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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.

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  • $\begingroup$ 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. $\endgroup$
    – user_na
    Aug 16, 2017 at 14:06
  • $\begingroup$ Thanks. But I mean phonon and not photon. $\endgroup$
    – Farrokh Yousefi
    Aug 16, 2017 at 14:18
  • $\begingroup$ oh, sorry, my mistsake $\endgroup$
    – user_na
    Aug 18, 2017 at 6:00

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Yes you sum the DOS of the individual species to obtain the total DOS. See equation 7b here:

Vashishta, P., Rajiv K. Kalia, and I. Ebbsjö. "Structural correlations and phonon density of states in GeSe 2: A molecular-dynamics study of molten and amorphous states." Physical Review B 39.9 (1989): 6034.

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