Choosing τ_max for chignolin

Measured with md-tools 0.5.4; not re-run for 0.6.1. Background for REST2: chignolin. Nothing here is needed to RUN that page — it is the measurement behind the τ span it uses, and the τ = 0.3 ladder it justifies was re-run at 0.6.1 with the same overall acceptance of 0.133.

Why 0.3 and not 0.5

The paracetamol ladder spans τ 0 → 0.5 in four states and accepts 0.222. The same span over chignolin, in six states, does not work:

ladder	solute atoms	states	τ span	overall acceptance
paracetamol	20	4	0 → 0.5	0.222
chignolin	138	6	0 → 0.5	0.010
chignolin	138	6	0 → 0.3	0.133

Both chignolin runs took the same 8 minutes and the same 1935 ns/day per replica — the cost is identical and only the spacing differs. The middle row is a ladder that completes, reports, and exchanges almost nothing: at 1% the six states are close to six independent simulations, and the whole point of REST2 is lost while every file still looks right.

The reason is size. The energy difference between neighbouring states grows with the solute, so the τ spacing that works for a 20-atom molecule is far too coarse for a 138-atom peptide. Halving the span halves the gap and acceptance rises thirteenfold.

md-tools reports acceptance and does not enforce it, and the ladder is linear in τ with no spacing optimisation (REST2). So this is a number to read every time: if the pairs are much below ~0.1, tighten tau_max or add states, and remember that adding states means adding GPUs.