Deep-neural-network solution of the electronic Schrödinger equation

By Jan Hermann, Zeno Schätzle, Frank No'e. Nature Chemistry, 2019

551 citations recorded by the source corpus.

The electronic Schrödinger equation can only be solved analytically for the hydrogen atom, and the numerically exact full configuration-interaction method is exponentially expensive in the number of electrons. Quantum Monte Carlo methods are a possible way out: they scale well for large molecules, they can be parallelized and their accuracy has, as yet, been only limited by the flexibility of the wavefunction ansatz used. Here we propose PauliNet, a deep-learning wavefunction ansatz that achieves nearly exact solutions of the electronic Schrödinger equation for molecules with up to 30 electrons. PauliNet has a multireference Hartree–Fock solution built in as a baseline, incorporates the physics of valid wavefunctions and is trained using variational quantum Monte Carlo. PauliNet outperforms previous state-of-the-art variational ansatzes for atoms, diatomic molecules and a strongly correlated linear H 10 , and matches the accuracy of highly specialized quantum chemistry methods on the transition-state energy of cyclobutadiene, while being computationally efficient. High-accuracy quantum chemistry methods struggle with a combinatorial explosion of Slater determinants in larger molecular systems, but now a method has been developed that learns electronic wavefunctions with deep neural networks and reaches high accuracy with only a few determinants. The method is applicable to realistic chemical processes such as the automerization of cyclobutadiene.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/5de0450082c5ecd04a02db24fb9eb9e6c5c218be

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Citations in the corpus

Equivariant message passing for the prediction of tensorial properties and molecular spectra (2021, background): “, 2020) or the prediction of wavefunctions (Hegde & Bowen, 2017; Schütt et al., 2019; Hermann et al., 2020).”
SE(3)-equivariant prediction of molecular wavefunctions and electronic densities (2021, methodology): “In this work, a generalized SiLU [52, 53] activation function (also known as Swish [54]) given by σ(x) = αx 1 + e−βx (5) is used, where α and β are both learned and separate parameters are kept for all feature channels and instances of σ [27] (see Section B.”
SpookyNet: Learning force fields with electronic degrees of freedom and nonlocal effects (2021, background): “A desirable side effect of this mapping is that the rate at which learned interaction functions can vary decreases with increasing r, which introduces a chemically meaningful inductive bias (electronic wave functions also decay exponentially with increasing distance from a nucleus).(28,74) The cutof”