Neural Scaling Laws Surpass Chemical Accuracy for the Many-Electron Schr\"odinger Equation

TL;DR

This paper shows that neural scaling laws combined with the LAVA optimization algorithm can achieve near-exact solutions to the many-electron Schrödinger equation, surpassing chemical accuracy across various molecules and properties.

Contribution

It introduces the Lookahead Variational Algorithm (LAVA) and demonstrates that neural network models can systematically improve energy accuracy, surpassing traditional chemical accuracy thresholds.

Findings

Neural models achieve subchemical accuracy (1 kJ/mol) for diverse molecules.

Energy errors decay as a power law with model size and resources.

Improved wavefunctions yield better physical properties and benchmarks.

Abstract

We demonstrate, for the first time, that neural scaling laws can deliver near-exact solutions to the many-electron Schr\"odinger equation across a broad range of realistic molecules. This progress is enabled by the Lookahead Variational Algorithm (LAVA), an effective optimization scheme that systematically translates increased model size and computational resources into greatly improved energy accuracy for neural network wavefunctions. Across all tested cases, including benzene, the absolute energy error exhibits a systematic power-law decay with respect to model capacity and computation resources. The resulting energies not only surpass the 1 kcal/mol "chemical-accuracy" threshold but also achieve 1 kJ/mol subchemical accuracy. Beyond energies, the scaled-up neural network also yields better wavefunctions with improved physical symmetries, alongside accurate electron densities, dipole moments, and other important properties. Our approach offers a promising way forward to addressing many long-standing challenges in quantum chemistry. For instance, we improve energetic properties for systems such as the potential energy curve of nitrogen dimer as dissociation is approached and the cyclobutadiene automerization reaction barrier, producing definitive benchmarks, particularly in regimes where experimental data are sparse or highly uncertain. We also shed light on the decades-old puzzle of the cyclic ozone stability with highly accurate calculations for the cyclic-to-open ozone barrier. These results provide near-exact reference calculations with unprecedented accuracy, universal reliability and practical applicability, establishing a foundation for AI-driven quantum chemistry.