Transfer learning for affordable and high quality tunneling splittings from instanton calculations

TL;DR

This paper demonstrates that transfer learning combined with ring-polymer instanton theory can accurately predict tunneling splittings in molecules like malonaldehyde using significantly fewer high-level calculations, making high-accuracy quantum predictions more affordable.

Contribution

The study introduces a transfer learning approach that reduces the number of high-level electronic structure calculations needed for accurate tunneling splitting predictions in instanton calculations.

Findings

Only 25-50 high-level data points are needed for CCSD(T)-level accuracy.

The high-level PES has a mean error of 0.3 kcal/mol for energies up to 40 kcal/mol.

Tunneling splittings are accurately predicted within 2 cm$^{-1}$ of high-level calculations.

Abstract

The combination of transfer learning (TL) a low level potential energy surface (PES) to a higher level of electronic structure theory together with ring-polymer instanton (RPI) theory is explored and applied to malonaldehyde. The RPI approach provides a semiclassical approximation of the tunneling splitting and depends sensitively on the accuracy of the PES. With second order M{\o}ller-Plesset perturbation theory (MP2) as the low-level (LL) model and energies and forces from coupled cluster singles, doubles and perturbative triples (CCSD(T)) as the high-level (HL) model, it is demonstrated that CCSD(T) information from only 25 to 50 judiciously selected structures along and around the instanton path suffice to reach HL-accuracy for the tunneling splitting. In addition, the global quality of the HL-PES is demonstrated through a mean average error of 0.3 kcal/mol for energies up to 40 kcal/mol above the minimum energy structure (a factor of 2 higher than the energies employed during TL) and $< 2 $ cm$^{-1}$ for harmonic frequencies compared with computationally challenging normal mode calculations at the CCSD(T) level.