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 Moller-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.

Automated summary

This study explores the combination of transfer learning with a low-level potential energy surface and high-level electronic structure theory, and applies it to malonaldehyde. The results demonstrate that high-level accuracy for tunneling splitting can be achieved by selecting 25-50 judiciously chosen structures, and the resulting high-level PES exhibits good overall quality.