Shortcut: ATOMIC_SMAC

Module	symfunc
Description	Usage
Calculate the atomic smac CV

Details and examples

Calculate the atomic smac CV

This shortcut offers another example of a symmetry function. This action was inspired by SMAC and the distribution of angles in the first coordination sphere around an atom to determine if the environment around the atom is ordered. For atom $i$ the symmetry function is calculated using:

$$s_i = [ 1 - \gamma(c_i) ] \frac{ \sum_j \sum{k \ne j} \sigma(r_{ij})\sigma(r_{ik}) \sum_n G\left( \frac{ \theta_{jik} - \phi_n}{b_n}\right) }{\sum{k \ne j} \sigma(r_{ij})\sigma(r_{ik})} \qquad \textrm{where} \qquad c_i = \sum_j \sigma(r_{ij})$$

In this expression $r_{ij}$ is the distance between atom $i$ and atom $j$ and $\sigma$ is a switching function that acts upon this distance. $c_i$ is thus the number of atoms that are within a certain cutoff of atom $i$ and $\gamma$ is another switching function that acts upon this quantity. This switching function ensures that the symmetry function is zero for atoms that are regions where the density is low. $\theta_{jik}$ is the angle between the vector connecting atoms $i$ and $j$ and the vector connecting atoms $i$ and $k$. This angle is the argument for the set of Gaussian kernel functions, $G$, that are centered on $\phi_n$ and that have bandwidths of $b_n$. The function above is thus determining if the angles between the bonds in the first coordination sphere around atom $i$ are similar to the $\phi_n$ values that have been specified by the user or not.

The following example demonstrates how this symmetry function can be used in practise.

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

smacThe ATOMIC_SMAC action with label smac calculates the following quantities:
 Quantity   
 Type   
 Description  
smac_sum
scalar
the sum of the colvars: ATOMIC_SMACCalculate the atomic smac CV This action is a shortcut. More details SPECIESthe list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments=1-64 KERNEL1The kernels used in the function of the angle={GAUSSIAN CENTER=pi/2 SIGMA=1.0} KERNEL2The kernels used in the function of the angle={GAUSSIAN CENTER=pi/4 SIGMA=1.0} SWITCH_COORDThis keyword is used to define the coordination switching function={EXP R_0=4.0} SWITCHthe switching function that it used in the construction of the contact matrix={RATIONAL R_0=2.0 D_0=2.0} SUM calculate the sum of all the quantities
# PLUMED interprets the command:
# smac: ATOMIC_SMAC SPECIES=1-64 KERNEL1={GAUSSIAN CENTER=pi/2 SIGMA=1.0} KERNEL2={GAUSSIAN CENTER=pi/4 SIGMA=1.0} SWITCH_COORD={EXP R_0=4.0} SWITCH={RATIONAL R_0=2.0 D_0=2.0} SUM
# as follows (Click the red comment above to revert to the short version of the input):
The ATOMIC_SMAC action with label smac calculates the following quantities:
 Quantity   
 Description  
smac.sum
the sum of the colvarssmac_cmapThe CONTACT_MATRIX action with label smac_cmap calculates the following quantities:
 Quantity   
 Type   
 Description  
smac_cmap.w
matrix
a matrix containing the weights for the bonds between each pair of atoms
smac_cmap.x
matrix
the projection of the bond on the x axis
smac_cmap.y
matrix
the projection of the bond on the y axis
smac_cmap.z
matrix
the projection of the bond on the z axis: CONTACT_MATRIXAdjacency matrix in which two atoms are adjacent if they are within a certain cutoff. More details GROUPspecifies the list of atoms that should be assumed indistinguishable=1-64 COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix SWITCHthe input for the switching function that acts upon the distance between each pair of atoms. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL R_0=2.0 D_0=2.0}
smac_ksumThe GSYMFUNC_THREEBODY action with label smac_ksum calculates the following quantities:
 Quantity   
 Type   
 Description  
smac_ksum.n
vector
the function defined by the FUNCTION1 keyword
smac_ksum.d
vector
the function defined by the FUNCTION2 keyword: GSYMFUNC_THREEBODYCalculate functions of the coordinates of the coordinates of all pairs of bonds in the first coordination sphere of an atom More details WEIGHTthe matrix that contains the weights that should be used for each connection=smac_cmap.w ARGthree matrices containing the bond vectors of interest=smac_cmap.x,smac_cmap.y,smac_cmap.z FUNCTION1the parameters of the function you would like to compute={FUNC=exp(-(ajik-pi/2)^2/(2*1.0*1.0))+exp(-(ajik-pi/4)^2/(2*1.0*1.0)) LABEL=n} FUNCTION2the parameters of the function you would like to compute={FUNC=1 LABEL=d}
smac_onesThe CONSTANT action with label smac_ones calculates the following quantities:
 Quantity   
 Type   
 Description  
smac_ones
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=64
smac_denomThe MATRIX_VECTOR_PRODUCT action with label smac_denom calculates the following quantities:
 Quantity   
 Type   
 Description  
smac_denom
vector
the vector that is obtained by taking the product between the matrix and the vector that were input: MATRIX_VECTOR_PRODUCTCalculate the product of the matrix and the vector More details ARGthe label for the matrix and the vector/scalar that are being multiplied=smac_cmap.w,smac_ones
smac_mtdenomThe MORE_THAN action with label smac_mtdenom calculates the following quantities:
 Quantity   
 Type   
 Description  
smac_mtdenom
vector
the vector obtained by doing an element-wise application of a function that is one if the if the input is more than a threshold to the input vectors: MORE_THANUse a switching function to determine how many of the input variables are more than a certain cutoff. More details ARGthe values input to this function=smac_denom SWITCHThis keyword is used if you want to employ an alternative to the continuous swiching function defined above={EXP R_0=4.0}
smac_smacThe CUSTOM action with label smac_smac calculates the following quantities:
 Quantity   
 Type   
 Description  
smac_smac
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=smac_ksum.n,smac_mtdenom,smac_ksum.d FUNCthe function you wish to evaluate=x*y/z PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
smac_sumThe SUM action with label smac_sum calculates the following quantities:
 Quantity   
 Type   
 Description  
smac_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=smac_smac 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=smac.* FILEthe name of the file on which to output these quantities=colvar

