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1. Application of Pascal's Triangle in
¹H-NMR Spectroscopy
MPhil Chemistry | Hajira Bibi

2. Introduction
• ¹H-NMR reveals hydrogen environments in molecules.
• Multiplets appear due to spin-spin splitting.
• Peak intensities follow Pascal’s Triangle.

3. What is Pascal’s Triangle?
• Triangular array of binomial coefficients.
• Each row represents (a + b)^n.
• Used in NMR to determine relative intensities of multiplets.

4. Pascal’s Triangle: Multiplet Patterns
n=0 → Singlet → 1
n=1 → Doublet → 1:1
n=2 → Triplet → 1:2:1
n=3 → Quartet → 1:3:3:1
n=4 → Quintet → 1:4:6:4:1
n=5 → Sextet → 1:5:10:10:5:1

5. Spin-Spin Coupling and Multiplets
• Neighboring non-equivalent protons cause splitting.
• n neighbors → (n+1) multiplet peaks.
• Intensities align with Pascal’s Triangle.

6. Role of Pascal’s Triangle in NMR
• Predicts number of peaks (n+1 rule).
• Guides intensity distribution.
• Helps identify neighboring proton environments.

7. Application in Structural Elucidation
• CH₃ next to CH₂ → Quartet (1:3:3:1)
• CH₂ next to CH₃ → Triplet (1:2:1)
• Deconvolutes overlapping multiplets.
• Supports accurate molecular structure analysis.

8. Limitations
• Valid for first-order spectra only.
• Not for aromatic/second-order cases.
• Equivalent protons must be correctly identified.

9. Conclusion
• Pascal’s Triangle simplifies multiplet analysis.
• Essential for interpreting splitting in ¹H-NMR.
• Crucial in organic structure elucidation.

10. References
1. Pavia et al., Introduction to Spectroscopy
2. Silverstein et al., Spectrometric Identification
3. Claridge, High-Resolution NMR Techniques
4. Atkins & de Paula, Physical Chemistry
5. Gunther, NMR Spectroscopy