Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks

By David Pfau, J. Spencer, Alexander G. de G. Matthews, W. Matthew C. Foulkes. Physical Review Research, 2019

609 citations recorded by the source corpus.

Given access to accurate solutions of the many-electron Schr\"odinger equation, nearly all chemistry could be derived from first principles. Exact wavefunctions of interesting chemical systems are out of reach because they are NP-hard to compute in general, but approximations can be found using polynomially-scaling algorithms. The key challenge for many of these algorithms is the choice of wavefunction approximation, or Ansatz, which must trade off between efficiency and accuracy. Neural networks have shown impressive power as accurate practical function approximators and promise as a compact wavefunction Ansatz for spin systems, but problems in electronic structure require wavefunctions that obey Fermi-Dirac statistics. Here we introduce a novel deep learning architecture, the Fermionic Neural Network, as a powerful wavefunction Ansatz for many-electron systems. The Fermionic Neural Network is able to achieve accuracy beyond other variational quantum Monte Carlo Ans\"atze on a variety of atoms and small molecules. Using no data other than atomic positions and charges, we predict the dissociation curves of the nitrogen molecule and hydrogen chain, two challenging strongly-correlated systems, to significantly higher accuracy than the coupled cluster method, widely considered the most accurate scalable method for quantum chemistry at equilibrium geometry. This demonstrates that deep neural networks can improve the accuracy of variational quantum Monte Carlo to the point where it outperforms other ab-initio quantum chemistry methods, opening the possibility of accurate direct optimisation of wavefunctions for previously intractable molecules and solids.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry, Physical and Theoretical Chemistry

View Paper: https://www.semanticscholar.org/paper/f6ddb545c6c883f66e3066d3c1f60717104e3a4a

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In Atomic and Molecular Physics, and Optics

In Materials Chemistry

In Physical and Theoretical Chemistry

Citations in the corpus

SpookyNet: Learning force fields with electronic degrees of freedom and nonlocal effects (2021, methodology): “Our end-to-end learning approach is shared by many recent ML methods that aim to solve the Schr¨odinger equation 53–55 and mirrors the inputs that are also used in ab initio calculations.”