1 Phonon Spectrum

• ^[1](For ZA mode) Quantitatively, the frequency-wave vector relationship, in the vicinity of the \Gamma point, can be formulated (\omega<80 cm-1) as \omega=cq^2=\sqrt{D/\rho}q^2 so D=c^2\rho where D and \rho correspond to the bending modulus and the mass area density of the nanosheet, respectively. You can get D by fitting c.

P.S. the in-plane longitudinal (L) and transverse (T) modes. While the TA and LA modes display the normal linear dispersion around the G-point, the ZA mode shows a q² energy dispersion which is explained in Ref.[1] as a consequence of the D_6h point-group symmetry of graphene.

problem: why is ZA mode for graphene (by phonopy) lenear rather than parabolic?

2 Bending Stiffness^[2]

The Bending Stiffness D is determined by fitting the calculated bending energy per unit area E_{ben} of a boron nanotube as a function of tube radius r, based on an analytical expression E_{ben}=Dr^{−2}/2.

3 Frequencies of molecular on Surface

1. Fix all atoms of Surface
2. make the atoms of molecular free

• note that the selective dynamics flags always refer to cartesian coordinates.
• How many zero frequency modes should be observed and why? Try to use the linear response code (IBRION=8 and EDIFF=1E-8) to obtain reference results. For finite differences, are the results sensitive to the step width POTIM. In this specific case, the drift in the forces is too large to obtain the zero frequency modes “exactly,” and it is simplest to increase the cutoff ENCUT to 800 eV. The important and physically meaningful frequencies are, however, insensitive to the choice of the cutoff.