Big Data Meets Quantum Chemistry Approximations: The Δ-Machine Learning Approach
Open accessAbstract
Chemically accurate and comprehensive studies of the virtual space of all possible molecules are severely limited by the computational cost of quantum chemistry. We introduce a composite strategy that adds machine learning corrections to computationally inexpensive approximate legacy quantum methods. After training, highly accurate predictions of enthalpies, free energies, entropies, and electron correlation energies are possible, for significantly larger molecular sets than used for training. For thermochemical properties of up to 16k isomers of C7H10O2 we present numerical evidence that chemical accuracy can be reached. We also predict electron correlation energy in post Hartree-Fock methods, at the computational cost of Hartree-Fock, and we establish a qualitative relationship between molecular entropy and electron correlation. The transferability of our approach is demonstrated, using semiempirical quantum chemistry and machine learning models trained on 1 and 10% of 134k organic molecules, to reproduce enthalpies of all remaining molecules at density functional theory level of accuracy.
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Δ-learning is typically computationally much more efficient than training an NNP directly using only data from a high-level method, because the correction (Δ-) surface is expected to be much smoother than the full potential energy surface.
“Δ-learning is typically computationally much more efficient than training of an NNP directly using only data from a high-level method. The reason is that the correction- (Δ-) surface is expected to be much smoother than the full potential energy surface.”
From A reactive neural network framework for water-loaded acidic zeolites (2024) · cites this paper as [33]
The Conclusions (pp. 7–8) report that Δ-ML lowers the computational cost of high-level predictions and that the remaining deviations are smaller and possibly smoother. The Results (p. 3) also report that Δ-ML models outperform a baseline-free ML model trained directly on target energies. But the paper uses kernel ridge regression, not an NNP, and does not establish that training Δ-learning is typically more computationally efficient than training a high-level NNP or that its correction potential-energy surface is smoother than the full surface. (LLM, conf=0.87)
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“…that the learned representations of the NNP baseline models can be used for data-ef fi cient learning of higher (hybrid) DFT level corrections ( Δ -learning) 33 for speci fi c use cases, in addition to developing machine-learned collective variables for the acceleration of rare event sampling 34 .”
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- Authors
- Ramakrishnan, R., Dral, P. O., Rupp, M., & von Lilienfeld, O. A.
- Affiliations
- University of Basel (CH)
- Friedrich-Alexander-Universität Erlangen-Nürnberg (DE)
- Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, Department of Chemistry, University of Basel, Klingelbergstraße 80, CH-4056 Basel, Switzerland
- Venue
- Journal of Chemical Theory and Computation
- Publisher
- American Chemical Society (ACS)
- Published
- 2015-04-23
- Volume
- 11
- Issue
- 5
- Pages
- 2087-2096
- ISSN
- 1549-9618 (ISSN-L)
- 1549-9626
- OpenAlex
- W1971044734
- Cited by
- 911
- References
- 50
- Citations by year
- 2026: 102 · 2025: 119 · 2024: 102 · 2023: 118 · 2022: 108 · 2021: 110 · 2020: 81 · 2019: 71 · 2018: 43 · 2017: 34 · 2016: 13 · 2015: 10
- FWCI
- 13.51
- Type
- journal article
- Language
- en
- Open access
- green
- edoc.unibas.ch
- Licence
- other-oa
- Locations
- Journal of Chemical Theory and Computation (publishedVersion)
- PubMed (publishedVersion)
- edoc (University of Basel) (acceptedVersion, other-oa)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- arXiv (Cornell University)
- edoc (University of Basel)
- Funders
- Schweizerische Nationalfonds zur Förderung der Wissenschaftlichen Forschung (PP00P2_138932)
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Machine Learning in Materials Science
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Computational Drug Discovery Methods
- Keywords
- Δ-machine learning, thermochemical properties, enthalpy prediction, free energy prediction, entropy prediction, electron correlation energy, transferability, semiempirical quantum chemistry, density functional theory
- MeSH terms
- Machine Learning, Electrons, Isomerism, Ketones, Quantum Theory, Thermodynamics
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