Adaptive QM/MM no longer trades structure for energy: a neural correction cancels switching forces, restoring clean solvation and conserving the Hamiltonian

In adaptive QM/MM simulations, the same solvent molecule switching between resolutions produces nonphysical transition forces, leaving simulations to choose between structural distortion and energy drift. The potential-oriented approach keeps those forces, so the solvation structure shows an unphysical spike near 6.0 Å and an overly deep interstitial minimum, and the simulation crashes at about 20 ps; the force-oriented approach removes them artificially, giving a more reasonable structure but requiring a nonconservative bookkeeping term whose energy drifts continuously. In bulk water with 2138 molecules, the potential-oriented SCMP radial distribution function shows those artifacts and the force-oriented bookkeeping term rises monotonically, while the Integrated Molecular Model runs long NVE trajectories without energy drift.

The correction potential comes from a multilayer perceptron whose input is only the multiscale weight functions of each partition, not atomic coordinates. The weight-function gradients vanish in the pure QM and pure MM bulk regions, so the correction force is strictly confined to the transition region, does not leak into the bulk, and automatically satisfies Newton's third law and momentum conservation. The network has two hidden layers of 512 and 256 nodes with SiLU activation, is trained with a Huber loss and iterative train-and-simulate active learning, and stops when the Jensen-Shannon divergence of consecutive-cycle RDFs falls below 1.0×10⁻⁴, after 4 cycles for bulk water and 5 for the K+ and H3O+ systems.

A correction potential trained on aqueous K+ can be applied directly to other monovalent cations without retraining. Previously each new solute required retraining or rebuilding the correction function; here the Na+ and NH4+ RDFs lose their boundary artifacts under zero-shot use and match the force-oriented reference. The same model applied to Ca2+ and Cl– brings the boundary artifacts back, indicating that zero-shot transfer requires the target solute to share a similar macroscopic solvation structure with the training data.

With the transition forces removed, the H3O+ diffusion coefficient can be measured directly from NVE trajectories without a thermostat. The force-oriented SCMP diffusion coefficient varies with the Langevin friction coefficient, from (5.7±1.0)×10⁻¹ Ų/ps at γ0=100 ps⁻¹ to (10.5±1.1)×10⁻¹ Ų/ps at γ0=10 ps⁻¹. The Integrated Molecular Model gives (6.3±1.3)×10⁻¹ Ų/ps from pure NVE trajectories, which the authors attribute its slight shortfall from the experimental 9.4±0.1×10⁻¹ Ų/ps to classical nuclei and DFTB3's overbinding of hydrogen bonds.

Validation covers bulk water and aqueous solutions containing a single K+, Na+, NH4+, Ca2+, Cl– or H3O+, with DFTB3/3OB in the high-precision region and the flexible SPC-Fw water model in the low-precision region, using SCMP with N=80 partitions of 32 QM solvent molecules each. The bulk water system has 2138 molecules, the ionic systems have 2137 water molecules in a 40.00 Å cubic box, and the H3O+ system has 2047 water molecules in a 39.48 Å box. The authors note that N=80 is a conservative choice and that earlier work showed N=40 or 48 also works for aqueous solvation.

Because the network takes only weight functions as input, it is a reduced projection of full atomic coordinates and the instantaneous residual force is nonzero; the authors argue its conditional ensemble average vanishes for the given descriptor. No pure QM reference was run for K+, since a single-ion RDF needs tens of picoseconds of sampling and the DFTB3 water model forms voids under NVT/NVE and over-dense solvent under NPT. The H3O+ diffusion coefficient is slightly below experiment, which the authors attribute to classical nuclei and DFTB3 overbinding. Zero-shot transfer does not hold for Ca2+ or Cl–.