
Chapter 13: Spectroscopy 

Index of Hydrogen Deficiency (IHD)

The Index of Hydrogen Deficiency (IHD), is a count of how
many molecules of H_{2} 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 pbonds
up (but take care not to count any rings twice !)

If you have a molecular formula, C_{c}H_{h}N_{n}O_{o}X_{x},
then the following equation can be derived:
IHD = 0.5 * [2c+2hx+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, CH_{4}, and methanol, CH_{3}OH).

Nitrogen forms three bonds. This means for "n" nitrogens, "n" extra hydrogen
atoms are needed (compare the H count for methane, CH_{4}, and
methyl amine, CH_{3}NH_{2}), therefore, add "n".

The factor of 0.5 accounts for us counting H atoms, but adding
hydrogen, H_{2 }, 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 ?
C_{6}H_{10}

C_{6}H_{6}

C_{4}H_{8}O

C_{4}H_{9}N

C_{2}Cl_{2}





