Shortcut: RESTRAINT

Module	bias
Description	Usage
Adds harmonic and/or linear restraints on one or more variables.

Details and examples

Adds harmonic and/or linear restraints on one or more variables.

Either or both of SLOPE and KAPPA must be present to specify the linear and harmonic force constants respectively. If the input arguments are scalars the resulting potential is given by:

$\sum_i \frac{k_i}{2} (x_i-a_i)^2 + m_i*(x_i-a_i)$ .

The following example input illustrates how you can apply a potential of this type. This input tells plumed to restrain the distance between atoms 3 and 5 and the distance between atoms 2 and 4, at different equilibrium values, and to print the energy of the restraint

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

d1The DISTANCE action with label d1 calculates the following quantities: Quantity    Type    Description  
d1 scalar the DISTANCE between this pair of atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=3,5
d2The DISTANCE action with label d2 calculates the following quantities: Quantity    Type    Description  
d2 scalar the DISTANCE between this pair of atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=2,4
restraintThe RESTRAINT action with label restraint calculates the following quantities: Quantity    Type    Description  
restraint.bias scalar the instantaneous value of the bias potential
restraint.force2 scalar the instantaneous value of the squared force due to this bias potential: RESTRAINTAdds harmonic and/or linear restraints on one or more variables. This action has hidden defaults. More details ARGthe values the harmonic restraint acts upon=d1,d2 ATthe position of the restraint=1.0,1.5 KAPPA specifies that the restraint is harmonic and what the values of the force constants on each of the variables are=150.0,150.0
restraint: RESTRAINTAdds harmonic and/or linear restraints on one or more variables. This action uses the defaults shown here. More details ARGthe values the harmonic restraint acts upon=d1,d2 ATthe position of the restraint=1.0,1.5 KAPPA specifies that the restraint is harmonic and what the values of the force constants on each of the variables are=150.0,150.0  SLOPE specifies that the restraint is linear and what the values of the force constants on each of the variables are=0.0,0.0
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=restraint.bias

If by contrast the inputs are vectors as in the example below:

