Shortcut: GYRATION_TENSOR

Module	colvar
Description	Usage
Calculate the gyration tensor using a user specified vector of weights
output value	type
the gyration tensor that was computed from the weights	matrix

Input

The atoms that serve as the input for this action are specified using one or more of the keywords in the following table.

Further details and examples

Calculate the gyration tensor using a user specified vector of weights

The elements of the $3 \times 3$ gyration tensor are defined as:

$$G_{\alpha\beta} = \frac{\sum_i^{n} w_i (\alpha_i-\alpha_{\rm COM})(\beta_i - \beta_{\rm COM})}{\sum_i^{n} w_i}$$

where $\alpha_i$ and $\beta_i$ can be the $x$, $y$ or $z$ coordinates of atom $i$ and $\alpha_{\rm COM}$ and $\beta_{\rm COM}$ can be the $x$, $y$ or $z$ components of the center, which is calculated using:

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

The following example shows how you can calculate and print the gyration tensor from the positions of the fist 10 atoms using PLUMED

Click on the labels of the actions for more information on what each action computes

gThe GYRATION_TENSOR action with label g calculates the following quantities:
 Quantity   
 Type   
 Description  
g
matrix
the gyration tensor that was computed from the weights: GYRATION_TENSORCalculate the gyration tensor using a user specified vector of weights This action is a shortcut. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1-10
# PLUMED interprets the command:
# g: GYRATION_TENSOR ATOMS=1-10
# as follows (Click the red comment above to revert to the short version of the input):
g_centThe CENTER_FAST action with label g_cent calculates the following quantities:
 Quantity   
 Type   
 Description  
g_cent
atoms
virtual atom calculated by CENTER_FAST action: CENTERCalculate the center for a group of atoms, with arbitrary weights. More details ATOMSthe group of atoms that you are calculating the Gyration Tensor for=1,2,3,4,5,6,7,8,9,10
g_wThe CONSTANT action with label g_w calculates the following quantities:
 Quantity   
 Type   
 Description  
g_w
vector
the constant value that was read from the plumed input: ONESCreate a constant vector with all elements equal to one More details SIZEthe number of ones that you would like to create=10
g_distsThe DISTANCE action with label g_dists calculates the following quantities:
 Quantity   
 Type   
 Description  
g_dists.x
vector
the x-component of the vector connecting the two atoms
g_dists.y
vector
the y-component of the vector connecting the two atoms
g_dists.z
vector
the z-component of the vector connecting the two atoms: DISTANCECalculate the distance/s between pairs of atoms. More details COMPONENTS calculate the x, y and z components of the distance separately and store them as label ATOMS1the pair of atom that we are calculating the distance between=g_cent,1 ATOMS2the pair of atom that we are calculating the distance between=g_cent,2 ATOMS3the pair of atom that we are calculating the distance between=g_cent,3 ATOMS4the pair of atom that we are calculating the distance between=g_cent,4 ATOMS5the pair of atom that we are calculating the distance between=g_cent,5     # Action input conctinues with 5 further ATOMSn keywords, 
gThe MATRIX_PRODUCT action with label g calculates the following quantities:
 Quantity   
 Type   
 Description  
g
matrix
the product of the two input matrices: COVARIANCE_MATRIXCalculate a covariance matix More details ARGthe vectors of data from which we are calculating the covariance=g_dists.x,g_dists.y,g_dists.z WEIGHTSthis keyword takes the label of an action that calculates a vector of values=g_w
# --- End of included input --- PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=g FILEthe name of the file on which to output these quantities=colvar

The 9 elements of the gyration matrix will be output to the file colvar here.

Similar functionality to the functionality in the example above is used in the GYRATION shortcut. There is, however, no fast version of the GYRATION_TENSOR command in the way that there is a fast version of the GYRATION command that is used when the weights are all one or when the masses are used as the weights.

References

More information about how this action can be used is available in the following articles: - J. Vymětal, J. Vondrášek, Gyration- and Inertia-Tensor-Based Collective Coordinates for Metadynamics. Application on the Conformational Behavior of Polyalanine Peptides and Trp-Cage Folding. The Journal of Physical Chemistry A. 115, 11455–11465 (2011)

Syntax

The following table describes the keywords and options that can be used with this action