The prediction of topologically partitioned intra‑atomic and inter‑atomic energies by the machine learning method kriging

The construction of a novel protein force field called FFLUX, which uses topological atoms, is founded on high-rank and fully polarizable multipolar electrostatics. The machine learning method kriging successfully predicts multipole moments of a given atom with as only input the nuclear coordinates of the atoms surrounding this given atom. Thus, trained kriging models accurately capture the polarizable multipolar electrostatics of amino acids. Here we show that successful kriging models can also be constructed for non-electrostatic energy contributions. As a result, the full potential energy surface of the (molecular) system trained for can be predicted by the corresponding set of atomic kriging models. In particular, we report on the performance of kriging models for each atom’s (A) (1) total atomic energy (E IQA A ), (2) intra-atomic energy (E intra A ) (both kinetic and potential energy), (3) exchange energy (\(V_{XC}^{{AA^{\prime } }}\)) and (4) electrostatic energy (\(V_{\text{cl}}^{{AA^{{\prime }} }}\)) of atom A with the rest of the system (A′), and (5) interatomic energy (\(V_{\text{inter}}^{{AA^{{\prime }} }}\)). The total molecular energy can be reconstructed from the kriging predictions of these atomic energies. For the three case studies investigated (i.e. methanol, N-methylacetamide and peptide-capped glycine), the molecular energies were produced with mean absolute errors under 0.4, 0.8 and 1.1 kJ mol−1, respectively.