Collectivity index

This values are a numerical measure of how many atoms are affected by a given mode. This measure has been taken from a paper by Rafael Brüschweiler, Collective protein dynamics and nuclear spin relaxation.

The formula that defines this measure is:

$\kappa_i=\frac{1}{N}\exp\left\{-\sum_{n=1}^{N}u_{i,n}^2\log u_{i,n}^2\right\}$

$u_{i,n}^2=\alpha\frac{Q_{i,3n-2}^2+Q_{i,3n-1}^2+Q_{i,3n}^2}{m_n}$

$N$ is the number of atoms, $Q$ is the eigenvector. $\alpha$ is a value uset to normalize the eigenvector.

High values for $\kappa_i$ means that the corresponding eigenvector affects many of the atoms, while lower values means that the eigenvector has a more local behaviour.

The output show collective indexes calculated for the first principal components obtained with either standard or gaussian RMDs fitting.