Dynamics

Molecular dynamics based on Newton’s classical equations of motion, integrated with the velocity Verlet algorithm.

Note

For production MD simulations, consider using integrations with LAMMPS or ASE for more efficient dynamics. The eOn dynamics engine is primarily used as a building block for accelerated methods (Parallel Replica, TAD, Hyperdynamics).

To run a standalone dynamics simulation, set job to dynamics in the [Main] section:

[Main]
job = dynamics
temperature = 300

[Dynamics]
time_step = 1.0
time = 1000.0
thermostat = andersen

Or via rgpycrumbs:

from rgpycrumbs.eon.helpers import write_eon_config

config = {
    "Main": {"job": "dynamics", "temperature": 300},
    "Dynamics": {"time_step": 1.0, "time": 1000.0, "thermostat": "andersen"},
}
write_eon_config(config, Path("config.ini"))

Thermostats

Six thermostat options are available:

Thermostat	Key	Description
Andersen	andersen	Stochastic velocity reassignment with collision probability per step
Nose-Hoover	nose_hoover	Deterministic extended-system thermostat (chains of length 2)
Langevin	langevin	Stochastic friction + random force, good for non-equilibrium
None	none	NVE ensemble (constant energy, no temperature control)
PILE	pile	Ring-polymer Langevin equation on the normal modes
PIGLET	piglet	Normal-mode GLE on the internal modes, Langevin on the centroid

Andersen thermostat

Controls temperature via random velocity reassignment. The collision period determines how frequently atoms are thermalized:

[Dynamics]
thermostat = andersen
andersen_alpha = 1.0
andersen_collision_period = 100.0

Langevin thermostat

Applies friction and random forces. The friction coefficient controls the coupling strength to the heat bath:

[Dynamics]
thermostat = langevin
langevin_friction = 0.01

Langevin and Nose-Hoover treat each Cartesian component on its own. A fixed component is stored with zero velocity, so the Nose-Hoover step leaves it in place, and the chain counts only the free components. Langevin draws no random force on a fixed component and writes no step there.

Path-integral sampling

pile and piglet integrate a ring polymer. The velocity Verlet step above stays the classical update and does not move the beads. Each step evaluates every bead in one force batch, so calculator groups carry the beads together. A fixed component is left out of that update: its force and its momentum stay zero, and the bead step skips it.

path_beads is the bead count. path_springs = trotter uses the primitive ring-polymer frequencies. path_springs = eco uses economised springs fitted to harmonic radii of gyration up to path_eco_omega_max. Economised springs are refused with piglet. The instanton refuses them as well, because that discretisation assumes Trotter springs.

path_eco_omega_max is an angular frequency in inverse internal time units. One internal time unit is 10.18 fs, so 1.0 is 9.82e13 rad/s and hbar omega = 0.0647 eV.

piglet reads one drift matrix and one covariance per internal mode from path_gle_file. The file holds the mode count and the matrix size, then for each mode the drift matrix and the covariance, row by row. The drift matrix is in inverse internal time units. The covariance is in kelvin: kB times it is the covariance of the mass-scaled extended momenta in eV, so a canonical GLE at the ring temperature has N T on the diagonal, with N = path_beads and T the [Main] temperature. A file with one matrix pair fewer than the bead count covers the internal modes; one with a pair per bead skips the first, centroid, pair. The centroid keeps a separate Langevin thermostat. path_pile_tau is that damping time in femtoseconds, and path_pile_scale multiplies the critical damping of the internal modes when the thermostat is pile. path_seed seeds the path-integral random numbers.

The ring starts from pos.con with momenta drawn at the ring temperature. The first half of the steps equilibrates it; over the second half the job averages the centroid-virial kinetic energy, the quantum kinetic energy of the N-bead ring, and writes it to the log beside the classical nFree kB T / 2. final.con holds the ring’s centroid and its velocity.

Through the library (eonc::pathintegral::RingPolymer), the sampler can also hold the centroid on a hyperplane and average the Cartesian force along the normal. That average is the mean force for thermodynamic integration along a band, and its negative is the derivative of the potential of mean force; the instanton job’s PI-QTST planes use it. The dynamics job does not set a hyperplane.

Time parameters

All times are specified in femtoseconds (fs). The internal time unit conversion is handled automatically.

• time_step: integration timestep (default: 1.0 fs)

• time: total simulation time (default: 1000.0 fs)

The number of steps is computed as floor(time / time_step).

Configuration

[Dynamics]

pydantic model eon.schema.DynamicsConfig

Fields:

• time_step (float)

• time (float)

• thermostat (Literal['none', 'andersen', 'langevin', 'nose_hoover', 'pile', 'piglet'])

• path_beads (int)

• path_springs (Literal['trotter', 'eco'])

• path_eco_omega_max (float)

• path_gle_file (str)

• path_pile_tau (float)

• path_pile_scale (float)

• path_seed (int)

• andersen_collision_period (float)

• andersen_alpha (float)

• nose_mass (float)

• langevin_friction (float)

field time_step: float = 1.0

The duration of each MD step, in femtoseconds.

field time: float = 1000.0

Total MD time, in femtoseconds.

field thermostat: Literal['none', 'andersen', 'langevin', 'nose_hoover', 'pile', 'piglet'] = 'none'

Options: - none: NVE dynamics with the verlet algorithm. Initial velocities set by temperature. - andersen: Andersen thermostat with the Verlet algorithm. - langevin: Langevin thermostat with the Verlet algorithm. - nose_hoover: Nosé-Hoover thermostat with the Verlet algorithm. - pile: path-integral Langevin equation on the ring-polymer normal modes. - piglet: normal-mode GLE on the internal modes, Langevin on the centroid.

Thermostat to use for the dynamics simulation.

field path_beads: int = 8

Beads in a pile or piglet trajectory.

Constraints:

• ge = 1

field path_springs: Literal['trotter', 'eco'] = 'trotter'

Trotter ring-polymer springs, or economised springs. eco is refused with piglet.

field path_eco_omega_max: float = 0.0

Highest physical frequency, in internal frequency units, reproduced by economised springs.

Constraints:

• ge = 0.0

field path_gle_file: str = ''

Normal-mode GLE matrices for piglet. The file starts with the mode count and the matrix dimension, then each mode’s drift matrix and covariance.

field path_pile_tau: float = 100.0

Centroid Langevin damping time, in femtoseconds.

Constraints:

• gt = 0.0

field path_pile_scale: float = 1.0

Scales the critical damping of the internal PILE modes.

Constraints:

• gt = 0.0

field path_seed: int = 1

Seed for the path-integral random numbers.

Constraints:

• ge = 0

field andersen_collision_period: float = 100.0

The collision period (in fs) for the Andersen thermostat.

field andersen_alpha: float = 1.0

The collision strength in the Andersen thermostat.

field nose_mass: float = 1.0

The effective mass of the additional degree of freedom in the Nosé-Hoover thermostat, which determines the coupling frequency of the thermostat.

field langevin_friction: float = 0.01

The damping coefficient for Langevin dynamics (1/fs).

See also

• Parallel replica for accelerated dynamics via replica parallelism

• Hyperdynamics for bias-potential acceleration

• Optimizer for structure optimization