Degree of Unsaturation
Calculate rings + double bonds from molecular formula (DBE/IHD)
The Formula
DBE = C - H/2 + N/2 + 1
or equivalently:
DBE = (2C + 2 + N - H - X)/2
Where:
- DBE = Degree of unsaturation (Double Bond Equivalent)
- C = Number of carbon atoms
- H = Number of hydrogen atoms (and D, T)
- N = Number of nitrogen atoms (trivalent)
- X = Number of halogens (F, Cl, Br, I)
- O, S = Ignored (divalent atoms don't affect count)
Alternative Names:
- • IHD: Index of Hydrogen Deficiency
- • Rings + Double Bonds
- • Degree of Deficiency
- • Unsaturation Number
Interpretation of DBE Value
DBE = 0
Saturated, acyclic compound
Example: C₄H₁₀ (butane) - no rings, no double bonds
DBE = 1
One ring OR one double bond
• Cyclohexane (C₆H₁₂) - one ring
• 1-Hexene (C₆H₁₂) - one C=C
• Formaldehyde (CH₂O) - one C=O
DBE = 2
Two rings/double bonds OR one triple bond
• Bicyclo[2.2.1]heptane - two rings
• 1,3-Butadiene (C₄H₆) - two C=C
• Acetylene (C₂H₂) - one C≡C (counts as 2)
DBE = 4
Aromatic ring (benzene = 3 double bonds + 1 ring)
• Benzene (C₆H₆) - aromatic ring
• Toluene (C₇H₈) - benzene ring
• Aniline (C₆H₇N) - benzene ring
Counting Rules
- • Each ring = 1 DBE
- • Each C=C or C=O = 1 DBE
- • Each C≡C or C≡N = 2 DBE
- • Benzene ring = 4 DBE (1 ring + 3 double bonds)
Common Mistakes
Counting Oxygen
Oxygen is IGNORED! Don't subtract or add O to the formula.
Treating X like C
Halogens (F, Cl, Br, I) count like H, not C! Subtract them.
Negative DBE
If DBE < 0, you made an error! Recheck the formula.
Pro Tip
DBE can help deduce structure from molecular formula + spectroscopy!