Neural Scaling Laws Achieve Sub-Chemical Accuracy for Molecular Schrödinger Solutions

Solving the many-electron Schrödinger equation remains a fundamental challenge in chemistry. Yet, Du Jiang, Xuelan Wen, and Yixiao Chen, all from ByteDance Seed, alongside colleagues at Peking University and the California Institute of Technology, now demonstrate a breakthrough using artificial intelligence. Their work establishes that neural networks, when scaled appropriately, can surpass the long-sought “chemical accuracy” threshold of 1 kcal/mol in calculating the energies of complex molecules. This achievement stems from a novel optimization scheme, the Lookahead Variational Algorithm, which efficiently translates increased computational resources into significantly improved accuracy for neural network-based wavefunctions. The resulting calculations not only provide exceptionally precise energies, but also yield accurate molecular properties and offer definitive benchmarks for challenging chemical systems, potentially revolutionising areas where experimental data are limited or uncertain and paving the way for AI-driven advances in the field.

Researchers contribute equally to this work. This study demonstrates, for the first time, that neural scaling laws can deliver near-exact solutions to the many-electron Schrödinger equation across a broad range of realistic molecules. This progress is enabled by the Lookahead Variational Algorithm (LAVA). This effective optimisation scheme 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 accuracy threshold, but also approach the precision of computationally expensive methods such as coupled cluster theory with single, double, and perturbative triple excitations.

Neural Networks Unlock High Accuracy Quantum Chemistry

Researchers have achieved a significant breakthrough in quantum chemistry, demonstrating a method capable of delivering solutions to the many-electron Schrödinger equation with unprecedented accuracy. This advancement relies on training neural networks to represent the complex wavefunctions of molecules, and systematically increasing the size and computational resources dedicated to this process yields remarkably improved results. The team has, for the first time, achieved energies approaching 1 kJ/mol accuracy, substantially exceeding the traditionally accepted “chemical accuracy” threshold of 1 kcal/mol, and consistently observes a predictable improvement in accuracy as model capacity increases. This new approach, enabled by an optimization scheme called the Lookahead Variational Algorithm (LAVA), moves beyond the limitations of existing methods like Density Functional Theory and correlated wavefunction methods, which often rely on approximations and error cancellation.

Unlike these approaches, the neural network method directly optimizes the wavefunction itself, providing a more reliable and accurate representation of molecular systems, and crucially, delivers cancellation-free energies and observables. The team’s systematic study confirms that increasing the size of the neural network predictably reduces errors, establishing clear “scaling laws” for quantum chemical calculations. The implications of this work extend to resolving long-standing challenges in chemistry, as demonstrated by the team’s ability to generate highly accurate benchmarks for several complex systems. They have established a new, high-quality reference for the cyclobutadiene transition barrier, a molecule notoriously difficult to model accurately, and produced a significantly improved potential energy curve for the nitrogen dimer, crucial for modeling astrophysical environments.

Furthermore, the method provides definitive insight into the stability of cyclic ozone, resolving a decades-old debate surrounding its unusual properties. These results establish a new standard for predictive quantum chemistry, offering a pathway to near-exact solutions for molecular systems with up to 12 atoms. By achieving accuracy comparable to experimental uncertainty and the complete basis set limit, this approach promises to unlock new possibilities for understanding and designing molecules, and provides a foundation for AI-driven advancements in the field. The ability to generate accurate wavefunctions, alongside energies, also allows for the precise calculation of physical properties like electron density and dipole moments.