourier Transform (FT) converts this raw data into an interpretable spectrum (Intensity vs. Wavenumber). #### ATR-IR (Attenuated Total Reflection) - Based on internal reflection. - IR beam passes through a crystal; reflection creates an evanescent wave extending into the sample. - Sample absorbs energy from the evanescent wave, attenuating the reflected beam, which is then measured. #### Transmission vs. Absorption - Historically, measuring transmission ($T = I/I_0$) was easier than absorption. - While absorbance ($A = -\log T$) is directly proportional to concentration (Beer-Lambert Law), transmission spectra remain standard in organic chemistry. ### The Physics of Vibration: Hooke's Law Chemical bonds behave like springs connecting two masses (atoms). The frequency of vibration is given by Hooke's Law: $$\nu = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}$$ Where: - $\nu$ = Frequency (wavenumber in cm$^{-1}$) - $c$ = Speed of light - $k$ = Force constant (bond stiffness). Stronger bonds $\implies$ Higher $k \implies$ Higher frequency. - $\mu$ = Reduced mass, calculated as: $$\mu = \frac{m_1 m_2}{m_1 + m_2}$$ **Key Takeaway:** Frequency is directly proportional to bond strength and inversely proportional to the mass of the vibrating atoms. ### Factors Affecting Frequency #### A. Mass Effect (Isotope Effect) Heavier atoms vibrate slower (lower wavenumber). - C–H: 3000 cm$^{-1}$ (Lightest) - C–D (Deuterium): 2200 cm$^{-1}$ (Heavier) - C–O: 1100 cm$^{-1}$ - C–Cl: 700 cm$^{-1}$ (Heaviest) #### B. Bond Strength Stronger bonds vibrate faster (higher wavenumber). - C$\equiv$C (Triple bond): 2200 cm$^{-1}$ - C$=$C (Double bond): 1650 cm$^{-1}$ - C–C (Single bond): 1200 cm$^{-1}$ ### Vibration Modes & Regions #### Vibration Modes Molecules exhibit various vibrational modes: - **Stretching:** - Symmetric: Atoms move in the same direction. - Asymmetric: Atoms move in opposite directions. - **Bending modes:** Rocking, wagging, twisting, scissoring. #### The Four Regions of the IR Spectrum The IR spectrum is categorized from high to low frequency (left to right): 1. **X–H Region:** 4000-2500 cm$^{-1}$ (Bonds to H: O-H, N-H, C-H). 2. **Triple Bond Region:** 2500-2000 cm$^{-1}$ (C$\equiv$C, C$\equiv$N). 3. **Double Bond Region:** 2000-1500 cm$^{-1}$ (C$=$O, C$=$C, C$=$N). 4. **Single Bond Region (Fingerprint):** 1500-400 cm$^{-1}$ (C-C, C-O, C-N, C-X). ### The X–H Region Details (4000-2500 cm$^{-1}$) Although O, N, and C have similar masses, their bond strengths to hydrogen differ, leading to distinct peak positions: | Bond | Approximate Range (cm$^{-1}$) | Strength Logic | |---|---|---| | O–H | 3650-3200 | Strongest bond, highest frequency. | | N–H | 3500-3300 | Weaker than O-H. | | C–H | 3300-2800 | Weakest of the three group. | #### The Amine (N-H) "Hump" - **Observation:** Primary amine ($\text{NH}_2$) groups typically show a doublet (two peaks/humps). - **Reason:** This arises from the two fundamental N-H stretching modes: - **Asymmetric stretch:** Both N-H bonds move in opposite directions. Requires more energy (higher wavenumber). - **Symmetric stretch:** Both N-H bonds move in the same direction. Requires less energy (lower wavenumber). - **Diagnostic Value:** - Two peaks: Indicates a primary amine ($\text{NH}_2$). - One peak: Indicates a secondary amine ($\text{R}_2\text{NH}$). ### Special Effects on Frequency #### 1. Effect of H-Bonding - **Concept:** Hydrogen bonding "drags" on the H atom, lengthening and weakening the original covalent bond (O-H or N-H). - **Result:** The vibration frequency decreases (peak shifts to lower wavenumber). - **Note:** Free N-H is higher; H-bonded N-H appears lower (around 3300 cm$^{-1}$). #### 2. Conjugation (Resonance) - **Concept:** When a C$=$O double bond is adjacent to a C$=$C double bond, they share electrons, giving the C$=$O some "single bond character." - **Result:** Single bonds are weaker than double bonds, so the frequency decreases. #### 3. Ring Strain Effect (Cyclic Ketones) - **Trend:** As the ring size decreases (e.g., cyclobutanone vs. cyclohexanone), the C$=$O frequency increases. - Smallest Ring = Highest Frequency. - **Reason (Hybridization):** In a small, strained ring, the carbon atom forming the ring uses orbitals with more p-character for the internal ring bonds. Due to orbital