# Phonon Density of State

Suppose there is a material such as graphane which has two atoms, Carbon and Hydrogen (I mean that it has two or more atoms). How can I calculate phonon Density of State (DoS) for such system? Can I calculate DoS separately for each atoms and then sum those to obtain total DoS? Is this correct: $$D_{C}(\omega)=\frac {m_{C}}{k_b T} \int_0^{\infty} \frac {\langle V_C(0)V_C(t)\rangle}{\langle V_C(0)V_C(0)\rangle} dt$$ and $$D_{H}(\omega)=\frac {m_{H}}{k_b T} \int_0^{\infty} \frac {\langle V_H(0)V_H(t)\rangle}{\langle V_H(0)V_H(0)\rangle} dt$$ Therefore,

$$D_\mathrm{system}(\omega) = D_{C}(\omega)+D_{H}(\omega)$$

If this is correct, please provide me a reference, so I can refer to it.

• I think this might be a question of the photon energy. For very high energy where the Bandstructure of graphene is not important, this might be a reasonable approch. But surely, in the energy where the band structure is important, this approximation will be wrong. – user_na Aug 16 '17 at 14:06
• Thanks. But I mean phonon and not photon. – Farrokh Yousefi Aug 16 '17 at 14:18
• oh, sorry, my mistsake – user_na Aug 18 '17 at 6:00