The DOI matches its Crossref record; 28 of the 28 references it cites were found in a registry or an index.
Permutationally invariant potential energy surfaces in high dimensionality
Abstract
We review recent progress in developing potential energy and dipole moment surfaces for polyatomic systems with up to 10 atoms. The emphasis is on global linear least squares fitting of tens of thousands of scattered ab initio energies using a special, compact fitting basis of permutationally invariant polynomials in Morse-type variables of all the internuclear distances. The computational mathematics underlying this approach is reviewed first, followed by a review of the practical approaches used to obtain the data for the fits. A straightforward symmetrization approach is also given, mainly for pedagogical purposes. The methods are illustrated for potential energy surfaces for , (H2O)2 and CH3CHO. The relationship of this approach to other approaches is also briefly reviewed.
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.
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
The Magma Algebra System I: The User Language
BOSMA, W., CANNON, J., & PLAYOUST, C. (1997) · Journal of Symbolic Computation · doi:10.1006/jsco.1996.0125 · Cited by 7,094
General foundations of high‐dimensional model representations
Rabitz, H., & Aliş, Ö. F. (1999) · Journal of Mathematical Chemistry · doi:10.1023/a:1019188517934 · Cited by 904
Carter, S., Culik, S. J., & Bowman, J. M. (1997) · The Journal of Chemical Physics · doi:10.1063/1.474210 · Cited by 564
Self-citationVariational quantum approaches for computing vibrational energies of polyatomic molecules
Bowman, J. M., Carrington, T., & Meyer, H.-D. (2008) · Molecular Physics · doi:10.1080/00268970802258609 · Cited by 486
Self-citationMULTIMODE: A code to calculate rovibrational energies of polyatomic molecules
Bowman, J. M., Carter, S., & Huang, X. (2003) · International Reviews in Physical Chemistry · doi:10.1080/0144235031000124163 · Cited by 477
Self-citationMolecular potential-energy surfaces for chemical reaction dynamics
Collins, M. A. (2002) · Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta) · doi:10.1007/s00214-002-0383-5 · Cited by 400
Ab initio potential energy and dipole moment surfaces for H5O2+
Huang, X., Braams, B. J., & Bowman, J. M. (2005) · The Journal of Chemical Physics · doi:10.1063/1.1834500 · Cited by 292
Self-citationGonzalez-Lafont, A., Truong, T. N., & Truhlar, D. G. (1991) · The Journal of Physical Chemistry · doi:10.1021/j100165a009 · Cited by 289
Efficient Implementation of High Dimensional Model Representations
Alış, Ö. F., & Rabitz, H. (2001) · Journal of Mathematical Chemistry · doi:10.1023/a:1010979129659 · Cited by 257
C ONSTRUCTING M ULTIDIMENSIONAL M OLECULAR P OTENTIAL E NERGY S URFACES FROM A B I NITIO D ATA
Hollebeek, T., Ho, T.-S., & Rabitz, H. (1999) · Annual Review of Physical Chemistry · doi:10.1146/annurev.physchem.50.1.537 · Cited by 245
Cited by
On representing chemical environments
Bartók, A. P., Kondor, R., & Csányi, G. (2013) · Physical Review B · doi:10.1103/physrevb.87.184115 · Cited by 2,572
Constructing high‐dimensional neural network potentials: A tutorial review
Behler, J. (2015) · International Journal of Quantum Chemistry · doi:10.1002/qua.24890 · Cited by 884
Four Generations of High-Dimensional Neural Network Potentials
Behler, J. (2021) · Chemical Reviews · doi:10.1021/acs.chemrev.0c00868 · Cited by 873
Physics-Inspired Structural Representations for Molecules and Materials
Musil, F., Grisafi, A., Bartók, A. P., Ortner, C., Csányi, G., & Ceriotti, M. (2021) · Chemical Reviews · doi:10.1021/acs.chemrev.1c00021 · Cited by 523
Role of Conical Intersections in Molecular Spectroscopy and Photoinduced Chemical Dynamics
Domcke, W., & Yarkony, D. R. (2012) · Annual Review of Physical Chemistry · doi:10.1146/annurev-physchem-032210-103522 · Cited by 508
Metadata
- Authors
- Braams, B. J., & Bowman, J. M.
- Venue
- International Reviews in Physical Chemistry
- Publisher
- Informa UK Limited
- Published
- 2009-10
- Volume
- 28
- Issue
- 4
- Pages
- 577-606
- ISSN
- 0144-235X (ISSN-L)
- 1366-591X
- OpenAlex
- W1964882117
- Cited by
- 937
- References
- 28
- FWCI
- 13.75
- Type
- journal article
- Language
- en
- Open access
- closed
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
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Permutationally invariant potential energy surfaces in high dimensionality. https://app.cochat.ai/papers/10.1080/01442350903234923
- The paper
- Braams, B. J., & Bowman, J. M. (2009). Permutationally invariant potential energy surfaces in high dimensionality. International Reviews in Physical Chemistry. https://doi.org/10.1080/01442350903234923
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.