Feynman Path Tube–Guided Surrogate Ring-Polymer Dynamics for Quantum Nuclear Transfer in the Gas Phase and on Surfaces

Nuclear quantum effects (e.g., zero-point motion and tunneling) can control hydrogen transfer and diffusion, but fully quantum dynamics is rarely feasible for realistic systems. Ring-polymer molecular dynamics (RPMD) samples quantum statistics with a classical ring polymer, yet ab initio RPMD is costly because electronic-structure energies and forces are required for every bead at every time step. Here, we introduce a Feynman path tube-guided surrogate RPMD framework that propagates all beads on an on-the-fly surrogate ring-polymer Hamiltonian with an uncertainty estimate: ab initio data are acquired only when the uncertainty exceeds a threshold and are shared across beads and trajectories. Combined with well-tempered metadynamics, the method targets quantum free-energy surfaces and activation barriers. On gas-phase OH + H₂O and CH₄ + Cl benchmarks with full-dimensional reference potentials, surrogate ab initio RPMD reproduces brute-force RPMD profiles within 0.1-0.2 kcal/mol, preserves the symmetry of the OH + H₂O identity exchange, and resolves subkcal barriers. We then compute ab initio RPMD free-energy surfaces for proton transfer on TiO₂(011), H migration on graphene, and H₂ dissociative chemisorption on Cu(111), including a two-dimensional surface and minimum free-energy path on the metal. Across all five systems, the number of ab initio calls grows sublinearly with bead number, delivering speedups of 10³-10⁵ ring-polymer bead-steps per QM evaluation and reducing the expensive force workload by three to more than 4 orders of magnitude. Tube-aware surrogate sharing therefore makes quantum-statistical free-energy sampling with ab initio RPMD practical for both molecular and interfacial reactions.