The input above would calculate 64 instances of $s_i$ using the formula above. In each of these two Gaussian Kernels are used in the sum over $n$. The parameters for the switching function $\sigma$ are specified using the SWITCH keyword, while the parameters for $\gamma$ are specified using SWITCH_COORD. As you can see if you expand the shortcut in the input above, the 64 values for $s_i$ are stored in a vector. All the elements of this vector are then added together to produce the single quantity that is output in the colvar file.

Notice that you can also use different groups of atoms by using the SPECIESA and SPECIESB keywords as shown below:

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

smacThe ATOMIC_SMAC action with label smac calculates the following quantities:
 Quantity   
 Type   
 Description  
smac_sum
scalar
the sum of the colvars: ATOMIC_SMACCalculate the atomic smac CV This action is a shortcut. More details SPECIESAthe list of atoms for which the symmetry function is being calculated=1-64 SPECIESBthe list of atoms that can be in the environments of each of the atoms for which the symmetry function is being calculated=65-128 KERNEL1The kernels used in the function of the angle={GAUSSIAN CENTER=pi/2 SIGMA=1.0} KERNEL2The kernels used in the function of the angle={GAUSSIAN CENTER=pi/4 SIGMA=1.0} SWITCH_COORDThis keyword is used to define the coordination switching function={EXP R_0=4.0} SWITCHthe switching function that it used in the construction of the contact matrix={RATIONAL R_0=2.0 D_0=2.0} SUM calculate the sum of all the quantities
# PLUMED interprets the command:
# smac: ATOMIC_SMAC SPECIESA=1-64 SPECIESB=65-128 KERNEL1={GAUSSIAN CENTER=pi/2 SIGMA=1.0} KERNEL2={GAUSSIAN CENTER=pi/4 SIGMA=1.0} SWITCH_COORD={EXP R_0=4.0} SWITCH={RATIONAL R_0=2.0 D_0=2.0} SUM
# as follows (Click the red comment above to revert to the short version of the input):
The ATOMIC_SMAC action with label smac calculates the following quantities:
 Quantity   
 Description  
smac.sum
the sum of the colvarssmac_cmapThe CONTACT_MATRIX action with label smac_cmap calculates the following quantities:
 Quantity   
 Type   
 Description  
smac_cmap.w
matrix
a matrix containing the weights for the bonds between each pair of atoms
smac_cmap.x
matrix
the projection of the bond on the x axis
smac_cmap.y
matrix
the projection of the bond on the y axis
smac_cmap.z
matrix
the projection of the bond on the z axis: CONTACT_MATRIXAdjacency matrix in which two atoms are adjacent if they are within a certain cutoff. More details GROUPAwhen you are calculating the adjacency matrix between two sets of atoms this keyword is used to specify the atoms along with the keyword GROUPB=1-64 GROUPBwhen you are calculating the adjacency matrix between two sets of atoms this keyword is used to specify the atoms along with the keyword GROUPA=65-128 COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix SWITCHthe input for the switching function that acts upon the distance between each pair of atoms. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL R_0=2.0 D_0=2.0}
smac_ksumThe GSYMFUNC_THREEBODY action with label smac_ksum calculates the following quantities:
 Quantity   
 Type   
 Description  
smac_ksum.n
vector
the function defined by the FUNCTION1 keyword
smac_ksum.d
vector
the function defined by the FUNCTION2 keyword: GSYMFUNC_THREEBODYCalculate functions of the coordinates of the coordinates of all pairs of bonds in the first coordination sphere of an atom More details WEIGHTthe matrix that contains the weights that should be used for each connection=smac_cmap.w ARGthree matrices containing the bond vectors of interest=smac_cmap.x,smac_cmap.y,smac_cmap.z FUNCTION1the parameters of the function you would like to compute={FUNC=exp(-(ajik-pi/2)^2/(2*1.0*1.0))+exp(-(ajik-pi/4)^2/(2*1.0*1.0)) LABEL=n} FUNCTION2the parameters of the function you would like to compute={FUNC=1 LABEL=d}
smac_onesThe CONSTANT action with label smac_ones calculates the following quantities:
 Quantity   
 Type   
 Description  
smac_ones
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=64
