frequency of radiation: E = hv
is not the same as vibrational frequency
v = (1/2π)*sqrt(k/μ)
The former refers to the wave properties of a photon while the latter refers to the mechanical properties of a system that follows spring mechanics.
Now in spectroscopy there is a relationship between the wavelength of absorption and the vibrational frequency between two atoms, however the wavelength refers to the energy being absorbed, and the frequency to the vibration between two atoms.
Vibrational frequencies can be used in computational chemistry to calculate energies, as it turns out Hookes law provides very good approximations when performing these calculations. However, calculating energies using vibrational frequencies is very computing intensive.
In a very simplistic way you have
ΔU = ΔH + W
ΔU is the change in internal energy
ΔH is the change in enthalpy
W is work
under certain conditions for a system at equilibrium you can assume that ΔU = 0
ΔH =- W
for a vibrating system work can be described by hookes law
Ws=(1/2)kx02 -(1/2)kx02 where x are components of distance and k is the spring constant.
It also turns out that K the force constant is the second derivative of the potential energy of a system with respect to the bond length.
If you let P = potential energy and R= bond length then
k = d2V(R)/dR2