   GYRATION

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 is calculated without applying periodic boundary conditions so the atoms used for the calculation should all be part of the same molecule that should be made whole before calculating the cv, WHOLEMOLECULES.

The atoms involved can be specified using
 ATOMS the group of atoms that you are calculating the Gyration Tensor for
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 NOT_MASS_WEIGHTED ( default=off ) set the masses of all the atoms equal to one
Examples

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

WHOLEMOLECULES ENTITY0=10-20