Shortcut: PAIRENTROPY

Module	gridtools
Description	Usage
Calculate the KL Entropy from the radial distribution function
output value	type
the KL-entropy that is computed from the radial distribution function	scalar

Details and examples

Calculate the KL Entropy from the radial distribution function

This shortcut provides an implementation of the CV that is described in the paper that is cited below. Although, the implementation that is offered here is not the one that was used to produce the results described in that paper the values produced by this implementation have been tested against the implementation that was used in the paper, which can be found here.

An example input that calculates and prints the PAIRENTROPY CV is shown below:

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

ppThe PAIRENTROPY action with label pp calculates the following quantities: Quantity    Type    Description  
pp scalar the KL-entropy that is computed from the radial distribution function: PAIRENTROPYCalculate the KL Entropy from the radial distribution function This action is a shortcut. More details ...
   GROUPthe atoms that are being used to calculate the RDF=1-108 MAXRthe maximum distance to use for the rdf=2.0 GRID_BINthe number of bins to use when computing the RDF=20
   BANDWIDTHthe bandwidths for kernel density esimtation=0.13 KERNEL the type of kernel to use for computing the histograms for the RDF=gaussian
   CUTOFF the cutoff at which to stop evaluating the kernel functions is set equal to sqrt(2*x)*bandwidth in each direction where x is this number=6.25
...
# PLUMED interprets the command:
# pp: PAIRENTROPY ...
#    GROUP=1-108 MAXR=2.0 GRID_BIN=20
#    BANDWIDTH=0.13 KERNEL=gaussian
#    CUTOFF=6.25
# ...
# as follows (Click the red comment above to revert to the short version of the input):
pp_rdfThe CUSTOM action with label pp_rdf calculates the following quantities: Quantity    Type    Description  
pp_rdf grid the grid obtained by doing an element-wise application of an arbitrary function to the input grid: RDFCalculate the radial distribution function More details GROUPthe atoms that are being used to calculate the RDF=1-108 KERNEL the type of kernel to use for computing the histograms for the RDF=gaussian CUTOFF the cutoff at which to stop evaluating the kernel functions is set equal to sqrt(2*x)*bandwidth in each direction where x is this number=6.25 GRID_BINthe number of bins to use when computing the RDF=20 MAXRthe maximum distance to use for the rdf=2.0 BANDWIDTHthe bandwidths for kernel density esimtation=0.13 
pp_conv_t1The CUSTOM action with label pp_conv_t1 calculates the following quantities: Quantity    Type    Description  
pp_conv_t1 grid the grid obtained by doing an element-wise application of an arbitrary function to the input grid: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=pp_rdf,pp_rdf_x2 FUNCthe function you wish to evaluate=x*y*log(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
pp_conv_t2The CUSTOM action with label pp_conv_t2 calculates the following quantities: Quantity    Type    Description  
pp_conv_t2 grid the grid obtained by doing an element-wise application of an arbitrary function to the input grid: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=pp_rdf,pp_rdf_x2 FUNCthe function you wish to evaluate=(1-x)*y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
pp_convThe CUSTOM action with label pp_conv calculates the following quantities: Quantity    Type    Description  
pp_conv grid the grid obtained by doing an element-wise application of an arbitrary function to the input grid: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=pp_conv_t1,pp_conv_t2 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
pp_midpThe INTERPOLATE_GRID action with label pp_midp calculates the following quantities: Quantity    Type    Description  
pp_midp grid the function evaluated onto the interpolated grid: INTERPOLATE_GRIDInterpolate a smooth function stored on a grid onto a grid with a smaller grid spacing. More details ARGthe label for function on the grid that you would like to interpolate=pp_conv INTERPOLATION_TYPE the method to use for interpolation=linear MIDPOINTS interpolate the values of the function at the midpoints of the grid coordinates of the input grid
pp_intThe CUSTOM action with label pp_int calculates the following quantities: Quantity    Type    Description  
pp_int scalar an arbitrary function: INTEGRATE_GRIDCalculate the numerical integral of the function stored on the grid More details ARGthe label of the function on a grid that is being integrated=pp_midp PERIODICif the value of the output integral has a periodid domain then you use this keyword to specify the periodicity=NO
ppThe CUSTOM action with label pp calculates the following quantities: Quantity    Type    Description  
pp scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO ARGthe values input to this function=pp_int,pp_rdf_vol FUNCthe function you wish to evaluate=-(2*pi*x/y)*108
# --- 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=pp FILEthe name of the file on which to output these quantities=colvar

By expanding the shortct in the input above you can see how features that are already avaialble within PLUMED can be reused to calculate this CV. The resulting implementation is likely slower than the direct implementation that is available here. We hope, however, that this implementation helps others to understand how this CV is constructed.

If you would like to calculate the pair entropy based on the radial distribution of the atoms in GROUPB around GROUPA you can use an input similar to the one shown below:

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

ppThe PAIRENTROPY action with label pp calculates the following quantities: Quantity    Type    Description  
pp scalar the KL-entropy that is computed from the radial distribution function: PAIRENTROPYCalculate the KL Entropy from the radial distribution function This action is a shortcut. More details ...
   GROUPAthe atoms that you would like to compute the RDF about=1-108 GROUPBthe atoms that you would like to to use when computing the RDF around the atoms that were specified with GROUPA=109-300
   GRID_BINthe number of bins to use when computing the RDF=20 MAXRthe maximum distance to use for the rdf=2.0
   BANDWIDTHthe bandwidths for kernel density esimtation=0.13 KERNEL the type of kernel to use for computing the histograms for the RDF=gaussian
   CUTOFF the cutoff at which to stop evaluating the kernel functions is set equal to sqrt(2*x)*bandwidth in each direction where x is this number=6.25 DENSITYthe reference density to use when normalizing the RDF=1.0
...
# PLUMED interprets the command:
# pp: PAIRENTROPY ...
#    GROUPA=1-108 GROUPB=109-300
#    GRID_BIN=20 MAXR=2.0
#    BANDWIDTH=0.13 KERNEL=gaussian
#    CUTOFF=6.25 DENSITY=1.0
# ...
# as follows (Click the red comment above to revert to the short version of the input):
pp_rdfThe CUSTOM action with label pp_rdf calculates the following quantities: Quantity    Type    Description  
pp_rdf grid the grid obtained by doing an element-wise application of an arbitrary function to the input grid: RDFCalculate the radial distribution function More details GROUPAthe atoms that you would like to compute the RDF about=1-108 GROUPBthe atoms that you would like to to use when computing the RDF around the atoms that were specified with GROUPA=109-300 KERNEL the type of kernel to use for computing the histograms for the RDF=gaussian CUTOFF the cutoff at which to stop evaluating the kernel functions is set equal to sqrt(2*x)*bandwidth in each direction where x is this number=6.25 GRID_BINthe number of bins to use when computing the RDF=20 MAXRthe maximum distance to use for the rdf=2.0 DENSITYthe reference density to use when normalizing the RDF=1.0 BANDWIDTHthe bandwidths for kernel density esimtation=0.13 
pp_conv_t1The CUSTOM action with label pp_conv_t1 calculates the following quantities: Quantity    Type    Description  
pp_conv_t1 grid the grid obtained by doing an element-wise application of an arbitrary function to the input grid: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=pp_rdf,pp_rdf_x2 FUNCthe function you wish to evaluate=x*y*log(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
pp_conv_t2The CUSTOM action with label pp_conv_t2 calculates the following quantities: Quantity    Type    Description  
pp_conv_t2 grid the grid obtained by doing an element-wise application of an arbitrary function to the input grid: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=pp_rdf,pp_rdf_x2 FUNCthe function you wish to evaluate=(1-x)*y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
pp_convThe CUSTOM action with label pp_conv calculates the following quantities: Quantity    Type    Description  
pp_conv grid the grid obtained by doing an element-wise application of an arbitrary function to the input grid: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=pp_conv_t1,pp_conv_t2 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
pp_midpThe INTERPOLATE_GRID action with label pp_midp calculates the following quantities: Quantity    Type    Description  
pp_midp grid the function evaluated onto the interpolated grid: INTERPOLATE_GRIDInterpolate a smooth function stored on a grid onto a grid with a smaller grid spacing. More details ARGthe label for function on the grid that you would like to interpolate=pp_conv INTERPOLATION_TYPE the method to use for interpolation=linear MIDPOINTS interpolate the values of the function at the midpoints of the grid coordinates of the input grid
pp_intThe CUSTOM action with label pp_int calculates the following quantities: Quantity    Type    Description  
pp_int scalar an arbitrary function: INTEGRATE_GRIDCalculate the numerical integral of the function stored on the grid More details ARGthe label of the function on a grid that is being integrated=pp_midp PERIODICif the value of the output integral has a periodid domain then you use this keyword to specify the periodicity=NO
ppThe CUSTOM action with label pp calculates the following quantities: Quantity    Type    Description  
pp scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO ARGthe values input to this function=pp_int FUNCthe function you wish to evaluate=-2*pi*x*1.0
# --- 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=pp FILEthe name of the file on which to output these quantities=colvar

Notice that we have also used the DENSITY keyword to set the background density that is used when normalizing the radial distribution function explicity to 1 atom $/nm^{3}$ . When this keyword is not used, this density is calculated by dividing the number of atoms by the volume of the box as you can see if you expand the shortcut in the first input above.

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
GROUP	atoms	the atoms that are being used to calculate the RDF
GROUPA	atoms	the atoms that you would like to compute the RDF about
GROUPB	atoms	the atoms that you would like to to use when computing the RDF around the atoms that were specified with GROUPA

Full list of keywords

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

Keyword	Type	Default	Description
GROUP	input	none	the atoms that are being used to calculate the RDF
GROUPA	input	none	the atoms that you would like to compute the RDF about
GROUPB	input	none	the atoms that you would like to to use when computing the RDF around the atoms that were specified with GROUPA
GRID_BIN	compulsory	none	the number of bins to use when computing the RDF
KERNEL	compulsory	GAUSSIAN	the type of kernel to use for computing the histograms for the RDF
CUTOFF	compulsory	6.25	the cutoff at which to stop evaluating the kernel functions is set equal to sqrt(2x)bandwidth in each direction where x is this number
MAXR	compulsory	none	the maximum distance to use for the rdf
BANDWIDTH	compulsory	none	the bandwidths for kernel density esimtation
DENSITY	optional	not used	the reference density to use when normalizing the RDF

deprecated keywords

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

Keyword	Description
ATOMS	You should use GROUP instead of this keyword which was used in older versions of PLUMED and is provided for back compatibility only
SIGMA	You should use BANDWIDTH instead of this keyword which was used in older versions of PLUMED and is provided for back compatibility only

References

More information about how this action can be used is available in the following articles:

P. M. Piaggi, O. Valsson, M. Parrinello, Enhancing Entropy and Enthalpy Fluctuations to Drive Crystallization in Atomistic Simulations. Physical Review Letters. 119 (2017)

Quantity	Type	Description
pp	scalar	the KL-entropy that is computed from the radial distribution function