smac_denomThe MATRIX_VECTOR_PRODUCT action with label smac_denom calculates the following quantities:
 Quantity   
 Type   
 Description  
smac_denom
vector
the vector that is obtained by taking the product between the matrix and the vector that were input: MATRIX_VECTOR_PRODUCTCalculate the product of the matrix and the vector More details ARGthe label for the matrix and the vector/scalar that are being multiplied=smac_cmap.w,smac_ones
smac_mtdenomThe MORE_THAN action with label smac_mtdenom calculates the following quantities:
 Quantity   
 Type   
 Description  
smac_mtdenom
vector
the vector obtained by doing an element-wise application of a function that is one if the if the input is more than a threshold to the input vectors: MORE_THANUse a switching function to determine how many of the input variables are more than a certain cutoff. More details ARGthe values input to this function=smac_denom SWITCHThis keyword is used if you want to employ an alternative to the continuous swiching function defined above={EXP R_0=4.0}
smac_smacThe CUSTOM action with label smac_smac calculates the following quantities:
 Quantity   
 Type   
 Description  
smac_smac
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=smac_ksum.n,smac_mtdenom,smac_ksum.d FUNCthe function you wish to evaluate=x*y/z PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
smac_sumThe SUM action with label smac_sum calculates the following quantities:
 Quantity   
 Type   
 Description  
smac_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=smac_smac 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=smac.* FILEthe name of the file on which to output these quantities=colvar

In this input one $s_i$ value is evaluated for each of the 64 atoms specified in the SPECIESA keyword. In evaluating each of these $s_i$ values using the sum in the expression above runs over the 64 atoms that were specified using SPECIESB.

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
SPECIES	atoms	the list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments
SPECIESA	atoms	the list of atoms for which the symmetry function is being calculated
SPECIESB	atoms	the list of atoms that can be in the environments of each of the atoms for which the symmetry function is being calculated

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
altmin	scalar	ALT_MIN	the minimum value of the cv
min	scalar	MIN	the minimum colvar
max	scalar	MAX	the maximum colvar
between	scalar	BETWEEN	the number of colvars that have a value that lies in a particular interval
highest	scalar	HIGHEST	the largest of the colvars
lowest	scalar	LOWEST	the smallest of the colvars
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
SPECIES	input	none	the list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments
SPECIESA	input	none	the list of atoms for which the symmetry function is being calculated
SPECIESB	input	none	the list of atoms that can be in the environments of each of the atoms for which the symmetry function is being calculated
SWITCH	optional	not used	the switching function that it used in the construction of the contact matrix
KERNEL	optional	not used	The kernels used in the function of the angle
SWITCH_COORD	optional	not used	This keyword is used to define the coordination switching function

deprecated keywords

The keywords in the following table can still be used with this action but have been deprecated

Keyword	Description
LESS_THAN	calculate the number of variables that are less than a certain target value
MORE_THAN	calculate the number of variables that are more than a certain target value
ALT_MIN	calculate the minimum value
MIN	calculate the minimum value
MAX	calculate the maximum value
BETWEEN	calculate the number of values that are within a certain range
HIGHEST	this flag allows you to recover the highest of these variables
HISTOGRAM	calculate a discretized histogram of the distribution of values
LOWEST	this flag allows you to recover the lowest of these variables
SUM	calculate the sum of all the quantities
MEAN	calculate the mean of all the quantities