ABMD

This is part of the bias module

Adds a ratchet-and-pawl like restraint on one or more variables.

This action can be used to evolve a system towards a target value in CV space using an harmonic potential moving with the thermal fluctuations of the CV [72] [94] [28]. The biasing potential in this method is as follows:

\( V(\rho(t)) = \left \{ \begin{array}{ll} \frac{K}{2}\left(\rho(t)-\rho_m(t)\right)^2, &\rho(t)>\rho_m(t)\\ 0, & \rho(t)\le\rho_m(t), \end{array} \right . \)

where

\( \rho(t)=\left(CV(t)-TO\right)^2 \)

and

\( \rho_m(t)=\min_{0\le\tau\le t}\rho(\tau)+\eta(t) \).

The method is based on the introduction of a biasing potential which is zero when the system is moving towards the desired arrival point and which damps the fluctuations when the system attempts to move in the opposite direction. As in the case of the ratchet and pawl system, propelled by thermal motion of the solvent molecules, the biasing potential does not exert work on the system. \(\eta(t)\) is an additional white noise acting on the minimum position of the bias.

Examples

The following input sets up two biases, one on the distance between atoms 3 and 5 and another on the distance between atoms 2 and 4. The two target values are defined using TO and the two strength using KAPPA. The total energy of the bias is printed.

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

d1: DISTANCE 
ATOMS
the pair of atom that we are calculating the distance between. 
=3,5 The DISTANCE action with label d1 calculates a single scalar value
d2: DISTANCE 
ATOMS
the pair of atom that we are calculating the distance between. 
=2,4 The DISTANCE action with label d2 calculates a single scalar value
abmd: ABMD 
ARG
compulsory keyword 
the labels of the scalars on which the bias will act 
=d1,d2 
TO
compulsory keyword 
The array of target values 
=1.0,1.5 
KAPPA
compulsory keyword 
The array of force constants. 
=5.0,5.0 The ABMD action with label abmd calculates the following quantities:

 Quantity   
 Description  
abmd.bias
the instantaneous value of the bias potential
abmd.d1_min
one or multiple instances of this quantity can be referenced elsewhere in the input file.  These quantities will be named with the arguments of the bias followed by the character string _min. These quantities tell the user the minimum value assumed by rho_m(t). This particular component measures this quantity for the input CV named d1
abmd.d2_min
one or multiple instances of this quantity can be referenced elsewhere in the input file.  These quantities will be named with the arguments of the bias followed by the character string _min. These quantities tell the user the minimum value assumed by rho_m(t). This particular component measures this quantity for the input CV named d2
abmd.force2
the instantaneous value of the squared force due to this bias potential


PRINT 
ARG
compulsory keyword 
the labels of the values that you would like to print to the file 
=abmd.bias,abmd.d1_min,abmd.d2_min The PRINT action with label 

Glossary of keywords and components

Description of components

By default this Action calculates the following quantities. These quantities can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the quantity required from the list below.

Quantity	Description
bias	the instantaneous value of the bias potential
force2	the instantaneous value of the squared force due to this bias potential
_min	one or multiple instances of this quantity can be referenced elsewhere in the input file. These quantities will be named with the arguments of the bias followed by the character string _min. These quantities tell the user the minimum value assumed by rho_m(t).

Compulsory keywords

ARG	the labels of the scalars on which the bias will act
TO	The array of target values
KAPPA	The array of force constants.

Options

NUMERICAL_DERIVATIVES	( default=off ) calculate the derivatives for these quantities numerically
MIN	Array of starting values for the bias (set rho_m(t), otherwise it is set using the current value of ARG)
NOISE	Array of white noise intensities (add a temperature to the ABMD)
SEED	Array of seeds for the white noise (add a temperature to the ABMD)