Neural Pfaffians: Solving Many Many-Electron Schr\"odinger Equations

TL;DR

This paper introduces neural Pfaffians, a fully learnable neural wave function approach that efficiently enforces antisymmetry for many-electron systems, achieving high accuracy in quantum chemistry calculations.

Contribution

It proposes a novel neural wave function based on Pfaffians that generalizes across molecules without discrete orbital selection, improving accuracy and efficiency.

Findings

Achieves chemical accuracy in ground state and ionization energies.

Outperforms CCSD(T) CBS reference energies by 1.9 m$E_h$ on TinyMol.

Reduces energy errors compared to previous neural wave functions by up to tenfold.

Abstract

Neural wave functions accomplished unprecedented accuracies in approximating the ground state of many-electron systems, though at a high computational cost. Recent works proposed amortizing the cost by learning generalized wave functions across different structures and compounds instead of solving each problem independently. Enforcing the permutation antisymmetry of electrons in such generalized neural wave functions remained challenging as existing methods require discrete orbital selection via non-learnable hand-crafted algorithms. This work tackles the problem by defining overparametrized, fully learnable neural wave functions suitable for generalization across molecules. We achieve this by relying on Pfaffians rather than Slater determinants. The Pfaffian allows us to enforce the antisymmetry on arbitrary electronic systems without any constraint on electronic spin configurations or molecular structure. Our empirical evaluation finds that a single neural Pfaffian calculates the ground state and ionization energies with chemical accuracy across various systems. On the TinyMol dataset, we outperform the `gold-standard' CCSD(T) CBS reference energies by 1.9m$E_h$ and reduce energy errors compared to previous generalized neural wave functions by up to an order of magnitude.