Shortcut: COORD_ANGLES

Module	multicolvar
Description	Usage
Calculate functions of the distribution of angles between bonds in the first coordination spheres of a set of atoms

Deprecated

This action has been deprecated and is no longer supported. Use MATRIX_PRODUCT instead.

Details and examples

Calculate functions of the distribution of angles between bonds in the first coordination spheres of a set of atoms

This action ncan be used to calculate functions, $g$ , such as:

$f(x) = \sum_{ijk} s(r_{ij})s(r_{jk}) g(\theta_{ijk})$

where $\theta_{ijk}$ is the angle between the vector connecting atom $i$ and and $j$ and the vector connecting atom $j$ and atom $k$ and where $s(r)$ is a switching function. The switching functions in the expression above ensure that we can calculate all the angles in the first coordination spheres of an atom using an input like the one shown below:

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

c1The COORD_ANGLES action with label c1 calculates the following quantities: Quantity    Type    Description  
c1_sum scalar the sum of the colvars: COORD_ANGLESCalculate functions of the distribution of angles between bonds in the first coordination spheres of a set of atoms This action is a shortcut. More details ...
  CATOMSall the angles between the bonds that radiate out from these central atom are computed=1 GROUPa list of angls between pairs of bonds connecting one of the atoms specified using the CATOM command and two of the atoms specified here are computed=2-100 SWITCHthe switching function specifies that only those bonds that have a length that is less than a certain threshold are considered={RATIONAL R_0=1.0} SUM calculate the sum of all the quantities
...
# PLUMED interprets the command:
# c1: COORD_ANGLES ...
#   CATOMS=1 GROUP=2-100 SWITCH={RATIONAL R_0=1.0} SUM
# ...
# as follows (Click the red comment above to revert to the short version of the input):
The COORD_ANGLES action with label c1 calculates the following quantities: Quantity    Description  
c1.sum the sum of the colvarsc1_ddThe DISTANCE action with label c1_dd calculates the following quantities: Quantity    Type    Description  
c1_dd vector the DISTANCE for each set of specified atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMS1the pair of atom that we are calculating the distance between=1,2 ATOMS2the pair of atom that we are calculating the distance between=1,3 ATOMS3the pair of atom that we are calculating the distance between=1,4 ATOMS4the pair of atom that we are calculating the distance between=1,5 ATOMS5the pair of atom that we are calculating the distance between=1,6     # Action input conctinues with 94 further ATOMSn keywords, 
c1_swThe LESS_THAN action with label c1_sw calculates the following quantities: Quantity    Type    Description  
c1_sw vector the vector obtained by doing an element-wise application of a function that is one if the input is less than a threshold to the input vectors: LESS_THANUse a switching function to determine how many of the input variables are less than a certain cutoff. More details ARGthe values input to this function=c1_dd SWITCHThis keyword is used if you want to employ an alternative to the continuous swiching function defined above={RATIONAL R_0=1.0}
c1_compThe DISTANCE action with label c1_comp calculates the following quantities: Quantity    Type    Description  
c1_comp.x vector the x-component of the vector connecting the two atoms
c1_comp.y vector the y-component of the vector connecting the two atoms
c1_comp.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=1,2 ATOMS2the pair of atom that we are calculating the distance between=1,3 ATOMS3the pair of atom that we are calculating the distance between=1,4 ATOMS4the pair of atom that we are calculating the distance between=1,5 ATOMS5the pair of atom that we are calculating the distance between=1,6     # Action input conctinues with 94 further ATOMSn keywords, 
c1_norm2The COMBINE action with label c1_norm2 calculates the following quantities: Quantity    Type    Description  
c1_norm2 vector the vector obtained by doing an element-wise application of a linear combination to the input vectors: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=c1_comp.x,c1_comp.y,c1_comp.z POWERS the powers to which you are raising each of the arguments in your function=2,2,2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
c1_normThe CUSTOM action with label c1_norm calculates the following quantities: Quantity    Type    Description  
c1_norm vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=c1_norm2 FUNCthe function you wish to evaluate=sqrt(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
c1_norm_xThe CUSTOM action with label c1_norm_x calculates the following quantities: Quantity    Type    Description  
c1_norm_x vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=c1_comp.x,c1_norm FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
c1_norm_yThe CUSTOM action with label c1_norm_y calculates the following quantities: Quantity    Type    Description  
c1_norm_y vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=c1_comp.y,c1_norm FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
c1_norm_zThe CUSTOM action with label c1_norm_z calculates the following quantities: Quantity    Type    Description  
c1_norm_z vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=c1_comp.z,c1_norm FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
c1_stackThe VSTACK action with label c1_stack calculates the following quantities: Quantity    Type    Description  
c1_stack matrix a matrix that contains the input vectors in its columns: VSTACKCreate a matrix by stacking vectors together More details ARGthe values that you would like to stack together to construct the output matrix=c1_norm_x,c1_norm_y,c1_norm_z
c1_stackTThe TRANSPOSE action with label c1_stackT calculates the following quantities: Quantity    Type    Description  
c1_stackT matrix the transpose of the input matrix: TRANSPOSECalculate the transpose of a matrix More details ARGthe label of the vector or matrix that should be transposed=c1_stack
c1_swdThe OUTER_PRODUCT action with label c1_swd calculates the following quantities: Quantity    Type    Description  
c1_swd matrix a matrix containing the outer product of the two input vectors that was obtained using the function that was input: OUTER_PRODUCTCalculate the outer product matrix of two vectors More details ELEMENTS_ON_DIAGONAL_ARE_ZERO set all diagonal elements to zero ARGthe labels of the two vectors from which the outer product is being computed=c1_sw,c1_sw
c1_wmatThe CUSTOM action with label c1_wmat calculates the following quantities: Quantity    Type    Description  
c1_wmat 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=c1_swd FUNCthe function you wish to evaluate=0.5*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
c1_dpmatThe MATRIX_PRODUCT action with label c1_dpmat calculates the following quantities: Quantity    Type    Description  
c1_dpmat matrix the product of the two input matrices: MATRIX_PRODUCTCalculate the product of two matrices More details ELEMENTS_ON_DIAGONAL_ARE_ZERO set all diagonal elements to zero ARGthe label of the two matrices from which the product is calculated=c1_stack,c1_stackT
c1_anglesThe CUSTOM action with label c1_angles calculates the following quantities: Quantity    Type    Description  
c1_angles 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=c1_dpmat FUNCthe function you wish to evaluate=acos(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
c1_wsumThe CUSTOM action with label c1_wsum calculates the following quantities: Quantity    Type    Description  
c1_wsum 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=c1_wmat,c1_angles FUNCthe function you wish to evaluate=x*y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
c1_sumThe SUM action with label c1_sum calculates the following quantities: Quantity    Type    Description  
c1_sum scalar the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=c1_wsum PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- 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=c1.sum FILEthe name of the file on which to output these quantities=colvar

