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1.
G. C. Schatz, Rev. Mod. Phys. 61, 669 (1989).
http://dx.doi.org/10.1103/RevModPhys.61.669
2.
T. Hollebeek, T. S. Ho, and H. Rabitz, Annu. Rev. Phys. Chem. 50, 537 (1999).
http://dx.doi.org/10.1146/annurev.physchem.50.1.537
3.
B. J. Braams and J. M. Bowman, Int. Rev. Phys. Chem. 28, 577 (2009).
http://dx.doi.org/10.1080/01442350903234923
4.
Z. Xie and J. M. Bowman, J. Chem. Theory Comput. 6, 26 (2010).
http://dx.doi.org/10.1021/ct9004917
5.
J. M. Bowman, G. Czako, and B. N. Fu, Phys. Chem. Chem. Phys. 13, 8094 (2011).
http://dx.doi.org/10.1039/c0cp02722g
6.
K. Hornik, M. Stinchcombe, and H. White, Neural Networks 2, 359 (1989).
http://dx.doi.org/10.1016/0893-6080(89)90020-8
7.
T. B. Blank, S. D. Brown, A. W. Calhoun, and D. J. Doren, J. Chem. Phys. 103, 4129 (1995).
http://dx.doi.org/10.1063/1.469597
8.
D. F. R. Brown, M. N. Gibbs, and D. C. Clary, J. Chem. Phys. 105, 7597 (1996).
http://dx.doi.org/10.1063/1.472596
9.
C. M. Handley and P. L. A. Popelier, J. Phys. Chem. A 114, 3371 (2010).
http://dx.doi.org/10.1021/jp9105585
10.
J. Behler, Phys. Chem. Chem. Phys. 13, 17930 (2011).
http://dx.doi.org/10.1039/c1cp21668f
11.
J. Chen, X. Xu, X. Xu, and D. H. Zhang, J. Chem. Phys. 138, 154301 (2013).
http://dx.doi.org/10.1063/1.4801658
12.
B. Jiang and H. Guo, J. Chem. Phys. 139, 054112 (2013).
http://dx.doi.org/10.1063/1.4817187
13.
J. Li, B. Jiang, and H. Guo, J. Chem. Phys. 139, 204103 (2013).
http://dx.doi.org/10.1063/1.4832697
14.
D. H. Zhang and H. Guo, Annu. Rev. Phys. Chem. 67, 135 (2016).
http://dx.doi.org/10.1146/annurev-physchem-040215-112016
15.
J. Chen, X. Xu, X. Xu, and D. H. Zhang, J. Chem. Phys. 138, 221104 (2013).
http://dx.doi.org/10.1063/1.4811109
16.
F. V. Prudente, P. H. Acioli, and N. J. J. Soares, J. Chem. Phys. 109, 8801 (1998).
http://dx.doi.org/10.1063/1.477550
17.
H. Gassner, M. Probst, A. Lauenstein, and K. Hermansson, J. Phys. Chem. A 102, 4596 (1998).
http://dx.doi.org/10.1021/jp972209d
18.
J. Behler and M. Parrinello, Phys. Rev. Lett. 98, 146401/1 (2007).
http://dx.doi.org/10.1103/PhysRevLett.98.146401
19.
J. Behler, Int. J. Quantum Chem. 115, 1032 (2015).
http://dx.doi.org/10.1002/qua.24890
20.
G. K. Harm Derksen, Computational Invariant Theory, Encyclopaedia of Mathematical Sciences, 2nd ed. (Springer, 2015).
21.
D. Opalka and W. Domcke, J. Chem. Phys. 138, 224103 (2013).
http://dx.doi.org/10.1063/1.4808358
22.
S. A. King, J. Symbolic Comput. 48, 101 (2013).
http://dx.doi.org/10.1016/j.jsc.2012.05.002
23.
W. Decker, G.-M. Greuel, G. Pfister, and H. Schönemann, Singular 4–0–2—A computer algebra system for polynomial computations, 2015, http://www.singular.uni-kl.de.
24.
R. P. Stanley, Bull. Am. Math. Soc. 1, 475 (1979).
http://dx.doi.org/10.1090/S0273-0979-1979-14597-X
25.
G. Kemper and A. Steel, “Some algorithms in invariant theory of finite groups,” in Computational Methods for Representations of Groups and Algebras (Birkhauser Verlag Ag, Basel, 1999), Vol. 173, pp. 267285.
26.
N. Borie, “Effective invariant theory of permutation groups using representation theory,” inAlgebraic Informatics: Proceedings of the 6th International Conference, CAI 2015, Stuttgart, Germany, September 1-4, 2015, edited byA. Maletti (Springer International Publishing, Switzerland, 2015), pp. 5869.
http://dx.doi.org/10.1007/978-3-319-23021-4_6
27.
J. Li, J. Chen, Z. Zhao, D. Xie, D. H. Zhang, and H. Guo, J. Chem. Phys. 142, 204302 (2015).
http://dx.doi.org/10.1063/1.4921412
28.
J. Li and H. Guo, J. Chem. Phys. 143, 221103 (2015).
http://dx.doi.org/10.1063/1.4937570
29.
A. Li and H. Guo, J. Phys. Chem. A 118, 11168 (2014).
http://dx.doi.org/10.1021/jp5100507
30.
H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. Schütz et al., molpro, version 2012.1, a package ofab initio programs, 2012, see http://www.molpro.net.
31.
M. Majumder, S. E. Hegger, R. Dawes, S. Manzhos, X.-G. Wang, C. Tucker, J. Li, and H. Guo, Mol. Phys. 113, 1823 (2015).
http://dx.doi.org/10.1080/00268976.2015.1015642
32.
Z. Zhao, J. Chen, Z. Zhang, D. H. Zhang, D. Lauvergnat, and F. Gatti, J. Chem. Phys. 144, 204302 (2016).
http://dx.doi.org/10.1063/1.4950028
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/content/aip/journal/jcp/145/7/10.1063/1.4961454
2016-08-17
2016-09-26

Abstract

A more flexible neural network (NN) method using the fundamental invariants (FIs) as the input vector is proposed in the construction of potential energy surfaces for molecular systems involving identical atoms. Mathematically, FIs finitely generate the permutation invariant polynomial (PIP) ring. In combination with NN, fundamental invariant neural network (FI-NN) can approximate any function to arbitrary accuracy. Because FI-NN minimizes the size of input permutation invariant polynomials, it can efficiently reduce the evaluation time of potential energy, in particular for polyatomic systems. In this work, we provide the FIs for all possible molecular systems up to five atoms. Potential energy surfaces for OH and CH were constructed with FI-NN, with the accuracy confirmed by full-dimensional quantum dynamic scattering and bound state calculations.

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