LOCAL_AVERAGE
This is part of the symfunc module
It is only available if you configure PLUMED with ./configure –enable-modules=symfunc . Furthermore, this feature is still being developed so take care when using it and report any problems on the mailing list.

Calculate averages over spherical regions centered on atoms

As is explained in this video certain multicolvars calculate one scalar quantity or one vector for each of the atoms in the system. For example COORDINATIONNUMBER measures the coordination number of each of the atoms in the system and Q4 measures the 4th order Steinhardt parameter for each of the atoms in the system. These quantities provide tell us something about the disposition of the atoms in the first coordination sphere of each of the atoms of interest. Lechner and Dellago [65] have suggested that one can probe local order in a system by taking the average value of such symmetry functions over the atoms within a spherical cutoff of each of these atoms in the systems. When this is done with Steinhardt parameters they claim this gives a coordinate that is better able to distinguish solid and liquid configurations of Lennard-Jones atoms.

You can calculate such locally averaged quantities within plumed by using the LOCAL_AVERAGE command. This command calculates the following atom-centered quantities:

\[ s_i = \frac{ c_i + \sum_j \sigma(r_{ij})c_j }{ 1 + \sum_j \sigma(r_{ij}) } \]

where the \(c_i\) and \(c_j\) values can be for any one of the symmetry functions that can be calculated using plumed multicolvars. The function \(\sigma( r_{ij} )\) is a switchingfunction that acts on the distance between atoms \(i\) and \(j\). Lechner and Dellago suggest that the parameters of this function should be set so that it the function is equal to one when atom \(j\) is in the first coordination sphere of atom \(i\) and is zero otherwise.

The \(s_i\) quantities calculated using the above command can be again thought of as atom-centred symmetry functions. They thus operate much like multicolvars. You can thus calculate properties of the distribution of \(s_i\) values using MEAN, LESS_THAN, HISTOGRAM and so on. You can also probe the value of these averaged variables in regions of the box by using the command in tandem with the AROUND command.

Examples

This example input calculates the coordination numbers for all the atoms in the system. These coordination numbers are then averaged over spherical regions. The number of averaged coordination numbers that are greater than 4 is then output to a file.

Click on the labels of the actions for more information on what each action computes
tested on master
d1: COORDINATIONNUMBER 
SPECIES
this keyword is used for colvars such as coordination number.
=1-64
D_0
could not find this keyword
=1.3
R_0
could not find this keyword
=0.2 la: LOCAL_AVERAGE
ARG
could not find this keyword
=d1
SWITCH
the switching function that it used in the construction of the contact matrix
={RATIONAL D_0=1.3 R_0=0.2}
MORE_THAN
calculate the number of variables that are more than a certain target value.
={RATIONAL R_0=4} PRINT
ARG
the input for this action is the scalar output from one or more other actions.
=la.*
FILE
the name of the file on which to output these quantities
=colvar

This example input calculates the \(q_4\) (see Q4) vectors for each of the atoms in the system. These vectors are then averaged component by component over a spherical region. The average value for this quantity is then outputeed to a file. This calculates the quantities that were used in the paper by Lechner and Dellago [65]

