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Index of Hydrogen Deficiency (IHD)

The Index of Hydrogen Deficiency (or IHD) is also known as "units of unsaturation" and several other similar names.

The index of hydrogen deficiency is a count of how many molecules of H2 need to be added to a structure in order to obtain the corresponding saturated, acyclic species.   Hence, the IHD takes a count of how many rings and multiple bonds are present in the structure, so the IHD can also be thought of as (multiple bonds + rings) or

IHD = π + r

Note that the IHD for neutral molecules MUST be an integer (i.e. 0, 1, 2 etc.).

There are two ways in which the IHD can be used, both can be useful depending up on the situation:

(1) From a drawn structure

When you look at a structure, just count the number of rings and π bonds present (but take care not to count any rings twice !).
When counting π bonds, π bonds containing heteroatoms (e.g. O, N etc.) can be counted in exactly the same way as all C bonds.

(2) From the molecular formula.

The IHD can be calculated from a molecular formula... Consider the following generic molecular formula CcHhNnOoXx, then the following equation can be derived:

IHD = 0.5 * [2c+2-h-x+n]

Where does this equation come from ?

Determining the IHD for molecules can be useful for the following reasons: QUESTIONS : What is the IHD of each of the following molecular formulae ?


© Dr. Ian Hunt, Department of Chemistry, University of Calgary