conservation, the external bond (e.g., C$=$O) gets orbitals with more s-character. More s-character leads to a shorter, stiffer, stronger bond, and thus a higher frequency. #### 4. Symmetry in Triple Bonds - **Rule:** If a molecule is perfectly symmetrical (e.g., C$\equiv$C in acetylene), stretching the bond does not change the dipole moment. - **Result:** The vibration is IR Inactive (it will often not appear in the spectrum). #### 5. Fingerprint Region (1500-400 cm$^{-1}$) - This region is complex and "not easy to differentiate" due to numerous overlapping peaks. - It is dominated by bending vibrations (e.g., C-H bending), which require less energy than stretching vibrations. #### 6. Lactones vs. Lactams (Conjugation Effects) - **General Rule:** Lactams (cyclic amides) have a lower C$=$O frequency than Lactones (cyclic esters). - Lactone (C$=$O): Higher frequency - Lactam (C$=$O): Lower frequency - **Reason: Resonance (Internal Conjugation)** - **In Lactams (Nitrogen):** Nitrogen is less electronegative and a better electron donor than Oxygen. It pushes its lone pair into the carbonyl bond very effectively (strong resonance). The C$=$O bond gains significant "single bond character," leading to a weaker bond and lower frequency. - **In Lactones (Oxygen):** Oxygen is more electronegative and a weaker electron donor compared to Nitrogen. The resonance is weaker, so the C$=$O bond retains more of its "double bond character," resulting in a stiffer bond and higher frequency. ### Inorganic IR Spectroscopy: Metal-Carbonyl (M-CO) & Metal-Nitrosyl (M-NO) #### 1. Determinants of Peak Strength (Intensity) - **The Rule:** IR intensity depends on the change in dipole moment during vibration. - **Comparison:** - C$=$O: Highly polar bond, large dipole change $\implies$ Stronger, more intense peak. - C$=$C: Non-polar (or weakly polar) bond, small dipole change $\implies$ Weaker peak. #### 2. Metal-Ligand Back-Bonding ($\pi$-Back Donation) - **Mechanism:** The CO ligand acts as a $\sigma$-donor and a $\pi$-acceptor. The Metal (M) donates electron density back into the empty $\pi^*$ (antibonding) orbital of the CO ligand. - **Relationship:** More Back-Bonding = Weaker C-O Bond. Filling the $\pi^*$ antibonding orbital of CO decreases the bond order between C and O. - **Result:** The vibrational frequency ($\nu_{\text{CO}}$) decreases. - **Summary:** "Better donation from metal = Less vibrational freq." #### 3. Bridging CO vs. Terminal CO - **Terminal CO:** Bonded to a single metal center. Vibrates at a higher frequency (typically 2100-1900 cm$^{-1}$). - **Bridging CO:** Bonded to two or more metal centers. Increased interaction with multiple metal centers enhances back-donation effects or changes bond mechanics. - **Result:** Vibrates at a lower frequency (typically 1900-1700 cm$^{-1}$). #### 4. Ligand Substitution Effects (The Tungsten Example: $\text{W(CO)}_5\text{L}$) - **Question:** How does Ligand L affect the frequency of the CO groups? - **Logic:** If L is a better $\sigma$-donor (pushes electrons onto the Metal), the Metal becomes more electron-rich. The Metal then dumps this excess electron density into the $\pi^*$ orbitals of the CO ligands (increased back-bonding). - **Result:** The C-O bond weakens, and the CO frequency decreases. #### 5. Charge Trends (Isoelectronic Series) - **General Principle:** "Easier donation = lower freq." - **Comparison:** $[\text{V(CO)}_6]^-$ vs. $\text{Cr(CO)}_6$ vs. $[\text{Mn(CO)}_6]^+$ - $[\text{V(CO)}_6]^-$ (Most Negative): Highest electron density on the metal. Best donor. Massive back-bonding occurs $\implies$ Weakest C-O bond $\implies$ Lowest/Least Frequency. - $\text{Cr(CO)}_6$ (Neutral): Intermediate electron density. - $[\text{Mn(CO)}_6]^+$ (Most Positive): Least electron density (relative to anions). Holds electrons more tightly. Minimal back-bonding $\implies$ Stronger C-O bond $\implies$ Highest Frequency. - (Note: The provided example shows the trend to be $[\text{Mn(CO)}_6]^+ > \text{Cr(CO)}_6 > [\text{V(CO)}_6]^-$ in frequency, which is consistent with $[\text{V(CO)}_6]^-$ being a better electron donor than neutral $\text{Cr(CO)}_6$ and cationic $[\text{Mn(CO)}_6]^+$). #### 6. Study Reminder - Review $\pi$-acid / $\pi$-acceptor concepts from CFT-MO theory to understand orbital splitting and back-bonding.