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 3rd order Steinhardt parameters.
The 3rd order Steinhardt parameters allow us to measure the degree to which the first coordination shell around an atom is ordered. The Steinhardt parameter for atom, \(i\) is complex vector whose components are calculated using the following formula:
where \(Y_{3m}\) is one of the 3rd order spherical harmonics so \(m\) is a number that runs from \(-3\) to \(+3\). The function \(\sigma( r_{ij} )\) is a switchingfunction that acts on the distance between atoms \(i\) and \(j\). 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 Steinhardt parameters can be used to measure the degree of order in the system in a variety of different ways. The simplest way of measuring whether or not the coordination sphere is ordered is to simply take the norm of the above vector i.e.
This norm is small when the coordination shell is disordered and larger when the coordination shell is ordered. Furthermore, when the keywords LESS_THAN, MIN, MAX, HISTOGRAM, MEAN and so on are used with this colvar it is the distribution of these normed quantities that is investigated.
Other measures of order can be taken by averaging the components of the individual \(q_3\) vectors individually or by taking dot products of the \(q_{3}\) vectors on adjacent atoms. More information on these variables can be found in the documentation for LOCAL_Q3, LOCAL_AVERAGE and NLINKS.
Examples
The following command calculates the average Q3 parameter for the 64 atoms in a box of Lennard Jones and prints this quantity to a file called colvar:
Click on the labels of the actions for more information on what each action computes
the numerical indexes for the set of atoms in the group.
=1-64 The GROUP action with label q3_grp defines a group of atoms so that they can be referred to later in the inputq3_mat: CONTACT_MATRIX
GROUP
specifies the list of atoms that should be assumed indistinguishable.
=1-64
R_0
could not find this keyword
=0.2
D_0
could not find this keyword
=1.3
NN
compulsory keyword ( default=6 )
The n parameter of the switching function
=6
MM
compulsory keyword ( default=0 )
The m parameter of the switching function; 0 implies 2*NN
=0
COMPONENTS
( default=off ) also calculate the components of the vector connecting the atoms
in the contact matrix
The CONTACT_MATRIX action with label q3_mat calculates the following quantities:
Quantity
Description
q3_mat.w
The following command calculates the histogram of Q3 parameters for the 64 atoms in a box of Lennard Jones and prints these quantities to a file called colvar:
Click on the labels of the actions for more information on what each action computes
the numerical indexes for the set of atoms in the group.
=1-64 The GROUP action with label q3_grp defines a group of atoms so that they can be referred to later in the inputq3_mat: CONTACT_MATRIX
GROUP
specifies the list of atoms that should be assumed indistinguishable.
=1-64
R_0
could not find this keyword
=0.2
D_0
could not find this keyword
=1.3
NN
compulsory keyword ( default=6 )
The n parameter of the switching function
=6
MM
compulsory keyword ( default=0 )
The m parameter of the switching function; 0 implies 2*NN
=0
COMPONENTS
( default=off ) also calculate the components of the vector connecting the atoms
in the contact matrix
The CONTACT_MATRIX action with label q3_mat calculates the following quantities:
Quantity
Description
q3_mat.w
The following command could be used to measure the Q3 parameters that describe the arrangement of chlorine ions around the sodium atoms in sodium chloride. The imagined system here is composed of 64 NaCl formula units and the atoms are arranged in the input with the 64 Na \(^+\) ions followed by the 64 Cl \(-\) ions. Once again the average Q3 parameter is calculated and output to a file called colvar
Click on the labels of the actions for more information on what each action computes
the numerical indexes for the set of atoms in the group.
=1-64 The GROUP action with label q3_grp defines a group of atoms so that they can be referred to later in the inputq3_mat: CONTACT_MATRIX
GROUPA
.
=1-64
GROUPB
.
=65-128
R_0
could not find this keyword
=0.2
D_0
could not find this keyword
=1.3
NN
compulsory keyword ( default=6 )
The n parameter of the switching function
=6
MM
compulsory keyword ( default=0 )
The m parameter of the switching function; 0 implies 2*NN
=0
COMPONENTS
( default=off ) also calculate the components of the vector connecting the atoms
in the contact matrix
The CONTACT_MATRIX action with label q3_mat calculates the following quantities:
Quantity
Description
q3_mat.w
If you simply want to examine the values of the Q3 parameters for each of the atoms in your system you can do so by exploiting the command DUMPATOMS as shown in the example below. The following output file will output a file in an extended xyz format called q3.xyz for each frame of the analyzed MD trajectory. The first column in this file will contain a dummy name for each of the atoms, columns 2-4 will then contain the x, y and z positions of the atoms, column 5 will contain the value of the Q3 parameter, columns 6-12 will contain the real parts of the director of the \(q_{3m}\) vector while columns 12-19 will contain the imaginary parts of this director.
Click on the labels of the actions for more information on what each action computes
this keyword is used for colvars such as the coordination number.
=1-64
SPECIESB
this keyword is used for colvars such as the coordination number.
=65-128
D_0
could not find this keyword
=1.3
R_0
could not find this keyword
=0.2
MEAN
( default=off ) calculate the mean of all the quantities.
You cannot view the components that are calculated by each action for this input file. Sorry DUMPATOMS
ATOMS
the atom indices whose positions you would like to print out.
=q3
ARG
the input for this action is the scalar output from one or more other actions.
=q3_anorm
FILE
compulsory keyword
file on which to output coordinates; extension is automatically detected
=q3.xyz You cannot view the components that are calculated by each action for this input file. Sorry
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
_vmean
VMEAN
the norm of the mean vector
_vsum
VSUM
the norm of the mean vector
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.
LOWMEM
( default=off ) this flag does nothing and is present only to ensure back-compatibility
VMEAN
( default=off ) calculate the norm of the mean vector.
VSUM
( default=off ) calculate the norm of the sum of all the vectors
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.
