Neural Pfaffians: Solving Many Many-Electron Schrödinger Equations

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 e...

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Bibliographic Details
Published in:arXiv.org 2024-10
Main Authors: Gao, Nicholas, Günnemann, Stephan
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Antisymmetry
Computational efficiency
Computing costs
Electron spin
Electronic systems
Electrons
Error reduction
Ground state
Molecular structure
Permutations
Schrodinger equation
Wave functions
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Summary: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.
ISSN:2331-8422