NMR Spectroscopy Notes

Spin-Spin Coupling Pattern

• [n+1] rule: This rule helps predict the multiplicity (M) of a signal in an NMR spectrum.

  • M = n + 1, where 'n' is the number of equivalent neighboring protons.

  • If M ≠ n + 1, it indicates more complex coupling patterns or magnetic inequivalence.

  • \Delta n / J > 8: This condition generally indicates that the first-order splitting rules apply (n+1 rule).

  • $J<em>1 = J</em>2 = J$: All J values are equal.

• Chemical Bond

  • $H<em>a$ and $H</em>b$: Represent different hydrogen atoms in a molecule.

• Three-bond coupling in a C-C-Hb system.

  • If all J values are equal, the N+1 rule applies, leading to simple splitting patterns like doublet, triplet, and quartet.

Magnetic Inequivalence

• Difference in J values: If $J<em>{ab} ≠ J</em>{ac}$, it indicates that protons Hb and Hc are experiencing different coupling constants.

• Magnetically Inequivalent Protons: These are protons that, although possibly chemically equivalent, have different coupling constants to other nuclei in the molecule.

  • If $J<em>1 ≠ J</em>2 ≠ J$, the simple n+1 rule does not apply.

  • $M = M<em>x \times M</em>y \times M_z \dots$: This suggests that the overall multiplicity (M) is a product of individual multiplicities resulting from different couplings.

  • $M_x = n + 1$

Example of Magnetic Inequivalence

• NMR spectrum with peaks at 4.20, 4.15, 4.10, 4.05 ppm and 3.35, 3.30, 3.25, 3.20, 3.15, 3.10, 3.05, 3.00, 2.95, 2.90 ppm.

• Example molecules:

  • Aromatic ring derivatives with substituents like nitro (NO2) and chlorine (Cl).

  • Labels such as A, A', X, X' indicate different proton environments.

  • Peaks at 8.20, 8.18, 8.16, 8.14, 8.12 ppm and 7.56, 7.54, 7.52, 7.50, 7.48 ppm.

Chemical Equivalence vs. Magnetic Inequivalence

• Chemical Equivalence: Protons in chemically identical environments within a molecule.

  • Exhibit the same chemical shift.

  • Often related by a plane or axis of symmetry.

  • Result in one 1H NMR peak.

• Two 1H NMR peaks: Indicate two different sets of chemically equivalent protons.

• Three 1H NMR peaks: Indicate three different sets of chemically equivalent protons.

• Magnetic Equivalence Criteria: Two nuclei HA and HB are magnetically equivalent if:

  1. They are chemically equivalent (isochronous), i.e., $\Delta n = (nA – nB) = 0$.

  2. They have equal coupling (same J value) to all other nuclei.

• Magnetic equivalence is stricter than chemical equivalence.

• Examples:

  • H3C-CH3 O: Protons are likely chemically equivalent.

  • HO2C H CO2H Cl Cl: Protons may or may not be magnetically equivalent based on coupling.

• If $H<em>a = H’</em>a$ Then, $J (H<em>a -H</em>b) = J (H’<em>a -H</em>b)$ and $J (H<em>a -H’</em>b) = J (H’<em>a -H’</em>b)$: False

• If $H<em>a ≠ H’</em>a$ Then, $J (H<em>a -H</em>b) ≠ J (H’<em>a -H</em>b)$ and $J (H<em>a -H’</em>b) ≠ J (H’<em>a -H’</em>b)$: True

Pople Notation

• Magnetically equivalent protons: $A<em>2, B</em>2, X_2….$

• Magnetically inequivalent protons: $AA’, BB’, XX’$.

• Weakly coupled protons: "AX" system.

• Strongly coupled protons: "AB" system.

• Multiplet patterns of Magnetic inequivalence do NOT conform to first-order system.

• Higher order system for example: in p-chloronitrobenzene, HA and HA' are not magnetically equivalent since $J(H<em>A -H</em>X) ≠ J(H<em>{A'}-H</em>X)$. This is assigned as AA’XX’, NOT A2X2.

Magnetic Inequivalence Example

• Chemical shift equivalent, but not magnetic equivalent: Hb and Hb'.

• $^3J_{ab}$.

• $^3J<em>{ab} ≠ ^3J</em>{a'b'}$.

Magnetic Equivalence & Inequivalence Examples

• Example 1: H1 and H2 are chemically equivalent. They couple equally to H3 and H4, making them magnetically equivalent.

• Example 2: H1 and H2 are chemically equivalent. However, they couple differently to H3 and H4, making them magnetically inequivalent.

• Example 3: No probe nucleus is specified (Br). H1 and H4 are considered magnetically equivalent.

• Example 4: H1 and H4 are chemically equivalent but couple differently to F1 and F2, thus they are magnetically inequivalent. Similarly, F1 and F2 are magnetically inequivalent.

Spectra of First Order Spin System

• For a first-order spin system, the chemical shift difference ($\Delta \delta$) between coupled protons in Hz is much larger than their coupling constant J.

• \Delta \delta / J > 8

Common Coupling Patterns

• Doublet of Doublet (dd)

• Doublet of Triplet (dt = td)

• Doublet of Quartet (dq)

• Doublet of Doublet of Doublet (ddd)

• Doublet of Doublet of Triplet (ddt)

• All follow the condition: \Delta \delta / J > 8

Doublet of Doublet (dd)

• Coupling of a proton (or set of equal protons) with two different protons having different coupling constants.

• AMX system showcase

Doublet of Doublet (dd) vs Quartet

• Quartet: Relative intensities are 1:3:3:1.

• Doublet of doublets: Relative intensities are 1:1:1:1.

Examples of Doublet of doublets (dd): AMX

• Specific examples with chemical structures and corresponding dd patterns.

• NMR spectra showing peaks and splitting patterns.

• Coupling constants:

  • $J<em>{AM} = J</em>{MA} = 5.5 Hz$

  • $J<em>{AX} = J</em>{XA} = 2.6 Hz$

  • $J<em>{MX} = J</em>{XM} = 4.1 Hz$

• Chemical shifts (\δ) for different protons.

Doublet of Triplet (dt)

• Coupling of two protons with magnetic equivalence and one different proton with different coupling constant.

• Example molecules and spectra showing characteristic dt patterns

Doublet of Quartet (dq)

• Coupling of three protons with magnetic equivalence and one different proton with different coupling constant

• Example using ethanol (H3C-CH2-OH) in DMSO-d6.

Doublet of Doublet of Doublet (ddd)

• Coupling of three magnetic inequivalent protons with different coupling constants.

Doublet of Doublet of Triplet (ddt)

• Coupling with the proton H3.

• Coupling with the proton H2.

• Coupling with the methylenic protons.

Interesting Pattern: dt = td

• Drawing of a dt by different orders; Same spectrum obtain!!

• $J_{cis} = 10 Hz$

• $J_{H1CH2} = 7 Hz$

Vicinal Couplings: Cyclohexane Ring System

• 3J Vicinal couplings: Acyclic Stereochemistry

• Two possible products formed in Aldol reaction

• In non-polar solvent such as CDCl3, hydrogen bond is expected to form between OH and carbonyl group

• J{anti} > J{syn} (2.5 vs 9.0Hz)

Cis-trans Determination

• 3J Coupling Cis-trans Determination

Homo-Propargylic Coupling

• 5J Coupling: Homo-Propargylic Coupling

Propargylic Coupling

• 4J Coupling: Propargylic Coupling

W-Coupling

• 4J W-Coupling