PPR-Phonon-Participation-Ratio

Calculation of phonon participation rates -- used to characterize atomic vibrational information including the degree of localization and delocalization.

This project contains two calculation methods. As follows:

1. Calculate PPR from PDOS (classical MD)

Based on the atomic phonon density of states (PDOS) [Dickey 1969], the PPR is calculated to approximately measure the phonon localization with the following form [Bell 1970]:, $$ PPR(\omega) = \frac{1}{N} \frac{(\sum_{i}PDOS_{i}^{2}(\omega))^{2}}{\sum_{i}PDOS_{i}^{4}(\omega)}, $$ where $PDOS_{i}$ is the atomic PDOS, and N is the total number of atoms involved in the calculation. (From top Dr. penghua)

2. Calculate PPR from lattice dynamic (LD)

In this method, one can use the following formula to calculate the PPR,
$$ P_{\lambda}^{-1}=N \sum_{i}\left(\sum_{\alpha} e_{i \alpha, \lambda}^{*} e_{i \alpha, \lambda}\right)^{2} $$

where N is the total number of atoms in primitive cell. and $e_{i \alpha, \lambda}$ is the αth eigenvector component of eigenmode λ for the ith atom. Each eigenmode λ is specified by the wave-vector k and branch index s.