13.3 : IR 分光法: 分子振動のフックの法則近似

Hooke's law models atoms in a covalently bonded molecule as two vibrating masses connected by a spring, allowing their vibrational frequencies to be determined using an equation based on this principle.

The final equation is obtained by removing the Avogadro's number from the denominator of the reduced mass expression, and taking its square root.

As per this relation, the wavenumber of a vibration or its vibrational frequency is directly proportional to the force constant, K, and inversely proportional to the reduced mass of vibrating atoms, μ.

So, bonds between atoms with higher atomic masses vibrate at lower frequencies than those between atoms with lower atomic masses.

Bending force constants have a lower value than their stretching counterparts. So, C–H bending occurs at a lower frequency than C–H stretching.

As the K value depends on the bond's strength, stronger bonds with larger force constants vibrate at higher frequencies than weaker bonds.

Therefore, triple bonds vibrate at higher frequencies than double or single bonds between the same atoms.