Effective masses

Another way of regarding the effective mass of a mode can be derived from consideration of the simple harmonic oscillator:

$\begin{displaymath}E = \sqrt{\frac{k}{\mu}}. \end{displaymath}$

Diagonalization of the mass-weighted Hessian yields the energies, and from the normal coordinates the force-constants can readily be derived. From these two quantities, the effective mass can readily be calculated:

$\begin{displaymath}\mu = \frac{k}{E^2}. \end{displaymath}$

For a homonuclear diatomic, the effective mass calculated this way is equal to the mass of one atom.