Action: EXTENDED_LAGRANGIAN

Module	bias
Description	Usage
Add extended Lagrangian.

Details and examples

Add extended Lagrangian.

This action can be used to create fictitious collective variables that are coupled to the real ones. In this method potential and kinetic contributions are added to the energy of the system using

$V=\sum_i \frac{k_i}{2} (x_i-s_i)^2 + \sum_i \frac{\dot{s}_i^2}{2m_i}$ .

In this expression, $x_i$ is the $i$ th scalar-argument that is input to the bias potential so the resulting potential is similar to a RESTRAINT that is forced to take scalars in input. However, in this method the restraint center moves with time following Hamiltonian dynamics with mass $m_i$ .

This bias potential accepts thus vectorial keywords (one element per argument) to define the coupling constant (KAPPA) and a relaxation time $tau$ (TAU). The mass is them computed as $m=k(\frac{\tau}{2\pi})^2$ .

Notice that this action creates several components. The ones named XX_fict are the fictitious coordinates. It is possible to add further forces on them by means of other bias potential, e.g. to obtain an indirect METAD as in the first paper cited below. Also notice that the velocities of the fictitious coordinates are reported (XX_vfict). However, printed velocities are the ones at the previous step.

It is also possible to provide a non-zero friction (one value per component). This is then used to implement a Langevin thermostat, so as to implement the TAMD/dAFED method that is discussed in the second two papers cited below. Notice that here a massive Langevin thermostat is used, whereas usually TAMD employs an overamped Langevin dynamics while dAFED employs a Gaussian thermostat.

!!!! warning "bias not campatible with replica exchange"

 The bias potential is reported in the component bias.
 Notice that this bias potential, although formally compatible with
 replica exchange framework, probably does not work as expected in that case.
 Indeed, since fictitious coordinates are not swapped upon exchange,
 acceptace can be expected to be extremely low unless (by chance) two neighboring
 replicas have the fictitious variables located properly in space.

restart not supported

RESTART is not properly supported by this action. Indeed, at every start the position of the fictitious variable is reset to the value of the real variable, and its velocity is set to zero. This is not expected to introduce big errors, but certainly is introducing a small inconsistency between a single long run and many shorter runs.

Examples

The following input tells plumed to perform a metadynamics with an extended Lagrangian on two torsional angles.

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

phiThe TORSION action with label phi calculates the following quantities: Quantity    Type    Description  
phi scalar the TORSION involving these atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMSthe four atoms involved in the torsional angle=5,7,9,15
psiThe TORSION action with label psi calculates the following quantities: Quantity    Type    Description  
psi scalar the TORSION involving these atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMSthe four atoms involved in the torsional angle=7,9,15,17
exThe EXTENDED_LAGRANGIAN action with label ex calculates the following quantities: Quantity    Type    Description  
ex.bias scalar the instantaneous value of the bias potential
ex.phi_fict 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 _tilde. It is possible to add forces on these variable. This particular component measures this quantity for the input CV named phi
ex.phi_vfict 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 _tilde. It is NOT possible to add forces on these variable. This particular component measures this quantity for the input CV named phi
ex.psi_fict 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 _tilde. It is possible to add forces on these variable. This particular component measures this quantity for the input CV named psi
ex.psi_vfict 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 _tilde. It is NOT possible to add forces on these variable. This particular component measures this quantity for the input CV named psi: EXTENDED_LAGRANGIANAdd extended Lagrangian. This action has hidden defaults. More details ARGthe labels of the scalars on which the bias will act=phi,psi KAPPAspecifies that the restraint is harmonic and what the values of the force constants on each of the variables are=20,20.0 TAUspecifies that the restraint is harmonic and what the values of the force constants on each of the variables are=0.1,0.1
ex: EXTENDED_LAGRANGIANAdd extended Lagrangian. This action uses the defaults shown here. More details ARGthe labels of the scalars on which the bias will act=phi,psi KAPPAspecifies that the restraint is harmonic and what the values of the force constants on each of the variables are=20,20.0 TAUspecifies that the restraint is harmonic and what the values of the force constants on each of the variables are=0.1,0.1  FRICTION add a friction to the variable=0.0,0.0
METADUsed to performed metadynamics on one or more collective variables. More details ARGthe labels of the scalars on which the bias will act=ex.phi_fict,ex.psi_fict PACEthe frequency for hill addition=100 SIGMAthe widths of the Gaussian hills=0.35,0.35 HEIGHTthe heights of the Gaussian hills=0.1
# monitor the two variables
The METAD action with label  calculates the following quantities: Quantity    Description  
.bias the instantaneous value of the bias potentialPRINTPrint quantities to a file. More details STRIDE the frequency with which the quantities of interest should be output=10 ARGthe labels of the values that you would like to print to the file=phi,psi,ex.phi_fict,ex.psi_fict FILEthe name of the file on which to output these quantities=COLVAR

