MolShake (Module)

Overview

The MolShake module performs whole-molecule Monte Carlo “shakes” of every molecule in each of the supplied target configurations. The shakes comprise both rotational and translational moves, during which the internal geometry of the molecule is kept fixed.

Description

Basic Algorithm

For each molecule $m$ in a given configuration of $N$ molecules, the basic sequence of operations performed by MolShake is as follows:

1. Calculate the reference energy $E_{ref}$ arising from all interactions involving $m$
2. Generate a random displacement vector $v$ and rotation matrix $R$
3. Generate new coordinates for $m$ by moving it along $v$ by a distance (or step size) ${\delta }_r$ and simultaneously rotating it using the rotation matrix $R$ by an angle step ${\delta }_{\theta }$
4. Calculate the new energy $E_{new}$
5. Calculate the energy delta $\mathrm{\Delta }E=E_{new}-E_{ref}$. If $\mathrm{\Delta }E$ is negative, accept the new coordinates of $m$ and move to the next molecule. Otherwise, only accept the new coordinates if $\chi <\exp -\frac{\mathrm{\Delta }E}{RT}$, where $\chi$ is a random real number between 0 and 1, $R$ is the gas constant, and $T$ is the temperature of the configuration in Kelvin.

Acceptance Rates

The MolShake module uses independent step sizes for the translational and rotational components of the trial move. In order to adjust these step sizes, 10% of trial moves are made as pure rotations, and a further 10% as pure translations, with the remaining 80% being a combination of the two move types. Once moves have been attempted for all $N$ molecules in one configuration, the actual acceptance rates for the two move components are

$${\alpha }_{actual}^{trans}=\frac{N_{accepted}^{trans}}{N}$$

and

$${\alpha }_{actual}^{rot}=\frac{N_{accepted}^{rot}}{N}$$

The individual step sizes ${\delta }^{trans}$ and ${\delta }^{rot}$ can then be adjusted in order to tend towards the requested acceptance ratio, $\alpha$, in the next cycle:

$${\delta }_{new}^{trans}={\delta }_{old}^{trans}\frac{{\alpha }_{actual}^{trans}}{\alpha }$$

and

$${\delta }_{new}^{rot}={\delta }_{old}^{rot}\frac{{\alpha }_{actual}^{rot}}{\alpha }$$

If it occurs that no moves are accepted for either of the move types, the corresponding step size is multiplied by a factor of 0.8 instead of using the above equations. Following adjustment of the step sizes they are clamped such that ${\delta }_{min}\le {\delta }_{new}\le {\delta }_{max}$.

Options

Targets

Keyword	Arguments	Default	Description
Configuration	Configuration	–	Required Target configuration on which to operate.

Control

Keyword	Arguments	Default	Description
ShakesPerAtom	int	1	Number of shakes $n$ to attempt per atom
RestrictToSpecies	Species ...	–	Restrict Monte Carlo moves to only molecules of the specified species. Molecules of other species types remain at their current positions.

Rotations

Keyword	Arguments	Default	Description
RotationStepSize	double	1.0	Step size $\delta$ in degrees to use for the rotational component of the Monte Carlo moves. As detailed above, the step size is dynamically updated after the module has run, with the updated value being saved in the restart file.
RotationStepSizeMax	double	90.0	Maximum allowed value for rotational step size, ${\delta }_{max}^{rot}$, in Angstroms
RotationStepSizeMin	double	0.01	Minimum allowed value for rotational step size, ${\delta }_{min}^{rot}$, in Angstroms

Translations

Keyword	Arguments	Default	Description
TargetAcceptanceRate	double	0.33	Target acceptance rate $\alpha$ for Monte Carlo moves
TranslationStepSize	double	0.05	Step size $\delta$ in Angstroms for the translational component of the Monte Carlo moves. As detailed above, the step size is dynamically updated after the module has run, with the updated value being saved in the restart file.
TranslationStepSizeMax	double	1.0	Maximum allowed value for translational step size, ${\delta }_{max}^{trans}$, in Angstroms
TranslationStepSizeMin	double	0.001	Minimum allowed value for translational step size, ${\delta }_{min}^{trans}$, in Angstroms

Advanced

Keyword	Arguments	Default	Description
CutoffDistance	double	–	Interatomic cutoff distance $r$to use for energy calculation. The default is to use the global pair potential cutoff defined in the simulation. If necessary, a short cutoff value can be set during early equilibration runs to significantly speed up calculation times at the expense of realism.