Notes about IR spectroscopy

• Only bonds which have a change in dipole moment during the vibration can be excited by infrared. So symmetric bonds such as H-H and Cl-Cl do not absorb infrared, while H-Cl does.
• Different, independent vibrations are called normal modes.
• A linear molecule with N atoms has 3N - 5 normal modes
• A nonlinear molecule with N atoms has 3N - 6 normals modes

For example, carbon dioxide is linear with three atoms, so there are four normal modes:

• Each vibrational mode does not have only one ground state and one excited state. There is a range of states, v₁, v₂, v₃, etc. The fundamental transition for a normal mode (v₁ -> v₂) has a much higher absorbance, these are the most common IR peaks, which A-level and early undergrad courses focus on completely. But transitions from ground state to a level higher than v₂ exist - they are called overtones:

The energy level corresponding to v = ∞ is the bond disassociation energy - it can visualised as the level where vibrations are so energetic that the bonds fly apart. The gaps between energy levels converge to 0 as they approach the bond disassociation energy.

Energy gaps lower down are approximately equal to the fundamental transition. Since wavenumber is proportional to energy, we can expect the v₁ -> v₃ overtone and the v₁ -> v₄ overtone to be respectively twice and triple the wavenumber of the fundamental transition.

When interpreting spectra, overtones can overlap with fundamental absorptions, and people unfamiliar with overtones might attribute the peak to a functional group which doesn't exist. But usually the overtones can recognised by their low intensity.

• An absorption can exist which is the sum of two others, this is called a combination band.
• A absorption can exist which is has the value of one subtracted from another, this is called a difference band.

Not all peaks can combine or subtract to produce combination and difference bands - it depends on complicated rules which are beyond the scope of my textbook.

• Stronger bonds and lighter atoms vibrate faster. This explains why the C-H stretch is typically the peak at the highest wave number. It also explains why hydrogen attached to an sp² carbon vibrates at an even high wavenumber than a hydrogen attached to a sp³ - carbon - the sigma bond of a sp² carbon is stronger, since it contains more s character.

Can you tell why the the conjugated carbonyl below absorbs at a lower frequency than a non-conjugated one?

Answer: Resonance gives the carbonyl more single-bond character, weakening the bond, hence weakening the frequency of its vibration.