The following input tells plumed to perform a TAMD (or dAFED) calculation on two torsional angles, keeping the two variables at a fictitious temperature of 3000K with a Langevin thermostat with friction 10

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

phiThe TORSION action with label phi calculates the following quantities: Quantity    Type    Description  
phi scalar the TORSION involving these atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMSthe four atoms involved in the torsional angle=5,7,9,15
psiThe TORSION action with label psi calculates the following quantities: Quantity    Type    Description  
psi scalar the TORSION involving these atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMSthe four atoms involved in the torsional angle=7,9,15,17
exThe EXTENDED_LAGRANGIAN action with label ex calculates the following quantities: Quantity    Type    Description  
ex.bias scalar the instantaneous value of the bias potential
ex.phi_fict 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 _tilde. It is possible to add forces on these variable. This particular component measures this quantity for the input CV named phi
ex.phi_vfict 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 _tilde. It is NOT possible to add forces on these variable. This particular component measures this quantity for the input CV named phi
ex.psi_fict 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 _tilde. It is possible to add forces on these variable. This particular component measures this quantity for the input CV named psi
ex.psi_vfict 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 _tilde. It is NOT possible to add forces on these variable. This particular component measures this quantity for the input CV named psi: EXTENDED_LAGRANGIANAdd extended Lagrangian. More details ARGthe labels of the scalars on which the bias will act=phi,psi KAPPAspecifies that the restraint is harmonic and what the values of the force constants on each of the variables are=20,20.0 TAUspecifies that the restraint is harmonic and what the values of the force constants on each of the variables are=0.1,0.1 FRICTION add a friction to the variable=10,10 TEMPthe system temperature - needed when FRICTION is present=3000
# monitor the two variables
PRINTPrint quantities to a file. More details STRIDE the frequency with which the quantities of interest should be output=10 ARGthe labels of the values that you would like to print to the file=phi,psi,ex.phi_fict,ex.psi_fict FILEthe name of the file on which to output these quantities=COLVAR

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	the labels of the scalars on which the bias will act

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
_fict	scalar	one or multiple instances of this quantity can be referenced elsewhere in the input file
_vfict	scalar	one or multiple instances of this quantity can be referenced elsewhere in the input file

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 labels of the scalars on which the bias will act
KAPPA	compulsory	none	specifies that the restraint is harmonic and what the values of the force constants on each of the variables are
TAU	compulsory	none	specifies that the restraint is harmonic and what the values of the force constants on each of the variables are
FRICTION	compulsory	0.0	add a friction to the variable
NUMERICAL_DERIVATIVESThis keyword do not have examples	optional	false	calculate the derivatives for these quantities numerically
TEMP	optional	not used	the system temperature - needed when FRICTION is present

References

More information about how this action can be used is available in the following articles:

Quantity	Type	Description
phi	scalar	the TORSION involving these atoms

Quantity	Description
.bias	the instantaneous value of the bias potential