Action: QUATERNION_BOND_PRODUCT_MATRIX

Module	crystdistrib
Description	Usage
Calculate the product between a matrix of quaternions and the bonds connecting molecules

Details and examples

Calculate the product between a matrix of quaternions and the bonds connecting molecules

Calculate the product of a quaternion, times a vector, times the conjugate of the quaternion. Geometrically, this is the given vector projected onto the coordinate system defined by the quaternion. For context, the QUATERNION action defines an orthogonal coordinate frame given 3 atoms (i.e. one can define a coordinate system based on the structure of a given molecule). This action can then project a vector from the given molecular frame, toward another molecule, essentially pointing toward molecule 2, from the perspective of molecule 1. See QUATERNION for information about the molecular coordinate frame. Given a quaternion centered on molecule 1 $\mathbf{q1}$, and the vector connecting molecule 1, and some other molecule 2, $\mathbf{r_{21}}$, the following calculation is performed:

$$\mathbf{r} = \overline{\mathbf{q_1}} \mathbf{r_{21}} \mathbf{q_1}$$

where the overline denotes the quaternion conjugate. Internally, the vector $\mathbf{r_{21}}$ is treated as a quaternion with zero real part. Such a multiplication will always yield another quaternion with zero real part, and the results can be interpreted as an ordinary vector in $\mathbb{R}^3$ Nevertheless, this action has four components, the first of which, w, will always be entirely zeros. Finally, the resulting vector is normalized within the action, and the real length can be returned by multiplying each component by the norm of the vector given to the action. The quaternion should be a vector, and the distances a matrix.

In this example, 3 quaternion frames are calculated, and multiplied element-wise onto a distance matrix, yielding 9 vectors overall.

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

#calculate the quaternion frames for 3 molecules
quatThe QUATERNION action with label quat calculates the following quantities:
 Quantity   
 Type   
 Description  
quat.w
vector
the real component of quaternion
quat.i
vector
the i component of the quaternion
quat.j
vector
the j component of the quaternion
quat.k
vector
the k component of the quaternion: QUATERNIONCalculate unit quaternions for molecules. More details ATOMS1the three atom that we are using to calculate the quaternion=1,2,3 ATOMS2the three atom that we are using to calculate the quaternion=4,5,6 ATOMS3the three atom that we are using to calculate the quaternion=7,8,9
#also find the distance between the 3 origins of the molecule frames
c1The DISTANCE_MATRIX action with label c1 calculates the following quantities:
 Quantity   
 Type   
 Description  
c1.w
matrix
a matrix containing the weights for the bonds between each pair of atoms
c1.x
matrix
the projection of the bond on the x axis
c1.y
matrix
the projection of the bond on the y axis
c1.z
matrix
the projection of the bond on the z axis: DISTANCE_MATRIXCalculate a matrix of distances between atoms. This action has hidden defaults. More details GROUPthe atoms for which you would like to calculate the adjacency matrix=1,4,7 CUTOFF ignore distances that have a value larger than this cutoff=100.0 COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix
c1: DISTANCE_MATRIXCalculate a matrix of distances between atoms. This action uses the defaults shown here. More details GROUPthe atoms for which you would like to calculate the adjacency matrix=1,4,7 CUTOFF ignore distances that have a value larger than this cutoff=100.0 COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix  NL_CUTOFF The cutoff for the neighbor list=0.0 NL_STRIDE The frequency with which we are updating the atoms in the neighbor list=1
qpThe QUATERNION_BOND_PRODUCT_MATRIX action with label qp calculates the following quantities:
 Quantity   
 Type   
 Description  
qp.w
matrix
the real component of quaternion
qp.i
matrix
the i component of the quaternion
qp.j
matrix
the j component of the quaternion
qp.k
matrix
the k component of the quaternion: QUATERNION_BOND_PRODUCT_MATRIXCalculate the product between a matrix of quaternions and the bonds connecting molecules More details ARGthis action takes 8 arguments=quat.*,c1.*
#this is now a matrix showing how each molecule is oriented in 3D space
#relative to eachother's origins
#now use in a simple collective variable
opsThe CUSTOM action with label ops calculates the following quantities:
 Quantity   
 Type   
 Description  
ops
matrix
the matrix obtained by doing an element-wise application of an arbitrary function to the input matrix: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=qp.* VARthe names to give each of the arguments in the function=w,i,j,k FUNCthe function you wish to evaluate=w+i+j+k PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
#w could have been ignored because it is always zero.

Input

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

Keyword	Type	Description
ARG	vector/matrix	this action takes 8 arguments

Output components

This action calculates the values in the following table. These values can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the value required from the list below.

Name	Type	Description
w	matrix	the real component of quaternion
i	matrix	the i component of the quaternion
j	matrix	the j component of the quaternion
k	matrix	the k component of the quaternion

Full list of keywords

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

Keyword	Type	Default	Description
ARG	input	none	this action takes 8 arguments
SERIAL	optional	false	do the calculation in serial. Further information about this flag can be found here.
USEGPU	optional	false	run this calculation on the GPU. Further information about this flag can be found here.