Influence of low frequency modes on dynamical concertedness in double proton transfer dynamics

The paper establishes, by computation and careful discussion, that (i) the index-2 saddle’s linear instability rates are independent of (λ,λ′), motivating a cutoff Δτc≈5 from the unstable timescales; (ii) delay-time distributions shift from dynamically concerted at higher ωY to sequential at low ωY; and (iii) LD maps correlate strikingly with delay-time partitions, while noting it remains unclear which specific invariant manifolds mediate each mechanism . The model solution independently re-derives the λ,λ′-independence of the linearization, uses NHIM/LD theory to justify manifold detection, and explains the low-ωY trend via explicit O(1/ωY^2) cubic terms from the Y-coupling, all consistent with the paper’s equations of motion and findings . The only tension is that the paper is cautious about naming the exact manifold responsible for the mechanism split, whereas the model asserts this more directly; hence both are correct but via different emphases and levels of rigor.