Return to Contents Useful Concepts Useful Concepts
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 organic molecules MUST be a positive integer (i.e. 0, 1, 2 etc.). If you calculate something different (e.g. 1.5 then there is an error!)

There are two ways in which the IHD can be applied, and both can be useful depending up on the situation (a good student will be comfortable with both):

(1) From a drawn structure

When you look at a drawn structure, count the number of π bonds and rings present (i.e. π + r) (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 C π bonds.

For simple ring systems this can be straight forward, but not as obvious for more complex ring systems.

(2) From the molecular formula

The IHD can be calculated directly 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 ?

Study Tip:
Make sure you can do it both ways!
With a more complex structure, counting C and H atoms to go from a drawing to a molecular formula risks making an error.
With a larger molecular formula, creating a drawing that you know fits the MF risks making an error.

Try the example below !

cholesterol C27H46O

Determining the IHD for molecules can be useful for the following reasons:

QUESTIONS : What is the IHD of each of the following molecular formulae ?


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