Ab initio instanton rate theory is a computational method for rigorously including tunnelling effects into the calculations of chemical reaction rates based on a potentialenergy surface computed on the fly from electronic-structure theory. This approach is necessary to extend conventional transition-state theory into the deep-tunnelling regime, but it is also more computationally expensive as it requires many more ab initio calculations. We propose an approach which uses Gaussian process regression to fit the potential-energy surface locally around the dominant tunnelling pathway. The method can be converged to give the same result as from an on-the-fly ab initio instanton calculation but it requires far fewer electronic-structure calculations. This makes it a practical approach for obtaining accurate rate constants based on high-level electronic-structure methods. We show fast convergence to reproduce benchmark H + CH 4 results and evaluate new low-temperature rates of H + C 2 H 6 in full dimensionality at a UCCSD(T)-F12b/cc-pVTZ-F12 level.
We consider quantum tunnelling in asymmetric double-well systems for which the local minima in the two wells have the same energy, but the frequencies differ slightly. In a molecular context, this situation can arise if the symmetry is broken by isotopic substitutions. We derive a generalization of instanton theory for these asymmetric systems, leading to an semiclassical expression for the tunnelling matrix element and hence the energy-level splitting. We benchmark the method using a set of one-and two-dimensional models, for which the results compare favourably with numerically exact quantum calculations. Using the ringpolymer instanton approach, we apply the method to compute the level splittings in various isotopomers of malonaldehyde in full dimensionality and analyse the relative contributions from the zero-point energy difference and tunnelling effects.
Thermal rate constants for Mu + CH4, Mu + C2H6 and Mu + C3H8 and their equivalent reactions with H were evaluated with ab initio instanton rate theory. The potential-energy...
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.
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