Click on the labels of the actions for more information on what each action computes
tested on master
q4: Q4 
SPECIES
this keyword is used for colvars such as coordination number.
=1-64
SWITCH
the switching function that it used in the construction of the contact matrix
={RATIONAL D_0=1.3 R_0=0.2} la: LOCAL_AVERAGE
ARG
could not find this keyword
=q4
SWITCH
the switching function that it used in the construction of the contact matrix
={RATIONAL D_0=1.3 R_0=0.2}
MEAN
( default=off ) calculate the mean of all the quantities.
PRINT
ARG
the input for this action is the scalar output from one or more other actions.
=la.*
FILE
the name of the file on which to output these quantities
=colvar
Glossary of keywords and components
Description of components
Quantity Keyword Description
lessthan LESS_THAN the number of colvars that have a value less than a threshold
morethan MORE_THAN the number of colvars that have a value more than a threshold
altmin ALT_MIN the minimum value of the cv
min MIN the minimum colvar
max MAX the maximum colvar
between BETWEEN the number of colvars that have a value that lies in a particular interval
highest HIGHEST the largest of the colvars
lowest LOWEST the smallest of the colvars
sum SUM the sum of the colvars
mean MEAN the mean of the colvars
The atoms involved can be specified using
SPECIES this keyword is used for colvars such as coordination number. In that context it specifies that plumed should calculate one coordination number for each of the atoms specified. Each of these coordination numbers specifies how many of the other specified atoms are within a certain cutoff of the central atom. You can specify the atoms here as another multicolvar action or using a MultiColvarFilter or ActionVolume action. When you do so the quantity is calculated for those atoms specified in the previous multicolvar. This is useful if you would like to calculate the Steinhardt parameter for those atoms that have a coordination number more than four for example
Or alternatively by using
SPECIESA this keyword is used for colvars such as the coordination number. In that context it species that plumed should calculate one coordination number for each of the atoms specified in SPECIESA. Each of these cooordination numbers specifies how many of the atoms specifies using SPECIESB is within the specified cutoff. As with the species keyword the input can also be specified using the label of another multicolvar
SPECIESB this keyword is used for colvars such as the coordination number. It must appear with SPECIESA. For a full explanation see the documentation for that keyword
Compulsory keywords
NN ( default=6 ) The n parameter of the switching function
MM ( default=0 ) The m parameter of the switching function; 0 implies 2*NN
D_0 ( default=0.0 ) The d_0 parameter of the switching function
R_0 The r_0 parameter of the switching function
Options
HIGHEST ( default=off ) this flag allows you to recover the highest of these variables.
LOWEST ( default=off ) this flag allows you to recover the lowest of these variables.
SUM ( default=off ) calculate the sum of all the quantities.
MEAN

( default=off ) calculate the mean of all the quantities.

SWITCH the switching function that it used in the construction of the contact matrix
LESS_THAN calculate the number of variables that are less than a certain target value. This quantity is calculated using \(\sum_i \sigma(s_i)\), where \(\sigma(s)\) is a switchingfunction.. You can use multiple instances of this keyword i.e. LESS_THAN1, LESS_THAN2, LESS_THAN3...
MORE_THAN calculate the number of variables that are more than a certain target value. This quantity is calculated using \(\sum_i 1 - \sigma(s_i)\), where \(\sigma(s)\) is a switchingfunction.. You can use multiple instances of this keyword i.e. MORE_THAN1, MORE_THAN2, MORE_THAN3...
ALT_MIN calculate the minimum value. To make this quantity continuous the minimum is calculated using \( \textrm{min} = -\frac{1}{\beta} \log \sum_i \exp\left( -\beta s_i \right) \) The value of \(\beta\) in this function is specified using (BETA= \(\beta\)).
MIN calculate the minimum value. To make this quantity continuous the minimum is calculated using \( \textrm{min} = \frac{\beta}{ \log \sum_i \exp\left( \frac{\beta}{s_i} \right) } \) The value of \(\beta\) in this function is specified using (BETA= \(\beta\))
MAX calculate the maximum value. To make this quantity continuous the maximum is calculated using \( \textrm{max} = \beta \log \sum_i \exp\left( \frac{s_i}{\beta}\right) \) The value of \(\beta\) in this function is specified using (BETA= \(\beta\))
BETWEEN calculate the number of values that are within a certain range. These quantities are calculated using kernel density estimation as described on histogrambead.. You can use multiple instances of this keyword i.e. BETWEEN1, BETWEEN2, BETWEEN3...
HISTOGRAM calculate a discretized histogram of the distribution of values. This shortcut allows you to calculates NBIN quantites like BETWEEN.