Ring-Polymer Instanton Tunneling Splittings of Tropolone and Isotopomers using a Δ-Machine Learned CCSD(T) Potential: Theory and Experiment Shake Hands

Abstract

Tropolone, a 15-atom cyclic molecule, has received much interest both experimentally and theoretically due to its H-transfer tunneling dynamics. An accurate theoretical description is challenging owing to the need to develop a high-level potential energy surface (PES) and then to simulate quantum-mechanical tunneling on this PES in full dimensionality. Here, we tackle both aspects of this challenge and make detailed comparisons with experiments for numerous isotopomers. The PES, of near CCSD(T)-quality, is obtained using a Δ-machine learning approach starting from a pre-existing low-level DFT PES and corrected by a small number of approximate CCSD(T) energies obtained using the fragmentation-based molecular tailoring approach. The resulting PES is benchmarked against DF-FNO-CCSD(T) and CCSD(T)-F12 calculations. Ring-polymer instanton calculations of the splittings, obtained with the Δ-corrected PES are in good agreement with previously reported experiments and a significant improvement over those obtained using the low-level DFT PES. The instanton path includes heavy-atom tunneling effects and cuts the corner, thereby avoiding passing through the conventional saddle-point transition state. This is in contradistinction with typical approaches based on the minimum-energy reaction path. Finally, the subtle changes in the splittings for some of the heavy-atom isotopomers seen experimentally are reproduced and explained.

Proton-Tunneling Dynamics along Low-Barrier Hydrogen Bonds: A Full-Dimensional Instanton Study of 6-Hydroxy-2-formylfulvene

“…27 Using this metric, the tunneling proton was found to yield roughly 60% of the total action, whereas the oxygen atoms accounted for an additional 20% (see section 2 of the SI). These results suggest that tunneling dynamics depend markedly on the isotopic form of the proton, with a small contribution arising from the rest of the molecular framework, an assertion confirmed by the analyses performed on the 18 O isotopologue (Table 1). Indeed, the introduction of 18 O produces a subtle reduction in the tunneling splitting, a result that can be rationalized by the modest contribution of oxygen atoms to the overall action as well as by the smaller mass ratio between oxygen and hydrogen isotopes (viz., 1.125 for 18 O/ 16 O versus 2 for D/H).…”

“…In particular, this antisymmetrical coordinate shows the majority of electronic reorganization to occur during the intermediate proton-transfer stage. Such behavior mimics the hydron dynamics found in similar compounds such as malonaldehyde ,− and tropolone, ,− where distortion of the heavy-atom framework permits the system to attain an optimal geometry that reduces the effective tunneling pathlength. Remarkably, the instanton path does not pass through the transition-state configuration, as can be appreciated from the fact that the d OO and θ OHO structural parameters in Figure never attain the TS values.…”

“…Moreover, given the multidimensional character of tunneling-mediated pathways, intimate coupling among internal degrees of freedom can control both the mechanism and the rate of the ensuing dynamics. Even subtle displacements of heavy-atom centers in the complex of interest (e.g., donor/acceptor sites) can profoundly impact the nature of hydron migration. − As such, an accurate and quantitative description of NQEs has remained particularly challenging, since it requires an all-atom, all-electron simulation of the underlying dynamics.…”

“…Given the exponential dependence of tunneling probability on the reaction barrier height, the choice of electronic structure method is very important for quantitative calculations of tunneling-induced splitting. Although highly accurate ab initio paradigms like CCSD(T) could be employed within the RPI formalism, 18 the extreme computational cost of such approaches often limits their direct practical implementation. Recent advances on machine-learning models that allow for the parametrization of potential-energy surfaces at a high level of theory can be employed to circumvent these challenges, although such analyses still are very demanding.…”

“…Having located the requisite instanton pathway, the associated tunneling-induced splitting can be predicted by implementing the RPI approach. 27−29 Table 1 presents the ground-state tunneling metrics estimated for the parent HFF molecule as well as for two isotopologues involving replacement of the shuttling proton by a more massive deuteron or simultaneous substitution of the donor and acceptor oxygen centers by heavier 18 O atoms. Comparison with spectroscopic measurements performed on the H-atom and D-atom transfer reactions 21 shows the instanton calculations to be in good agreement with experiments, reproducing observed trends and producing a near-quantitative deuterium kinetic isotope effect (DKIE) Δ H /Δ D of 3.9 relative to the experimental value of 3.4.…”