Chapter 13: Spectroscopy
Index of Hydrogen Deficiency (IHD)
• The Index of Hydrogen Deficiency (IHD), 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 it takes a count of how many rings and multiple bonds are present in the structure.
• So, IHD can also be thought of as (multiple bonds + rings) or (p + r).
• When you look at a structure, just count rings and p-bonds up (but take care not to count any rings twice !)
• If you have a 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 maybe possible
• Quickly checking structures to see if they fit the molecular formula rather than simply counting H (when a mistake is easily possible)
Questions
• What is the IHD for each of the following molecular formulae ?
 C6H10 C6H6 C4H8O C4H9N C2Cl2