Transfer Learning for Affordable and High Quality Tunneling Splittings from Instanton Calculations

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 Møller–Plesset perturbation theory (MP2) as the low-level 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 25–50 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.