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Correction: A critical comparison of neural network potentials for molecular reaction dynamics with exact permutation symmetry
Jun
Li
*ab,
Kaisheng
Song
a and
Jörg
Behler
*b
aSchool of Chemistry and Chemical Engineering, Chongqing University, Chongqing 401331, China. E-mail: jli15@cqu.edu.cn
bUniversität Göttingen, Institut für Physikalische Chemie, Theoretische Chemie, Tammannstr. 6, 37077 Göttingen, Germany. E-mail: joerg.behler@uni-goettingen.de
First published on 8th December 2020
Abstract
Correction for ‘A critical comparison of neural network potentials for molecular reaction dynamics with exact permutation symmetry’ by Jun Li et al., Phys. Chem. Chem. Phys., 2019, 21, 9672–9682, DOI: 10.1039/C8CP06919K.
We have discovered an error in the published paper for the discussion on the significance of inclusion of the angular symmetry functions. As a result, the paragraph below eqn (14) needs be modified. All other conclusions are not affected by this correction.
For consistency and clarity, the following equations are given without relabeling. They provide descriptions for the local chemical environments of the central atom i being 1, 2, 3, and 4.
 | (9) |
 | (10) |
 | (11) |
 | (12) |
If only radial symmetry functions would be included, eqn (9)–(12) would only have Gi,tr2 (i = 1–4) left. Explicitly, they read,
 | (9a) |
 | (10a) |
The exchange of the two identical atoms 1 and 2 results in the permutation of the characterizations {G1,t} and {G2,t}, and has no effect on {G3,t} and {G4,t}. Explicitly,
 | (9b) |
 | (10b) |
 | (11a) |
 | (12a) |
However, if only (r13, r23) or (r14, r24) exchange, the resulting configurations are different generally. Taking the exchange of (r13, r23) as an example, the original {r12, r13, r14, r23, r24, r34} becomes {r12, r23, r14, r13, r24, r34},1 whose configuration and the corresponding characterizations have been changed. In other words, in the special A2BC case without angular symmetry functions, the resulting fingerprints do not introduce “false symmetry” properties with respect to the exchange of the artificial bond pair, either (r13, r23) or (r14, r24). However, the number of the fingerprints needs to be increased significantly to provide sufficient environment information. In other words, in some cases one can only use radial symmetry functions in the high-dimensional neural network potentials (HD-NNPs).
Prof. Bin Jiang is thanked for detailed discussion on this correction.
The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers.
References
- J. Li, B. Jiang and H. Guo, J. Chem. Phys., 2013, 139, 204103 CrossRef.
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