   GYRATION
 This is part of the colvar module

Calculate the radius of gyration, or other properties related to it.

The different properties can be calculated and selected by the TYPE keyword: the Radius of Gyration (RADIUS); the Trace of the Gyration Tensor (TRACE); the Largest Principal Moment of the Gyration Tensor (GTPC_1); the middle Principal Moment of the Gyration Tensor (GTPC_2); the Smallest Principal Moment of the Gyration Tensor (GTPC_3); the Asphericiry (ASPHERICITY); the Acylindricity (ACYLINDRICITY); the Relative Shape Anisotropy (KAPPA2); the Smallest Principal Radius Of Gyration (GYRATION_3); the Middle Principal Radius of Gyration (GYRATION_2); the Largest Principal Radius of Gyration (GYRATION_1). A derivation of all these different variants can be found in 

The radius of gyration is calculated using:

$s_{\rm Gyr}=\Big ( \frac{\sum_i^{n} m_i \vert {r}_i -{r}_{\rm COM} \vert ^2 }{\sum_i^{n} m_i} \Big)^{1/2}$

with the position of the center of mass $${r}_{\rm COM}$$ given by:

${r}_{\rm COM}=\frac{\sum_i^{n} {r}_i\ m_i }{\sum_i^{n} m_i}$

The radius of gyration usually makes sense when atoms used for the calculation are all part of the same molecule. When running with periodic boundary conditions, the atoms should be in the proper periodic image. This is done automatically since PLUMED 2.2, by considering the ordered list of atoms and rebuilding the broken entities using a procedure that is equivalent to that done in WHOLEMOLECULES . Notice that rebuilding is local to this action. This is different from WHOLEMOLECULES which actually modifies the coordinates stored in PLUMED.

In case you want to recover the old behavior you should use the NOPBC flag. In that case you need to take care that atoms are in the correct periodic image.

Examples

The following input tells plumed to print the radius of gyration of the chain containing atoms 10 to 20.

Click on the labels of the actions for more information on what each action computes rg: GYRATION TYPEcompulsory keyword ( default=RADIUS )
The type of calculation relative to the Gyration Tensor you want to perform =RADIUS ATOMSthe group of atoms that you are calculating the Gyration Tensor for. =10-20
PRINT ARGthe input for this action is the scalar output from one or more other actions. =rg STRIDEcompulsory keyword ( default=1 )
the frequency with which the quantities of interest should be output =1 FILEthe name of the file on which to output these quantities =colvar

Glossary of keywords and components
The atoms involved can be specified using
 ATOMS the group of atoms that you are calculating the Gyration Tensor for. For more information on how to specify lists of atoms see Groups and Virtual Atoms
Compulsory keywords
 TYPE ( default=RADIUS ) The type of calculation relative to the Gyration Tensor you want to perform
Options
 NUMERICAL_DERIVATIVES ( default=off ) calculate the derivatives for these quantities numerically NOPBC ( default=off ) ignore the periodic boundary conditions when calculating distances MASS_WEIGHTED ( default=off ) set the masses of all the atoms equal to one