Integrators

Velocity Verlet

Positions and velocities advance together with half-step kicks around a full drift. The scheme is time-reversible and symplectic, so the energy of an unthermostatted run fluctuates without drifting when the time step is small enough.

Swope et al. 1982

When to use it

Every molecular-dynamics run in CAPS. All-atom models with hydrogens need Δt ≤ 1 fs, or 2 fs with the bonds to hydrogen constrained (SHAKE/RATTLE or LINCS).

Source

core/src/dynamics.cpp

Tested by

Dynamics.NveConservesEnergy · Dynamics.SameSeedSameTrajectory

Departure from the reference

none

References

1. Swope, W. C., Andersen, H. C., Berens, P. H., Wilson, K. R., "A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: application to small water clusters", J. Chem. Phys. 76, 637–649 (1982). doi:10.1063/1.442716

Multiple time steps (r-RESPA)

The forces are split into fast bonded terms and slow non-bonded ones. Each outer step kicks the velocities with half the slow force, then advances n inner velocity-Verlet steps with the bonded force alone, and closes with the second half kick of the slow force. The propagator is a symmetric Trotter factorisation, so the scheme stays time-reversible and symplectic while the costly non-bonded forces are evaluated n times less often.

Tuckerman, Berne & Martyna 1992

When to use it

Long runs of all-atom models without bond constraints: a 2–4 fs outer step with a 0.5–1 fs inner step keeps the fast C–H stretches resolved. It is an alternative to constraining the bonds (SHAKE/RATTLE, LINCS), not used together with them; it runs with the Bussi thermostat or none, the barostats acting on the outer step.

Source

core/src/dynamics.cpp

Tested by

Dynamics.RespaConservesEnergyWithLongOuterSteps

Departure from the reference

none

References

1. Tuckerman, M., Berne, B. J., Martyna, G. J., "Reversible multiple time scale molecular dynamics", J. Chem. Phys. 97, 1990–2001 (1992). doi:10.1063/1.463137

Electric field during MD

A uniform external field on the partial charges during Dynamics: poling of polar rubbers, field-driven ion drift, the dielectric response at finite field. The LAMMPS input carries the same field (fix efield).

E in V/Å as LAMMPS real units; under periodic boundaries the field does work no potential accounts for, so the conserved energy drifts; a thermostat takes the heat out

When to use it

Strong fields, 0.01–1 V/Å (10⁸–10¹⁰ V/m), so the response shows above the thermal noise in nanoseconds; follow the cell dipole with the dielectric analysis (linear response: ⟨M⟩ = ε₀ V (ε − 1) E).

Source

core/src/dynamics.cpp

Tested by

tests/test_dynamics.cpp Dynamics.ElectricFieldAcceleratesACharge (a +1 e atom at rest moves ½at² along E; a neutral one stays)

Departure from the reference

no electronic polarisation (fixed charges)

Atoms held along some axes

Fixed atoms can be held along chosen axes only: a substrate held along z slides in its plane but cannot leave it; the held coordinates feel no force and keep no velocity in Relax, Dynamics and Equilibrate.

the held molecule always holds every coordinate; GROMACS: the group FrozenAxes with freezedim, VASP: selective dynamics per coordinate

When to use it

A fibre or filler surface allowed to relax in its plane but kept from drifting through the film; a wall that may breathe laterally; chain ends kept on a plane.

Source

core/src/dynamics.cpp

Tested by

tests/test_dynamics.cpp Dynamics.PartlyHeldAtoms (z held exactly while x and y move; a held x through a minimisation)

Departure from the reference

momentum is not conserved with held coordinates: the temperature counts the free coordinates

Rigid bodies in LAMMPS runs

Chosen molecules — filler particles, a rigid additive — move as rigid bodies in the LAMMPS files: their atoms keep their relative positions, the pairs inside a body are not computed, and the bodies have their own thermostat; the other atoms integrate as usual and an NPT barostat dilates only them.

LAMMPS fix rigid/nvt/small molecule (each molecule one body, Nosé–Hoover chains on the bodies; LAMMPS takes the bodies' constrained degrees of freedom out of the temperature); neigh_modify exclude molecule/intra; fix npt … dilate mobile

When to use it

Silica or carbon-black particles in a rubber matrix whose internal vibrations do not matter: longer time steps for the matrix are not affected, but the filler's thousands of internal bonds and pairs drop out of the cost.

Source

core/src/lammps_data.cpp

Tested by

tests/test_relax.cpp LammpsData.RigidBodiesBeforeTheBarostat (the group, the exclusion, the rigid fix before the barostat, velocities for the bodies; a held molecule never rigid); run in LAMMPS: 2 bodies of the polystyrene sample, 200 NPT steps

Departure from the reference

CAPS's own runs have no rigid-body integrator: there the molecules move as atoms (or hold them)