	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 coordination numbers of atoms so that you can then calculate functions of the distribution of coordination numbers such as the minimum, the number less than a certain quantity and so on.

So that the calculated coordination numbers have continuous derivatives the following function is used:

\[ s = \frac{ 1 - \left(\frac{r-d_0}{r_0}\right)^n } { 1 - \left(\frac{r-d_0}{r_0}\right)^m } \]

If R_POWER is set, this will use the product of pairwise distance raised to the R_POWER with the coordination number function defined above. This was used in White and Voth [114] as a way of indirectly biasing radial distribution functions. Note that in that reference this function is referred to as moments of coordination number, but here we call them powers to distinguish from the existing MOMENTS keyword of Multicolvars.

Examples

The following input tells plumed to calculate the coordination numbers of atoms 1-100 with themselves. The minimum coordination number is then calculated.

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

COORDINATIONNUMBER SPECIESthis keyword is used for colvars such as coordination number. 
=1-100 R_0 could not find this keyword 
=1.0 MINcalculate the minimum value. 
={BETA=0.1}  The COORDINATIONNUMBER action with label

@0_grp: GROUP ATOMSthe numerical indexes for the set of atoms in the group. 
=1-100 The GROUP action with label @0_grp defines a group of atoms so that they can be referred to later in the input
@0_mat: CONTACT_MATRIX GROUPspecifies the list of atoms that should be assumed indistinguishable. 
=1-100 R_0 could not find this keyword 
=1.0 D_0 could not find this keyword 
=0.0 NNcompulsory keyword ( default=6 )
The n parameter of the switching function 
=6 MMcompulsory keyword ( default=0 )
The m parameter of the switching function; 0 implies 2*NN 
=0 The CONTACT_MATRIX action with label @0_mat calculates a single scalar value
@0_ones: ONES SIZEcompulsory keyword 
the number of ones that you would like to create 
=100 The ONES action with label @0_ones calculates a single scalar value
@0: MATRIX_VECTOR_PRODUCT ARGthe input for this action is the scalar output from one or more other actions. 
=@0_mat,@0_ones The MATRIX_VECTOR_PRODUCT action with label @0 calculates a single scalar value
@0_caverage: MEAN ARGthe input to this function. 
=@0 PERIODICcompulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The MEAN action with label @0_caverage calculates a single scalar value
@0_me_min: CUSTOM ARGthe input to this function. 
=@0 FUNCcompulsory keyword 
the function you wish to evaluate 
=exp(0.1/x) PERIODICcompulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The CUSTOM action with label @0_me_min calculates a single scalar value
@0_mec_min: SUM ARGthe input to this function. 
=@0_me_min PERIODICcompulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The SUM action with label @0_mec_min calculates a single scalar value
@0_min: CUSTOM ARGthe input to this function. 
=@0_mec_min FUNCcompulsory keyword 
the function you wish to evaluate 
=0.1/log(x) PERIODICcompulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The CUSTOM action with label @0_min calculates a single scalar value

The following input tells plumed to calculate how many atoms from 1-100 are within 3.0 of each of the atoms from 101-110. In the first 101 is the central atom, in the second 102 is the central atom and so on. The number of coordination numbers more than 6 is then computed.

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

COORDINATIONNUMBER SPECIESAthis keyword is used for colvars such as the coordination number. 
=101-110 SPECIESBthis keyword is used for colvars such as the coordination number. 
=1-100 R_0 could not find this keyword 
=3.0 MORE_THANcalculate the number of variables that are more than a certain target value. 
={RATIONAL R_0=6.0 NN=6 MM=12 D_0=0}  The COORDINATIONNUMBER action with label

@0_grp: GROUP ATOMSthe numerical indexes for the set of atoms in the group. 
=101-110 The GROUP action with label @0_grp defines a group of atoms so that they can be referred to later in the input
@0_mat: CONTACT_MATRIX GROUPA. 
=101-110 GROUPB. 
=1-100 R_0 could not find this keyword 
=3.0 D_0 could not find this keyword 
=0.0 NNcompulsory keyword ( default=6 )
The n parameter of the switching function 
=6 MMcompulsory keyword ( default=0 )
The m parameter of the switching function; 0 implies 2*NN 
=0 The CONTACT_MATRIX action with label @0_mat calculates a single scalar value
@0_ones: ONES SIZEcompulsory keyword 
the number of ones that you would like to create 
=100 The ONES action with label @0_ones calculates a single scalar value
@0: MATRIX_VECTOR_PRODUCT ARGthe input for this action is the scalar output from one or more other actions. 
=@0_mat,@0_ones The MATRIX_VECTOR_PRODUCT action with label @0 calculates a single scalar value
@0_caverage: MEAN ARGthe input to this function. 
=@0 PERIODICcompulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The MEAN action with label @0_caverage calculates a single scalar value
@0_mt: MORE_THAN ARGthe input to this function. 
=@0 SWITCHThis keyword is used if you want to employ an alternative to the continuous swiching
function defined above. 
=RATIONAL,R_0=6.0,NN=6,MM=12,D_0=0 The MORE_THAN action with label @0_mtThe following input tells plumed to calculate the mean coordination number of all atoms with themselves and its powers. An explicit cutoff is set for each of 8. 
 Click on the labels of the actions for more information on what each action computes 
cn0: COORDINATIONNUMBER SPECIESthis keyword is used for colvars such as coordination number. 
=1-10 SWITCHthe switching function that it used in the construction of the contact matrix 
={RATIONAL R_0=1.0 D_MAX=8}  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 
cn1: COORDINATIONNUMBER SPECIESthis keyword is used for colvars such as coordination number. 
=1-10 SWITCHthe switching function that it used in the construction of the contact matrix 
={RATIONAL R_0=1.0 D_MAX=8}  R_POWERcompulsory keyword 
the power to which you want to raise the distance 
=1 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 
cn2: COORDINATIONNUMBER SPECIESthis keyword is used for colvars such as coordination number. 
=1-10 SWITCHthe switching function that it used in the construction of the contact matrix 
={RATIONAL R_0=1.0 D_MAX=8}  R_POWERcompulsory keyword 
the power to which you want to raise the distance 
=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 
PRINT ARGthe input for this action is the scalar output from one or more other actions. 
=cn0.mean,cn1.mean,cn2.mean STRIDEcompulsory keyword ( default=1 )
the frequency with which the quantities of interest should be output 
=1 FILEthe name of the file on which to output these quantities 
=cn_out  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   

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   

 R_POWER  the power to which you want to raise the distance   

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.   

 MOMENTS  the list of moments that you would like to calculate

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

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
R_POWER	the power to which you want to raise the distance

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.
MOMENTS	the list of moments that you would like to calculate