The DOI matches its Crossref record; 39 of the 41 references it cites were found in a registry or an index.
Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
Open accessAbstract
We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schrödinger equation is mapped onto a nonlinear statistical regression problem of reduced complexity. Regression models are trained on and compared to atomization energies computed with hybrid density-functional theory. Cross validation over more than seven thousand organic molecules yields a mean absolute error of ∼10 kcal/mol. Applicability is demonstrated for the prediction of molecular atomization potential energy curves.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Initial mean absolute errors (MAE) ,using the coulomb matrix representation,176 were around 10 kcal/mol.”
From QSAR without borders (2020) · cites this paper as [176]
In the citing paper
“QM7 contains 7165 energy-minimized molecules consisting of up to 7 heavy atoms and several properties computed with density functional theory (DFT)-.”
From QSAR without borders (2020) · cites this paper as [176]
In the citing paper
“Rupp et al.208 used kernel ridge regression for modeling molecular atomization energies with mean absolute error of ~10 kcal/mol.”
From QSAR without borders (2020) · cites this paper as [208]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Density-functional thermochemistry. III. The role of exact exchange
Becke, A. D. (1993) · The Journal of Chemical Physics · doi:10.1063/1.464913 · Cited by 103,767
Self-Consistent Equations Including Exchange and Correlation Effects
Kohn, W., & Sham, L. J. (1965) · Physical Review · doi:10.1103/physrev.140.a1133 · Cited by 64,135
Hohenberg, P., & Kohn, W. (1964) · Physical Review · doi:10.1103/physrev.136.b864 · Cited by 53,541
The Elements of Statistical Learning
Hastie, T., Tibshirani, R., & Friedman, J. (2009) · Springer Series in Statistics · doi:10.1007/978-0-387-84858-7 · Cited by 25,970
The Elements of Statistical Learning
Hastie, T., Friedman, J., & Tibshirani, R. (2001) · Springer Series in Statistics · doi:10.1007/978-0-387-21606-5 · Cited by 24,162
The Elements of Statistical Learning: Data Mining, Inference, and Prediction
Lu, Z. Q. J. (2010) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/j.1467-985x.2010.00646_6.x · Cited by 12,916
Rationale for mixing exact exchange with density functional approximations
Perdew, J. P., Ernzerhof, M., & Burke, K. (1996) · The Journal of Chemical Physics · doi:10.1063/1.472933 · Cited by 6,705
Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional
Ernzerhof, M., & Scuseria, G. E. (1999) · The Journal of Chemical Physics · doi:10.1063/1.478401 · Cited by 5,574
Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces
Behler, J., & Parrinello, M. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.146401 · Cited by 5,010
Handbook of Molecular Descriptors
Todeschini, R., & Consonni, V. (2000) · Methods and Principles in Medicinal Chemistry · doi:10.1002/9783527613106 · Cited by 4,107
Stewart, J. J. P. (2007) · Journal of Molecular Modeling · doi:10.1007/s00894-007-0233-4 · Cited by 3,652
An introduction to kernel-based learning algorithms
Müller, K. R., Mika, S., Rätsch, G., Tsuda, K., & Schölkopf, B. (2001) · IEEE Transactions on Neural Networks · doi:10.1109/72.914517 · Cited by 3,521
Self-citationGaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons
Bartók, A. P., Payne, M. C., Kondor, R., & Csányi, G. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.136403 · Cited by 3,242
Ab initio molecular simulations with numeric atom-centered orbitals
Blüm, V., Gehrke, R., Hanke, F., Havu, P., Havu, V., Ren, X., Reuter, K., & Scheffler, M. (2009) · Computer Physics Communications · doi:10.1016/j.cpc.2009.06.022 · Cited by 2,924
Atom-centered symmetry functions for constructing high-dimensional neural network potentials
Behler, J. (2011) · The Journal of Chemical Physics · doi:10.1063/1.3553717 · Cited by 1,663
Encyclopedia of computational chemistry
(1999) · Choice Reviews Online · doi:10.5860/choice.36-5691 · Cited by 1,148
Statistical Mechanics: Theory and Molecular Simulation
Tuckerman, M. E. (2023) · doi:10.1093/oso/9780198825562.001.0001 · Cited by 1,032
The strengths of chemical bonds
Cottrell, T. L. (1958) · Cited by 1,018
970 Million Druglike Small Molecules for Virtual Screening in the Chemical Universe Database GDB-13
Blum, L. C., & Reymond, J. (2009) · Journal of the American Chemical Society · doi:10.1021/ja902302h · Cited by 879
Benson, S. W. (1965) · Journal of Chemical Education · doi:10.1021/ed042p502 · Cited by 727
Hautier, G., Fischer, C. C., Jain, A., Mueller, T., & Ceder, G. (2010) · Chemistry of Materials · doi:10.1021/cm100795d · Cited by 580
Virtual screening: an endless staircase?
