Useful Concepts

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

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 C_cH_hN_nO_oX_x, then the following equation can be derived:

Where does this equation come from ?

• Well, the maximum number of hydrogen atoms for "c" carbon atoms is 2c+2 (think of the formulae of saturated hydrocarbons such as ethane, propane etc.).
• From this number, subtract the "h" hydrogens that you have.
• Since, like hydrogen, a halogen only forms one bond, then they can be treated as if they are hydrogens, so subtract them as well.
• Oxygen forms two bonds, therefore it has no impact (compare H count for methane, CH₄, and methanol, CH₃OH).
• Nitrogen forms three bonds. This means for "n" nitrogens, "n" extra hydrogen atoms are needed (compare the H count for methane, CH₄, and methyl amine, CH₃NH₂), therefore, add "n".
• The factor of 0.5 accounts for us counting H atoms, but adding hydrogen, H₂ , molecules. OK ?

• Seeing what types of structural units are possible
• Quickly checking structures to see if they fit the molecular formula rather than simply counting H (when a mistake is possible)

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