\(\renewcommand{\AA}{\text{Å}}\)

fix baoab command

Syntax

fix ID group-ID baoab Tstart Tstop damp seed keyword values ...

  • ID, group-ID are documented in fix command

  • baoab = style name of this fix command

  • Tstart, Tstop = desired temperature at start/end of run (temperature units)

  • damp = damping parameter (time units)

  • seed = random number seed (positive integer)

  • zero or more keyword/value pairs may be appended

  • keyword = zero

    zero value = no or yes
  no = do not zero the net random momentum each step (default)
  yes = zero the net random momentum each step

Examples

fix 1 all baoab 300.0 300.0 100.0 12345
fix 1 all baoab 1.0 1.0 10.0 48279 zero yes
fix 2 all baoab 300.0 400.0 200.0 77777

Added in version TBD.

Description

Apply the BAOAB Langevin integrator of (Leimkuhler) to the atoms in the fix group. This fix performs complete time integration of Newton’s equations of motion coupled to a Langevin heat bath – do not combine it with fix nve.

The Langevin equation of motion integrated by this fix is

\[m\,d\mathbf{v} = \mathbf{F}_c\,dt - \frac{m}{\tau}\,\mathbf{v}\,dt + \sqrt{\frac{2\,m\,k_B T}{\tau}}\,d\mathbf{W}_t,\]

where \(\mathbf{F}_c\) is the conservative force, \(\tau\) is the damping time (damp), \(T\) is the target temperature, and \(d\mathbf{W}_t\) is a Wiener increment.

The BAOAB splitting implements the following sub-steps for each MD timestep:

  • B – half-step velocity kick from conservative forces

  • A – half-step position drift

  • O – full-step exact Ornstein-Uhlenbeck (OU) update (thermostat)

  • A – half-step position drift

  • B – half-step velocity kick from conservative forces (using new forces)

The O step applies the exact solution of the OU process,

\[\mathbf{v} \leftarrow e^{-\gamma\,dt}\,\mathbf{v} + \sqrt{\frac{k_B T}{m}\bigl(1 - e^{-2\gamma dt}\bigr)}\;\mathbf{R}, \qquad \gamma = 1/\mathrm{damp},\]

where \(\mathbf{R}\) is a vector of independent standard Gaussian random numbers. This is exact for any timestep, unlike a first-order Euler discretization of the friction and noise.

BAOAB achieves second-order accuracy in configuration space: the stationary distribution of positions converges to the Boltzmann distribution with error \(O(dt^2)\), making it significantly more accurate than first-order Langevin integrators (such as the Euler-Maruyama scheme) at the same timestep. This is particularly important for computing configurational averages, free energies, and structural properties.

The target temperature can be ramped linearly from Tstart to Tstop over the course of a run by using the start and stop keywords of the run command.

The damp parameter has units of time and sets the relaxation time of the Langevin thermostat. Smaller values couple the system more strongly to the bath (faster thermalization, more friction); larger values give weaker coupling (less friction, closer to NVE dynamics). A typical starting value is 100 times the MD timestep.

If the zero keyword is set to yes, the net random momentum injected by the O step is subtracted each timestep so that the total momentum of the fix group does not drift. This is useful for bulk systems without periodic boundary conditions or when the group does not span the full system.

The cumulative energy exchanged between the atoms and the Langevin reservoir is always tracked and available via the ecouple thermo keyword. The sign convention is that a positive value means energy has flowed from the system into the reservoir (cooling), and negative means the reservoir has heated the system. Correspondingly the econserve thermo keyword reports the sum of etotal and ecouple and thus the conserved quantity of a constant temperature simulation.

This fix supports both per-type masses (mass command) and per-atom masses (atom styles such as sphere).

This fix can be used with dynamic atom groups.

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

The cumulative thermostat energy is written to and read from binary restart files so that energy accounting is continuous across restarts.

This fix produces a global scalar (the cumulative thermostat energy) that is extensive and accessible to thermo_style custom via the f_ID keyword.

This fix can ramp its target temperature over multiple runs using the start and stop keywords of the run command.

This fix is not invoked during energy minimization.

Restrictions

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.

This fix cannot be combined with fix shake or fix rattle.

Do not combine this fix with fix nve or any other time-integration fix on the same group of atoms. LAMMPS will print a warning in this case.

Default

The option defaults are zero = no.

(Leimkuhler) B. Leimkuhler and C. Matthews, “Rational Construction of Stochastic Numerical Methods for Molecular Sampling”, Appl. Math. Res. Express, 2013(1), 34-56 (2013). https://doi.org/10.1093/amrx/abs010