Schneider, G. (2010) · Nature Reviews Drug Discovery · doi:10.1038/nrd3139 · Cited by 537
Fink, T., & Reymond, J. (2007) · Journal of Chemical Information and Modeling · doi:10.1021/ci600423u · Cited by 468
Representing high-dimensional potential-energy surfaces for reactions at surfaces by neural networks
Lorenz, S., Groß, A., & Scheffler, M. (2004) · Chemical Physics Letters · doi:10.1016/j.cplett.2004.07.076 · Cited by 402
The Blue Obelisk—Interoperability in Chemical Informatics
Guha, R., Howard, M. T., Hutchison, G., Murray‐Rust, P., Rzepa, H. S., Steinbeck, C., Wegner, J. K., & Willighagen, E. (2006) · Journal of Chemical Information and Modeling · doi:10.1021/ci050400b · Cited by 390
Virtual Exploration of the Small‐Molecule Chemical Universe below 160 Daltons
Fink, T., Bruggesser, H., & Reymond, J. (2005) · Angewandte Chemie International Edition · doi:10.1002/anie.200462457 · Cited by 356
Kirkpatrick, P. N., & Ellis, C. (2004) · Nature · doi:10.1038/432823a · Cited by 334
Diffusion Maps, Reduction Coordinates, and Low Dimensional Representation of Stochastic Systems
Coifman, R., Kevrekidis, I., Lafon, S., Maggioni, M., & Nadler, B. (2008) · Multiscale Modeling & simulation · doi:10.1137/070696325 · Cited by 323
“Learn on the Fly”: A Hybrid Classical and Quantum-Mechanical Molecular Dynamics Simulation
Cśanyi, G., Albaret, T., Payne, M. C., & Vita, A. D. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.175503 · Cited by 312
Lynch, B. J., & Truhlar, D. G. (2003) · The Journal of Physical Chemistry A · doi:10.1021/jp0221993 · Cited by 272
Behler, J., Martoňák, R., Donadio, D., & Parrinello, M. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.185501 · Cited by 235
Variational Particle Number Approach for Rational Compound Design
von Lilienfeld, O. A., Lins, R. D., & Röthlisberger, U. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.153002 · Cited by 126
Classical and quasiclassical spectral analysis of CH5+ using an ab initio potential energy surface
Brown, A., Braams, B. J., Christoffel, K. M., Jin, Z., & Bowman, J. M. (2003) · The Journal of Chemical Physics · doi:10.1063/1.1622379 · Cited by 109
Molecular grand-canonical ensemble density functional theory and exploration of chemical space
von Lilienfeld, O. A., & Tuckerman, M. E. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2338537 · Cited by 109
Dynamically Polarizable Water Potential Based on Multipole Moments Trained by Machine Learning
Handley, C. M., & Popelier, P. L. A. (2009) · Journal of Chemical Theory and Computation · doi:10.1021/ct800468h · Cited by 71
Alchemical derivatives of reaction energetics
Sheppard, D., Henkelman, G., & von Lilienfeld, O. A. (2010) · The Journal of Chemical Physics · doi:10.1063/1.3474502 · Cited by 70
A Numerical Study on Learning Curves in Stochastic Multilayer Feedforward Networks
Müller, K. R., Finke, M., Murata, N., Schulten, K., & Амари, Ш.-И. (1996) · Neural Computation · doi:10.1162/neco.1996.8.5.1085 · Cited by 70
Self-citationAccurate ab initio energy gradients in chemical compound space
von Lilienfeld, O. A. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3249969 · Cited by 65
Preliminary assessment of a multifunctional potential energy function
Lim, T. (2010) · Molecular Physics · doi:10.1080/00268976.2010.484817 · Cited by 6
Flagged first, then by citations
2 of the 41 references couldn’t be matched to a known paper.
Research works printed but not linked: 1
- B. Schölkopf, 2002, Learning with Kernels
Cited by
Sorted by citations
Neural Message Passing for Quantum ChemistryPreprint
Gilmer, J., Schoenholz, S. S., Riley, P. F., Vinyals, O., & Dahl, G. E. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1704.01212 · Cited by 5,678
Machine learning for molecular and materials science
Butler, K. T., Davies, D. W., Cartwright, H., Isayev, O., & Walsh, A. (2018) · Nature · doi:10.1038/s41586-018-0337-2 · Cited by 4,968
MoleculeNet: a benchmark for molecular machine learning
Wu, Z., Ramsundar, B., Feinberg, E. N., Gomes, J., Geniesse, C., Pappu, A. S., Leswing, K., & Pande, V. (2018) · Chemical Science · doi:10.1039/c7sc02664a · Cited by 3,107
Automatic Chemical Design Using a Data-Driven Continuous Representation of Molecules
Gómez-Bombarelli, R., Wei, J. N., Duvenaud, D., Hernández-Lobato, J. M., Sánchez-Lengeling, B., Sheberla, D., Aguilera-Iparraguirre, J., Hirzel, T. D., Adams, R. P., & Aspuru-Guzik, A. (2018) · ACS Central Science · doi:10.1021/acscentsci.7b00572 · Cited by 3,106
Recent advances and applications of machine learning in solid-state materials science
Schmidt, J., Marques, M. R. G., Botti, S., & Marques, M. A. L. (2019) · npj Computational Materials · doi:10.1038/s41524-019-0221-0 · Cited by 2,786
Metadata
- Authors
- Rupp, M., Tkatchenko, A., Müller, K.-R., & von Lilienfeld, O. A.
- Affiliations
- University of California, Los Angeles (US)
- Max Planck Society (DE)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2012-01-31
- Volume
- 108
- Issue
- 5
- Pages
- 058301-058301
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2104489082
- Cited by
- 2,312
- References
- 41
- Citations by year
- 2026: 143 · 2025: 224 · 2024: 260 · 2023: 227 · 2022: 225 · 2021: 308 · 2020: 326 · 2019: 194 · 2018: 178 · 2017: 93 · 2016: 42 · 2015: 32 · 2014: 25 · 2013: 25 · 2012: 8
- FWCI
- 13.24
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- edoc (University of Basel) (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- Open Repository and Bibliography (University of Luxembourg) (submittedVersion, cc-by-nc-sa)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
- arXiv (Cornell University)
- edoc (University of Basel)
- Funders
- U.S. Department of Energy
- 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
- Life Sciences › Pharmacology, Toxicology and Pharmaceutics › Drug Discovery › Computational Drug Discovery Methods
- Keywords
- atomization energies, machine learning, organic compounds, hybrid density functional theory, regression models, nuclear charge
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
