Radius of Gyration [1]

The radius of gyration \(R_g\) quantifies the spatial extent of a structure around its center of mass. MakroLyzer reports a single value per frame for the full graph.

Definition

The squared radius of gyration is defined as

\[R_g^2 = \frac{1}{N} \sum_{i=1}^{N} \left(\vec{r}_i - \vec{r}_{\mathrm{com}}\right)^2\]

where \(N\) is the number of atoms in the graph, \(\vec{r}_i\) is the position vector of atom \(i\), and \(\vec{r}_{\mathrm{com}}\) is the center of mass position vector of the graph.

Additionally, the radius of gyration tensor G is computed as

\[\textbf{G}_{m,n} = \frac{1}{N} \sum_{i=1}^{N} \left(\vec{r}_i^{(m)} - \vec{r}_{\mathrm{com}}^{(m)}\right) \left(\vec{r}_i^{(n)} - \vec{r}_{\mathrm{com}}^{(n)}\right)\]

with \(\vec{r}_i^{(m)}\) representing the \(m^{\mathrm{th}}\) Cartesian coordinates of the position vector of the \(i^{\mathrm{th}}\) particle, and thus, G describes a symmetric 3 \(\times\) 3 matrix: It is used for the calculation of the anisotropy factor and the asphericity parameter.

Command Line Input

-Rg

--radiusOfGyration

Calculate \(R_g\). Optionally provide an output filename.

Default: Rg.csv

Example

MakroLyzer -xyz polymer.xyz -Rg myRgOutput.csv

Output

The output file contains one row per frame with the following columns:

Column	Description
Frame	Frame index in the trajectory
Rg / Angstrom	Radius of gyration for the full graph