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 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 ?

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