﻿

# Degree of unsaturation

The degree of unsaturation (also known as the index of hydrogen deficiency (IHD) or rings plus double bonds[1]) formula is used in organic chemistry to help draw chemical structures. The formula lets the user determine how many rings, double bonds, and triple bonds are present in the compound to be drawn. It does not give the exact number of rings or double or triple bonds, but rather the sum of the number of rings and double bonds plus twice the number of triple bonds. The final structure is verified with use of NMR, mass spectrometry and IR spectroscopy, as well as inspection.

## General formula

The formula for degree of unsaturation is

$DU = 1 + \frac{1}{2} \sum n_i(v_i-2)$

where ni is the number of atoms with valence vi.[2]

That is, an atom that has a valence of x contributes a total of x-2 to the degree of unsaturation. The result is then halved and increased by 1.

## Rings plus pi bonds formulation

For molecules containing only carbon, hydrogen, monovalent halogens, nitrogen, and oxygen, the formula

$Rings + pi Bonds = C - \frac{H}{2} - \frac{X}{2} + \frac{N}{2}+1\,$

where C = number of carbons, H = number of hydrogens, X= number of halogens and N = number of nitrogens,[3] gives an equivalent result. Oxygen and other divalent atoms do not contribute to the degree of unsaturation, as (2-2) = 0.

The degree of unsaturation is used to calculate the number of rings and pi bonds, where

• Rings count as one degree of unsaturation
• Double bonds count as one degree of unsaturation
• Triple bonds count as two degrees of unsaturation