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

d1The DISTANCE action with label d1 calculates the following quantities: Quantity    Type    Description  
d1 vector the DISTANCE for each set of specified atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMS1the pair of atom that we are calculating the distance between=3,5 ATOMS2the pair of atom that we are calculating the distance between=5,6 ATOMS3the pair of atom that we are calculating the distance between=6,7
d2The DISTANCE action with label d2 calculates the following quantities: Quantity    Type    Description  
d2 vector the DISTANCE for each set of specified atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMS1the pair of atom that we are calculating the distance between=2,4 ATOMS2the pair of atom that we are calculating the distance between=4,6 ATOMS3the pair of atom that we are calculating the distance between=6,8
restraintThe RESTRAINT action with label restraint calculates the following quantities: Quantity    Type    Description  
restraint_bias scalar the instantaneous value of the bias potential
restraint_force2 vector the instantaneous value of the squared force due to this bias potential: RESTRAINTAdds harmonic and/or linear restraints on one or more variables. This action is a shortcut and it has hidden defaults. More details ARGthe values the harmonic restraint acts upon=d1,d2 ATthe position of the restraint=1.0,1.5 KAPPA specifies that the restraint is harmonic and what the values of the force constants on each of the variables are=150.0,150.0
restraint: RESTRAINTAdds harmonic and/or linear restraints on one or more variables. This action is a shortcut and uses the defaults shown here. More details ARGthe values the harmonic restraint acts upon=d1,d2 ATthe position of the restraint=1.0,1.5 KAPPA specifies that the restraint is harmonic and what the values of the force constants on each of the variables are=150.0,150.0  STRIDE the frequency with which the forces due to the bias should be calculated=1 SLOPE specifies that the restraint is linear and what the values of the force constants on each of the variables are=0.0,0.0
# PLUMED interprets the command:
# restraint: RESTRAINT ARG=d1,d2 AT=1.0,1.5 KAPPA=150.0,150.0
# as follows (Click the red comment above to revert to the short version of the input):
restraint_cv_d1The COMBINE action with label restraint_cv_d1 calculates the following quantities: Quantity    Type    Description  
restraint_cv_d1 vector the vector obtained by doing an element-wise application of a linear combination to the input vectors: COMBINECalculate a polynomial combination of a set of other variables. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO ARGthe values input to this function=d1 PARAMETERS the parameters of the arguments in your function=1.0
restraint_harm_d1The CUSTOM action with label restraint_harm_d1 calculates the following quantities: Quantity    Type    Description  
restraint_harm_d1 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=0.5*150.0*x^2 ARGthe values input to this function=restraint_cv_d1
restraint_kap_d1The SUM action with label restraint_kap_d1 calculates the following quantities: Quantity    Type    Description  
restraint_kap_d1 scalar the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO ARGthe vector/matrix/grid whose elements shuld be added together=restraint_harm_d1
restraint_f2_d1The CUSTOM action with label restraint_f2_d1 calculates the following quantities: Quantity    Type    Description  
restraint_f2_d1 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=150.0*2*x+0.0*0.0 ARGthe values input to this function=restraint_harm_d1
restraint_cv_d2The COMBINE action with label restraint_cv_d2 calculates the following quantities: Quantity    Type    Description  
restraint_cv_d2 vector the vector obtained by doing an element-wise application of a linear combination to the input vectors: COMBINECalculate a polynomial combination of a set of other variables. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO ARGthe values input to this function=d2 PARAMETERS the parameters of the arguments in your function=1.5
restraint_harm_d2The CUSTOM action with label restraint_harm_d2 calculates the following quantities: Quantity    Type    Description  
restraint_harm_d2 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=0.5*150.0*x^2 ARGthe values input to this function=restraint_cv_d2
restraint_kap_d2The SUM action with label restraint_kap_d2 calculates the following quantities: Quantity    Type    Description  
restraint_kap_d2 scalar the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO ARGthe vector/matrix/grid whose elements shuld be added together=restraint_harm_d2
restraint_f2_d2The CUSTOM action with label restraint_f2_d2 calculates the following quantities: Quantity    Type    Description  
restraint_f2_d2 vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=150.0*2*x+0.0*0.0 ARGthe values input to this function=restraint_harm_d2
restraint_biasThe COMBINE action with label restraint_bias calculates the following quantities: Quantity    Type    Description  
restraint_bias scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO ARGthe values input to this function=restraint_kap_d1,restraint_kap_d2
restraintThe BIASVALUE action with label restraint calculates the following quantities: Quantity    Type    Description  
restraint.bias scalar the instantaneous value of the bias potential
restraint.restraint_bias_bias scalar one or multiple instances of this quantity can be referenced elsewhere in the input file. these quantities will named with  the arguments of the bias followed by the character string _bias. These quantities tell the user how much the bias is due to each of the colvars. This particular component measures this quantity for the input CV named restraint_bias: BIASVALUETakes the value of one variable and use it as a bias More details ARGthe labels of the scalar/vector arguments whose values will be used as a bias on the system=restraint_bias STRIDEthe frequency with which the forces due to the bias should be calculated=1
restraint_force2The COMBINE action with label restraint_force2 calculates the following quantities: Quantity    Type    Description  
restraint_force2 vector the vector obtained by doing an element-wise application of a linear combination to the input vectors: COMBINECalculate a polynomial combination of a set of other variables. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO ARGthe values input to this function=restraint_f2_d1,restraint_f2_d2
# --- End of included input --- PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=restraint.bias

Then the resulting potential is given by:

$\sum_i \sum_j \frac{k_i}{2} (x_{ij}-a_i)^2 + m_i*(x_{ij}-a_i)$

The sum over $i$ here is runs over the two arguments, while the sum over $j$ runs over the three components of the input vectors. Notice, that regardless of whether the input is a scalar, vector or matrix the number of $k_i$ , $a_i$ and $m_i$ values must be equal to the number of arguments to the action.

Input

The arguments that serve as the input for this action are specified using one or more of the keywords in the following table.

Keyword	Type	Description
ARG	scalar/vector	the values the harmonic restraint acts upon

Output components

This action calculates the values in the following table. These values can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the value required from the list below.

Name	Type	Description
bias	scalar	the instantaneous value of the bias potential
force2	scalar/vector	the instantaneous value of the squared force due to this bias potential

Full list of keywords

The following table describes the keywords and options that can be used with this action

Keyword	Type	Default	Description
ARG	input	none	the values the harmonic restraint acts upon
SLOPE	compulsory	0.0	specifies that the restraint is linear and what the values of the force constants on each of the variables are
KAPPA	compulsory	0.0	specifies that the restraint is harmonic and what the values of the force constants on each of the variables are
AT	compulsory	none	the position of the restraint

Quantity	Type	Description
d1	scalar	the DISTANCE between this pair of atoms