Numerical Notes

Constraint Tolerances and Thermostat Parameters

When using langevin_baoab_constrained!, the SHAKE and RATTLE solvers enforce distance constraints up to the tolerance specified in DistanceConstraints.

Interplay with `γ` and `T`

Larger friction γ and higher temperature T produce stronger stochastic kicks in the OU step.
This may increase the number of iterations needed for constraint convergence.
If the solver fails to converge within maxiter, consider relaxing tol slightly.

Mass Variance

Constraints involving very light particles (e.g. hydrogens) can converge more slowly if highly coupled with heavier atoms. This is expected and usually acceptable for simple bond constraints.

Degrees of Freedom and Temperature

The function instantaneous_temperature uses the full degrees of freedom by default. For constrained systems, users who want diagnostics consistent with statistical mechanics should instead call:

degrees_of_freedom(ps; constraints=cons, remove_com=false)

and use this value in temperature calculations.

Reproducibility

The stochastic step uses the provided RNG. Set a fixed seed (e.g. rng = MersenneTwister(1234)) in tests or benchmarks for reproducibility.