Accurate prediction of electron correlation energies of topological atoms by delta learning from the Müller approximation

FFLUX is a polarizable machine-learning force field that deploys pre-trained kernel-based models of quantum topological properties in molecular dynamics simulations. Despite a track record of successful applications, this unconventional force field still uses Lennard-Jones parameters to account for dispersion effects when performing in-bulk simulations. However, optimal Lennard-Jones parameters are system-dependent and not easy to calibrate. Fortunately, physics-informed dispersion energies can be obtained from the two-particle density matrix (2PDM) of any system using correlated wavefunctions. The only challenge is that the 2PDM is a humongous object whose calculation is very time-consuming and memory-greedy. In this proof-of-concept study, we utilize the Δ-learning method to address both problems using a small set of water trimers. More specifically, we obtain pure two-electron correlation energies with the aug-cc-pVDZ basis set at the cost of Müller-approximated 2PDM calculated at a very small basis set, 6-31+G(d). We also benchmark different Δ-learning tasks designed by changing the baseline and target method and/or the basis set. Our experiments suggest that two-electron correlation energies of weakly relaxed water trimers can be accurately predicted via Δ-learning with a maximum absolute error of 1.30 ± 0.32 kJ/mol traded against a colossal computational speed-up of roughly 40 times.