[srmnitc]

Problem

Solid.analyse_spring_constants rounded the mean MSD to 2 decimals. Below 0.005 Ų (low temperature, heavy or stiff elements) the MSD rounded to 0. The code then substituted 1 Ų, giving k = 3kT / 1 Ų. With an MSD of 0.004 Ų at 100 K, that makes k 0.026 eV/Ų instead of 6.46 eV/Ų. validate_spring_constants accepted the value because it lies inside [1e-4, 1e3], so the run went on with a badly matched Einstein crystal, large dissipation and a biased free energy. Only a warning was logged.

Two related problems:

• The convergence check compared the rounded MSD standard deviation against tolerance.spring_constant. That standard deviation is almost always rounded to 0, so the loop stopped on the first cycle.
• If the loop ran out of n_cycles, self.k was never set and the run crashed later.

Between 0.005 and 0.05 Ų, the rounding made k coarse (up to about ±50 %) but did not bias the free energy.

Fix

• Use the unrounded MSD. An MSD that is zero or not finite gives k = nan for that element. validate_spring_constants replaces it with another element's k (the case of an element without atoms, which the old fallback was there for), or raises when no element has a usable value.
• Converge on the relative change of k between cycles, compared against tolerance.spring_constant (default 0.1). k only needs to be approximate, so this normally stops at cycle 2.
• The loop is still bounded by md.n_cycles. If that runs out, the last estimate is used and a warning is logged.

Workaround for affected versions: set spring_constants explicitly.

Behaviour change

• With default settings, the spring constant loop now runs two cycles instead of one, so one extra n_small_steps run.
• Spring constants differ slightly from earlier versions because the MSD is no longer rounded.
• Single-element runs with a zero MSD now stop with an error instead of running with k = 3kT / 1 Ų.

Tests

• tests/test_spring_constants.py: 7 tests covering a small MSD, no rounding, zero MSD for one or all elements, user-supplied k overriding the estimate, stopping after two cycles, and the n_cycles cap. All 7 fail on main.
• Golden command streams are unchanged.
• Full suite including the LAMMPS lane: 474 passed, 3 skipped.