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.
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.
d1: COORDINATIONNUMBERSPECIES=1-64this keyword is used for colvars such as coordination number.D_0=1.3could not find this keywordR_0=0.2 la: LOCAL_AVERAGEcould not find this keywordARG=d1could not find this keywordSWITCH={RATIONAL D_0=1.3 R_0=0.2}the switching function that it used in the construction of the contact matrixMORE_THAN={RATIONAL R_0=4} PRINTcalculate the number of variables that are more than a certain target value.ARG=la.*the input for this action is the scalar output from one or more other actions.FILE=colvarthe name of the file on which to output these quantities
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]
q4: Q4SPECIES=1-64this keyword is used for colvars such as coordination number.SWITCH={RATIONAL D_0=1.3 R_0=0.2} la: LOCAL_AVERAGEthe switching function that it used in the construction of the contact matrixARG=q4could not find this keywordSWITCH={RATIONAL D_0=1.3 R_0=0.2}the switching function that it used in the construction of the contact matrixMEANPRINT( default=off ) calculate the mean of all the quantities.ARG=la.*the input for this action is the scalar output from one or more other actions.FILE=colvarthe name of the file on which to output these quantities
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 |
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 |
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 |
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 |
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. |