Neural networks accurately predict molecular energies across geometries
Foundation Neural-Network Quantum States for Molecular Potential Energy Surfaces in Second Quantization
Machine Learning
Summary
Finding the energy of molecules at different shapes is very important but can be slow and costly. The authors developed a special neural network that learns from a few known molecular shapes and then predicts energies and related properties for many other shapes without extra work. This method is much faster and still accurate, even for molecules like nitrogen and carbon monoxide. Their approach also helps the model understand how molecular orbitals change with shape to improve predictions.
What this means in practice
- •For computational chemists: Generate accurate molecular energies and properties efficiently across many geometries without re-optimizing wavefunctions.
- •For quantum chemistry software developers: Integrate a foundation neural-network model that reduces computation cost by orders of magnitude for evaluating molecular energy surfaces.
Authors
Lizhong Fu, Jianan Wei, Wenguan Wang, Honghui Shang
Abstract
Second-quantized neural-network quantum states have achieved accurate molecular energies, but extending them across molecular geometries requires a shared representation of the geometry-dependent wavefunction coefficients. We introduce geometry-conditioned foundation neural-network quantum states for molecular electronic structure in second quantization. A single autoregressive model learns a family of ground states from sparse anchor geometries and provides wavefunctions at untrained geometries without further optimization. Orbital alignment matches orbital identities and transports their phases, establishing an aligned orbital basis across geometries. Frozen energies reach chemical accuracy at every untrained query geometry for N$_2$, CO, and H$_4$. On additional molecular paths, the energy-trained wavefunctions yield dipoles, quadrupoles, and natural occupations without property labels. Across three paired N$_2$ training seeds, orbital alignment lowers the mean absolute energy error over all untrained query geometries from 34-37 mHa to 0.049-0.085 mHa. At approximately 1 mHa mean absolute error, frozen evaluation reduces the per-geometry cost by $986\times$ relative to independent optimization, yielding an estimated $25.8\times$ end-to-end GPU-cost reduction on a 161-point N$_2$ grid.