\(\renewcommand{\AA}{\text{Å}}\)

# fix gle command¶

## Syntax¶

```
fix ID id-group gle Ns Tstart Tstop seed Amatrix [noneq Cmatrix] [every stride]
```

ID, group-ID are documented in fix command

gle = style name of this fix command

Ns = number of additional fictitious momenta

Tstart, Tstop = temperature ramp during the run

Amatrix = file to read the drift matrix A from

seed = random number seed to use for generating noise (positive integer)

zero or more keyword/value pairs may be appended

keyword =

*noneq*or*every**noneq*Cmatrix = file to read the non-equilibrium covariance matrix from*every*stride = apply the GLE once every time steps. Reduces the accuracy of the integration of the GLE, but has *no effect* on the accuracy of equilibrium sampling. It might change sampling properties when used together with*noneq*.

## Examples¶

```
fix 3 boundary gle 6 300 300 31415 smart.A
fix 1 all gle 6 300 300 31415 qt-300k.A noneq qt-300k.C
```

## Description¶

Apply a Generalized Langevin Equation (GLE) thermostat as described in (Ceriotti). The formalism allows one to obtain a number of different effects ranging from efficient sampling of all vibrational modes in the system to inexpensive (approximate) modelling of nuclear quantum effects. Contrary to fix langevin, this fix performs both thermostatting and evolution of the Hamiltonian equations of motion, so it should not be used together with fix nve – at least not on the same atom groups.

Each degree of freedom in the thermostatted group is supplemented with Ns additional degrees of freedom s, and the equations of motion become

```
dq/dt=p/m
d(p,s)/dt=(F,0) - A(p,s) + B dW/dt
```

where F is the physical force, A is the drift matrix (that generalizes the friction in Langevin dynamics), B is the diffusion term and dW/dt un-correlated Gaussian random forces. The A matrix couples the physical (q,p) dynamics with that of the additional degrees of freedom, and makes it possible to obtain effectively a history-dependent noise and friction kernel.

The drift matrix should be given as an external file *Afile*,
as a (Ns+1 x Ns+1) matrix in inverse time units. Matrices that are
optimal for a given application and the system of choice can be
obtained from (GLE4MD).

Equilibrium sampling a temperature T is obtained by specifying the
target value as the *Tstart* and *Tstop* arguments, so that the diffusion
matrix that gives canonical sampling for a given A is computed automatically.
However, the GLE framework also allow for non-equilibrium sampling, that
can be used for instance to model inexpensively zero-point energy
effects (Ceriotti2). This is achieved specifying the *noneq*
keyword followed by the name of the file that contains the static covariance
matrix for the non-equilibrium dynamics. Please note, that the covariance
matrix is expected to be given in **temperature units**.

Since integrating GLE dynamics can be costly when used together with
simple potentials, one can use the *every* optional keyword to
apply the Langevin terms only once every several MD steps, in a
multiple time-step fashion. This should be used with care when doing
non-equilibrium sampling, but should have no effect on equilibrium
averages when using canonical sampling.

The random number *seed* must be a positive integer. A Marsaglia random
number generator is used. Each processor uses the input seed to
generate its own unique seed and its own stream of random numbers.
Thus the dynamics of the system will not be identical on two runs on
different numbers of processors.

Note also that the Generalized Langevin Dynamics scheme that is implemented by the fix gld scheme is closely related to the present one. In fact, it should be always possible to cast the Prony series form of the memory kernel used by GLD into an appropriate input matrix for fix gle. While the GLE scheme is more general, the form used by fix gld can be more directly related to the representation of an implicit solvent environment.

## Restart, fix_modify, output, run start/stop, minimize info¶

The instantaneous values of the extended variables are written to binary restart files. Because the state of the random number generator is not saved in restart files, this means you cannot do “exact” restarts with this fix, where the simulation continues on the same as if no restart had taken place. However, in a statistical sense, a restarted simulation should produce the same behavior. Note however that you should use a different seed each time you restart, otherwise the same sequence of random numbers will be used each time, which might lead to stochastic synchronization and subtle artifacts in the sampling.

The cumulative energy change in the system imposed by this fix is
included in the thermodynamic output keywords
*ecouple* and *econserve*. See the thermo_style
doc page for details.

This fix computes a global scalar which can be accessed by various output commands. The scalar is the same cumulative energy change due to this fix described in the previous paragraph. The scalar value calculated by this fix is “extensive”.

This fix can ramp its target temperature over multiple runs, using the
*start* and *stop* keywords of the run command. See the
run command for details of how to do this.

This fix is not invoked during energy minimization.

## Restrictions¶

The GLE thermostat in its current implementation should not be used with rigid bodies, SHAKE or RATTLE. It is expected that all the thermostatted degrees of freedom are fully flexible, and the sampled ensemble will not be correct otherwise.

In order to perform constant-pressure simulations please use fix press/berendsen, rather than fix npt, to avoid duplicate integration of the equations of motion.

This fix is part of the EXTRA-FIX package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info.