Sampling phonon spectra from molecular-dynamics simulations

Sampling phonon DOS from molecular dynamics simulation

The phonon density of states can be obtained as the power spectrum from the normalized velocity auto correlation function. The normalized velocity auto correlation function for a $N$-particle system is given by \begin{equation} f(t)\frac{\langle \sum_{i=1}^{N}\mathbf{v}_{i}(\delta T)mathbf{v}_{i}(\delta T + t)\rangle}{\mathbf{v}_{i}(\delta T)mathbf{v}_{i}(\delta T)} \end{equation}

Further information can be found on the following page. External tools as for example phonopy may also be considered. To compute the power spectra of the Fourier transformed projected velocity autocorrelations

[math]\displaystyle{ |G_{\nu}(\mathbf{q},\omega)|^{2}=\sum_{I,\alpha}\sum_{J,\beta} \int\left( \varepsilon_{I\nu}^{\beta}(\mathbf{q}) \sqrt{M_{I}}v_{I}^{\alpha}(t') \right )\left( \varepsilon_{J\nu}^{\beta}(\mathbf{q}) \sqrt{M_{J}}v_{J}^{\beta}(t'') \right )e^{i\mathbf{q} \cdot (\mathbf{R}_{I}(t')-\mathbf{R}_{J}(t''))}e^{-i\omega (t'-t'')}d(t'-t'') }[/math]

external tools are required. The following table summarizes a small list of codes which can compute projected velocity correlation functions from VASP output.

code	publication
DSLEAP	Lahnsteiner et.al.
phq	Zhang et.al.
DynaPhoPy	Carreras et.al.

Sampling phonon DOS from molecular dynamics simulation

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