emle-engine: a flexible electrostatic machine learning embedding package for multiscale molecular dynamics simulations

We present in this work the emle-engine package – the implementation of a new machine learning embedding scheme for hybrid machine learning potential / molecular mechanics (ML/MM) dynamics simulations. The package is based on an embedding scheme that uses a physics-based model of the electronic density and induction with a handful of tuneable parameters derived from in vacuo properties of the subsystem to be embedded. This scheme is completely independent of the in vacuo potential and requires only the positions of the atoms of the machine learning subsystem and the positions and partial charges of the molecular mechanics environment. These characteristics allow emle-engine to be employed in existing QM/MM software. We demonstrate that the implemented electrostatic machine learning embedding scheme (named EMLE) is stable in enhanced-sampling molecular dynamics simulations. Through calculation of free energy surfaces of alanine dipeptide in water with two different ML options for the in vacuo potential and two embedding models, we test the influence of EMLE. When compared to the reference DFT/MM surface, the EMLE embedding is clearly superior to the MM one based on fixed partial charges. The flexibility introduced in the EMLE model by the configurational dependence of the electronic density and the inclusion of the induction energy leads to a systematic reduction in the average and maximum error of the free energy surface when compared to MM embedding.