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  • Review Article
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Ab initio quantum chemistry with neural-network wavefunctions

Abstract

Deep learning methods outperform human capabilities in pattern recognition and data processing problems and now have an increasingly important role in scientific discovery. A key application of machine learning in molecular science is to learn potential energy surfaces or force fields from ab initio solutions of the electronic Schrödinger equation using data sets obtained with density functional theory, coupled cluster or other quantum chemistry (QC) methods. In this Review, we discuss a complementary approach using machine learning to aid the direct solution of QC problems from first principles. Specifically, we focus on quantum Monte Carlo methods that use neural-network ansatzes to solve the electronic Schrödinger equation, in first and second quantization, computing ground and excited states and generalizing over multiple nuclear configurations. Although still at their infancy, these methods can already generate virtually exact solutions of the electronic Schrödinger equation for small systems and rival advanced conventional QC methods for systems with up to a few dozen electrons.

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Fig. 1: Quantum chemistry and machine learning.
Fig. 2: Electronic-structure problem and its neural-network solutions.
Fig. 3: Variational Monte Carlo with neural networks.
Fig. 4: Neural-network architectures for selected real-space wavefunctions.
Fig. 5: Automerization of cyclobutadiene with neural-network ansatzes.
Fig. 6: Electronic energies for molecules and solids in second quantization.

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Acknowledgements

The authors acknowledge funding from the German Ministry for Education and Research (Berlin Institute for the Foundations of Learning and Data, BIFOLD), the Berlin Mathematics Research Center MATH+ (AA1-6 and AA2-8) and European Commission (ERC CoG 772230 ScaleCell). G.C. is supported by the Swiss National Science Foundation under Grant No. 200021_200336, and by the NCCR MARVEL, a National Centre of Competence in Research, under Grant No. 205602. The authors are grateful to N. Yoshioka for providing us with the raw data of ref. 157. W.M.C.F. and his co-workers gratefully acknowledge PRACE for awarding them access to the JUWELS Booster supercomputer (https://apps.fz-juelich.de/jsc/hps/juwels/booster-overview.html); the HPC RIVR Consortium (https://www.hpc-rivr.si) and EuroHPC JU for providing computing resources on the Vega HPC system at the Institute of Information Science (https://www.izum.si) and the UK Engineering and Physical Sciences Research Council for providing computing resources at the Baskerville Tier 2 HPC service (https://www.baskerville.ac.uk). Baskerville was funded by the EPSRC and UKRI through the World Class Labs scheme (EP/T022221/1) and the Digital Research Infrastructure programme (EP/W032244/1) and is operated by Advanced Research Computing at the University of Birmingham.

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Hermann, J., Spencer, J., Choo, K. et al. Ab initio quantum chemistry with neural-network wavefunctions. Nat Rev Chem 7, 692–709 (2023). https://doi.org/10.1038/s41570-023-00516-8

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