TETRAHEDRAL

	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 the degree to which the environment about ions has a tetrahedral order.

We can measure the degree to which the atoms in the first coordination shell around any atom, \(i\) is is arranged like a tetrahedron using the following function.

\[ s(i) = \frac{1}{\sum_j \sigma( r_{ij} )} \sum_j \sigma( r_{ij} )\left[ \frac{(x_{ij} + y_{ij} + z_{ij})^3}{r_{ij}^3} + \frac{(x_{ij} - y_{ij} - z_{ij})^3}{r_{ij}^3} + \frac{(-x_{ij} + y_{ij} - z_{ij})^3}{r_{ij}^3} + \frac{(-x_{ij} - y_{ij} + z_{ij})^3}{r_{ij}^3} \right] \]

Here \(r_{ij}\) is the magnitude of the vector connecting atom \(i\) to atom \(j\) and \(x_{ij}\), \(y_{ij}\) and \(z_{ij}\) are its three components. 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 the function is equal to one when atom \(j\) is in the first coordination sphere of atom \(i\) and is zero otherwise.

Examples

The following command calculates the average value of the TETRAHEDRAL parameter for a set of 64 atoms all of the same type and outputs this quantity to a file called colvar.

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

contract shortcuts

tt: TETRAHEDRAL 
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}  
MEAN
( default=off ) calculate the mean of all the quantities. 
 The TETRAHEDRAL action with label tt calculates a single scalar value
PRINT 
ARG
the input for this action is the scalar output from one or more other actions. 
=tt.mean 
FILE
the name of the file on which to output these quantities 
=colvar The PRINT action with label 

tt_grp: GROUP 
ATOMS
the numerical indexes for the set of atoms in the group. 
=1-64 The GROUP action with label tt_grp defines a group of atoms so that they can be referred to later in the input
tt_mat: CONTACT_MATRIX 
GROUP
specifies the list of atoms that should be assumed indistinguishable. 
=1-64 
SWITCH
specify the switching function to use between two sets of indistinguishable atoms.
=RATIONAL,D_0=1.3,R_0=0.2 
COMPONENTS
( default=off ) also calculate the components of the vector connecting the atoms
in the contact matrix 
 The CONTACT_MATRIX action with label tt_mat
The following command calculates the number of TETRAHEDRAL parameters that are greater than 0.8 in a set of 10 atoms. In this calculation it is assumed that there are two atom types A and B and that the first coordination sphere of the 10 atoms of type A contains atoms of type B. The formula above is thus calculated for ten different A atoms and within it the sum over \(j\) runs over 40 atoms of type B that could be in the first coordination sphere.

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




tt: TETRAHEDRAL 
SPECIESA
this keyword is used for colvars such as the coordination number. 
=1-10 
SPECIESB
this keyword is used for colvars such as the coordination number. 
=11-40 
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=0.8}  The TETRAHEDRAL action with label tt calculates a single scalar value
PRINT 
ARG
the input for this action is the scalar output from one or more other actions. 
=tt.* 
FILE
the name of the file on which to output these quantities 
=colvar The PRINT action with label 


tt_grp: GROUP 
ATOMS
the numerical indexes for the set of atoms in the group. 
=1-10 The GROUP action with label tt_grp defines a group of atoms so that they can be referred to later in the input
tt_mat: CONTACT_MATRIX 
GROUPA
. 
=1-10 
GROUPB
. 
=11-40 
SWITCH
specify the switching function to use between two sets of indistinguishable atoms.
=RATIONAL,D_0=1.3,R_0=0.2 
COMPONENTS
( default=off ) also calculate the components of the vector connecting the atoms
in the contact matrix 
 The CONTACT_MATRIX action with label tt_mat
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   

 FUNCTION  
the function of the bond vectors that you would like to evaluate   

 PHI  
( default=0.0 ) The Euler rotational angle phi   

 THETA  
( default=0.0 ) The Euler rotational angle theta   

 PSI  
( default=0.0 ) The Euler rotational angle psi   

 ALPHA  
( default=3.0 ) The alpha parameter of the angular function that is used for FCCUBIC   

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  



 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.