Neural Pfaffians: Solving Many Many-Electron Schrödinger Equations
This work addresses the problem of high computational cost in quantum chemistry simulations for researchers, offering a more efficient and accurate method for calculating ground state energies, though it is incremental in improving upon existing neural wave function approaches.
The paper tackled the challenge of enforcing permutation antisymmetry in generalized neural wave functions for many-electron systems by using Pfaffians instead of Slater determinants, achieving chemical accuracy across various systems and outperforming CCSD(T) CBS reference energies by 1.9mEh on the TinyMol dataset.
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.