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Theory and implementation

nMOLDYN calculates the power spectrum of the VACF, which in case of the mass-weighted VACF defines the phonon discrete DOS, (see Section 4.2.4.5) defined as:

|  |  | (4.43)

is the total number of time steps and is the frequency step. can be computed either for the isotropic case or with respect to a user-defined axis. The spectrum is computed from the unnormalized VACF, such that DOS(0) gives an approximate value for the diffusion constant (see Eqs. 4.21 and 4.22). is smoothed by applying a Gaussian window in the time domain [76] (see Section A). Its width in the time domain is , where is the length of the simulation. We remark that the diffusion constant obtained from DOS is biased due to the spectral smoothing procedure since the VACF is weighted by this window Gaussian function. nMOLDYN computes the density of states starting from both atomic velocities and atomic coordinates. In this case the velocities are computed by numerical differentiation of the coordinate trajectories correcting first for possible jumps due to periodic boundary conditions.

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