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 [9] [11] [camilloni11abmd.] 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.

Description of components

By default this Action calculates the following quantities. These quanties 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 will be refereceable elsewhere in the input file. These quantities will be named as min_# and the number of the argument to which they refer.These quantities tell the user the minimum value assumed by rho_m(t).

Compulsory keywords

ARG	the input for this action is the output from one or more other actions. The particular output that you used is referenced using that action of interests label. If the label appears on its own then the value of the relevant Action is taken. If * or . appears the information from all arguments is taken. Some actions have multi-component outputs, each component of the output has a specific label so for instance an action labelled dist may have three componets x, y and z. To take just the x component you should use dist.x, if you wish to take all three components then use dist.*
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)

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.

DISTANCE ATOMS=3,5 LABEL=d1
DISTANCE ATOMS=2,4 LABEL=d2
ABMD ARG=d1,d2 TO=1.0,1.5 KAPPA=5.0,5.0 LABEL=abmd
PRINT ARG=abmd.bias,abmd.min_1,abmd.min_2

(See also DISTANCE and PRINT).