Graph-Theoretic Neural Network Fragmentation with Covariant Direct Molecular Force Learning: Enabling Coupled-Cluster Accuracy AIMD for Fluxional Systems
A robust, graph-theoretic molecular fragmentation framework integrated with machine learning to directly model post-Hartree-Fock nuclear forces at coupled cluster accuracy, laying the foundation for advanced, LLM-inspired transfer learning in modern chemical dynamics simulations.
Abstract
Accurate ab initio molecular dynamics (AIMD) simulations of complex, fluxional chemical systems are severely limited by the high computational scaling of correlated electronic structure methods. To overcome this bottleneck, we present a robust, graph-theoretic molecular fragmentation framework integrated with machine learning to directly model post-Hartree-Fock nuclear forces at coupled cluster accuracy. Bypassing the limitations of automatic differentiation on learned energy surfaces that may struggle with link-atom Jacobians, our approach directly predicts nuclear force vectors. By projecting these vectors onto fragment-fixed principal axes of inertia, we establish co-variant descriptors that naturally preserve rotational, translational, and permutational invariance. The methodology achieves exceptional high parameter efficiency through a vector-valued training protocol that reduces trainable parameters by over an order of magnitude, while an unsupervised mini-batch k-means space tessellation algorithm constructs highly representative training databases using only 10% to 20% of reference configurations. We rigorously validated this framework on the highly fluxional solvated Zundel cation H_{13}O_6^+ ). Our fully machine-learning-predicted AIMD trajectories successfully reproduced complex dynamical signatures and key structural characteristics, including radial distribution functions and the velocity autocorrelation power spectrum. Ultimately, this scalable, systematically improvable framework bridges the gap between high-level correlated wavefunction theories and long-timescale reactive sampling, laying the foundation for advanced, LLM-inspired transfer learning in modern chemical dynamics simulations.
Mandala is a modular software framework for learning block-sparse electronic-structure matrices with E(3)-equivariant graph neural networks that connects electronic-structure learning and observable-guided modeling while retaining a representation tied to quantum-mechanical operators rather than only scalar or vector targets as in MLIPs.
B. Brzoza, Wiktoria Szopa, Z. Elabid et al.· 0 citations
This work not only establishes a pioneering paradigm for interpretable ML-driven force field refinement but also provides the first feature engineering solution incorporating chemical, physical, and structural information specifically designed for the machine learning of energetic molecular crystals.
Qi He, Pengju Wang, Xudong He et al.· Molecules· 0 citations
Coupled-cluster theory defines the accuracy standard for molecular electronic-structure properties but scales too steeply for routine application, whereas density-functional theory is affordable yet systematically biased. We resolve this trade-off with a single equivariant network, MEHnet-MG, that predicts an effective one-electron Hamiltonian from one inexpensive B3LYP/def2-SVP calculation and derives a broad suite of properties from it (energy, optical gap, dipole, quadrupole, polarizability, Mulliken atomic charges, and Mayer bond orders) at coupled-cluster accuracy across nine main-group elements, including the under-served phosphorus, sulfur, and chlorine chemistries. The model is trained on a new in-house dataset of multi-property labels computed at the CCSD(T) level for all nine elements. On a held-out test set, it reduces the error of every property by a factor of 3.8 to 230 relative to semi-local, hybrid, and double-hybrid DFT (referenced to composite CCSD(T)/cc-pVTZ; Methods), while adding only ~25 ms wall time per molecule, delivering coupled-cluster-quality predictions at the cost of a single DFT calculation. Critically, deriving every property from a predicted Hamiltonian rather than pooling per-atom features builds the correct size-scaling into the model architecture: on pi-conjugated oligothiophenes it matches finite-field CCSD polarizability and the EOM-CCSD optical gap to ~2% at the largest sizes where those references remain affordable (44 and 37 atoms, where a single CCSD field point already costs ~500x the model's entire inference) and extrapolates the corrected trends to 58-atom chains, a regime where pooling-based architectures fail by construction. Accurate extrapolation is therefore set by the model's inductive bias rather than by the training data.
Predicting molecular self-diffusion coefficients (D*) across chemical space remains challenging due to sparse experimental data and the high computational cost of molecular simulations. We present a data-centric machine learning framework that integrates experimental diffusion measurements with molecular dynamics simulations through a semisupervised distillation strategy. Unlike conventional approaches that treat limited experiments or simulations as direct ground truth, our method selectively incorporates simulation-derived D* only when they align with the uncertainty bounds of a Random Forest model initially trained on experimental D*. This enables controlled data set expansion, from 130 unique experimentally measured molecules to over 1,000 unique substances, while preserving label reliability. We further employ pretrained large language model embeddings to encode transferable chemical context beyond conventional descriptors, reducing predictive variance and improving generalization across chemically diverse systems. The resulting model achieves improved accuracy, with a held-out test set R2 of 0.87, an overall R2 of 0.92, and a test set mean absolute error of 0.13 × 10-9 m2 s-1 after iterative distillation across more than 1,000 chemically diverse molecules under near-ambient conditions (295-300 K). We further demonstrate that learned D* act as transferable, physically interpretable descriptors in skin permeability modeling, where their inclusion reduces test set error and improves correlation relative to models relying solely on conventional physicochemical descriptors. This work establishes a scalable framework for bridging sparse experimental measurements with broadly generalizable predictions, enabling interpretable and transferable modeling across distinct molecular transport phenomena.
Hojin Jung, Su-min Song, Sabari Kumar et al.· Journal of Chemical Informat...· 0 citations
This work introduces implicit machine learning force fields, which replace explicit stacks of neural network layers with self-consistent fixed-point equations, and demonstrates this across three major classes of graph neural networks: invariant, equivariant Cartesian tensor, and SO(3)-equivariant spherical-tensor architectures.
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This work proposes an operator-centric framework in which the external (nuclear) potential, expressed in an AO basis, serves as the model input and builds hierarchical, body-ordered representations of atomic configurations that closely mirror the principles underlying several popular atom-centered descriptors.
Jigyasa Nigam, T. Smidt, G. Dusson· Journal of Chemical Physics· 2 citations
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