The input above will output the sum of all the angles in the first coordination sphere.

As you can see if you expand the shortcut in the input above, the calculation of the above sum is obtained by calculating a Hadamard product of an OUTER_PRODUCT matrix and a MATRIX_PRODUCT. We have thus deprecated this action as we believe that there is value in learning to use the more complicated syntax directly.

Input

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

Keyword	Type	Description
CATOMS	atoms	all the angles between the bonds that radiate out from these central atom are computed
GROUP	atoms	a list of angls between pairs of bonds connecting one of the atoms specified using the CATOM command and two of the atoms specified here are computed

Output components

This action can calculate the values in the following table when the associated keyword is included in the input for the action. 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	Keyword	Description
lessthan	scalar	LESS_THAN	the number of colvars that have a value less than a threshold
morethan	scalar	MORE_THAN	the number of colvars that have a value more than a threshold
between	scalar	BETWEEN	the number of colvars that have a value that lies in a particular interval
sum	scalar	SUM	the sum of the colvars
mean	scalar	MEAN	the mean of the colvars

Full list of keywords

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

Keyword	Type	Default	Description
CATOMS	input	none	all the angles between the bonds that radiate out from these central atom are computed
GROUP	input	none	a list of angls between pairs of bonds connecting one of the atoms specified using the CATOM command and two of the atoms specified here are computed
SWITCH	compulsory	none	the switching function specifies that only those bonds that have a length that is less than a certain threshold are considered
LESS_THAN	optional	not used	calculate the number of variables that are less than a certain target value. Options for this keyword are explained in the documentation for LESS_THAN.
MORE_THAN	optional	not used	calculate the number of variables that are more than a certain target value. Options for this keyword are explained in the documentation for MORE_THAN.
BETWEEN	optional	not used	calculate the number of values that are within a certain range. Options for this keyword are explained in the documentation for BETWEEN.
HISTOGRAM	optional	not used	calculate a discretized histogram of the distribution of values
SUM	optional	not used	calculate the sum of all the quantities
MEAN	optional	not used	calculate the mean of all the quantities

Quantity	Type	Description
c1_sum	scalar	the sum of the colvars