Highly Accurately Fitted Potential Energy Surfaces for Polyatomic Reactive Systems
Bina FU*(),Jun CHEN,Tianhui LIU,Kejie SHAO,Dong H. ZHANG*()
State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, Liaoning Province, P. R. China
Over the past decade, significant progress has been made in theoretical and experimental research in the field of chemical reaction dynamics, moving from triatomic reactions to larger polyatomic reactions. This has challenged the theoretical and computational approaches to polyatomic reaction dynamics in two major areas: the potential energy surface and the dynamics. Highly accurate potential energy surfaces are essential for achieving accurate dynamical information in quantum dynamics calculations. The increased number of degrees of freedom in larger systems poses a significant challenge to the accurate construction of potential energy surfaces. Recently, there has been substantial progress in the development of potential energy surfaces for polyatomic reactive systems. In this article, we review the recent developments made by our group in constructing highly accurately fitted potential energy surfaces for polyatomic reactive systems, based on a neural network approach. A key advantage of the neural network approach is its more faithful representation of the ab initio points. We recently proposed a systematic procedure, based on neural network fitting, for the construction of accurate potential energy surfaces with very small root mean square errors. Based on the neural network approach, we successfully developed potential energy surfaces for polyatomic reactions in the gas phase, including the reactive systems OH3, HOCO, and CH5, and the dissociation of gas-phase molecules on metal surfaces, such as H2O on the Cu(111) surface. These potential energy surfaces were fitted to an unprecedented level of accuracy, representing the most accurate potential energy surfaces calculated for these systems, and were rigorously tested using quantum dynamics calculations. The quantum dynamics calculations based on these potential energy surfaces produce accurate results, which are in good agreement with experiments. We have also proposed a new method for developing permutationally invariant potential energy surfaces, named fundamental-invariant neural networks. Mathematically, fundamental invariants are used to finitely generate the permutation-invariant polynomial ring; thus, fundamental-invariant neural networks can approximate any function to arbitrary accuracy. The use of fundamental invariants minimizes the size of the input permutation-invariant polynomials, which reduces the evaluation time for potential energy calculations, especially for polyatomic systems. Potential energy surfaces for OH3 and CH4 were constructed using fundamental-invariant neural networks, with their accuracies confirmed by full-dimensional quantum dynamics and bound-state calculations. These developments in the construction of highly accurate potential energy surfaces are expected to extend the theoretical study of reaction dynamics to larger and more complex systems.
Fund: the National Natural Science Foundation of China(21722307);the National Natural Science Foundation of China(21673233);the National Natural Science Foundation of China(21590804);the National Natural Science Foundation of China(21433009);the National Natural Science Foundation of China(21688102);the Strategic Priority Research Program of the Chinese Academy of Sciences(XDB17000000)
Bina FU,Dong H. ZHANG
Fig 1 (a) Illustration of the functional structure of a feed forward neural networks; (b) the computing rule of a neuron in the hidden layer.
Fig 2 The spacial distribution of ab initio data points as a function of O-H2 and O-H3, with the red dividing lines for the OH + H2, H + H2O, and OH3 interaction parts 36.
Fig 3 The fitting errors for all the data points in NN1, NN2 and NN3 PESs, as a function of their corresponding ab initio energies with respect to OH + H236.
Fig 4 Reaction probabilities of H2 + OH → H2O + H from six-dimensional time dependent wave packet calculations on NN1, NN2 and NN3 PESs at the total angular momentum Jtot = 0 36.
Fig 5 Reaction probabilities of H2O + H → H2O + H′ from six-dimensional time dependent wave packet calculations on NN1, NN2 and NN3 PESs at the total angular momentum Jtot = 0 36.
Fig 6 (a) Comparison of total reaction probabilities for OH + CO ® H + CO2 on two sets of PESs averaged over three fittings and (b) comparison of total reaction probabilities on one of the sets shown in (a) and a PES averaged over three fitting based on 10% less data points 37.
Fig 7 The spacial distribution of ab initio data points as a funcion of RC-H4 and RC-H5, with the dividing lines for the H + CH4, H2 + CH3, and CH5 interaction parts 56.
Fig 8 The reaction probabilities for the H + CH4 → H2 + CH3 reaction on the NN PES and another NN PES fitted with 90% of all data points 56.
Fig 9 The seven-dimensional dissociation probabilities for H2O initially in the ground rovibrational state at fixed top and bridge sites calculated on four PESs we selected randomly from the total of 81 PESs (a, b, c, and d denote part Ⅰ, Ⅱ, Ⅲ, and Ⅳ, respectively) 83.
Fig 10 Fixed-site contour plots of the PES as a function of the vertical distance of H2O (Zcom) and the distance between the dissociating H atom and the center mass of OH (r2), with other coordinates fixed at the corresponding saddle-point geometries. The saddle point geometries are inserted in the right upper corner 83.
Bowman J. M. ; Schatz G. C. Annu. Rev. Phys. Chem. 1995, 46, 169.
Zhang J. Z. H. ; Dai J. ; Zhu W. J. Phys. Chem. A 1997, 101, 2746.
Miller M. H. J. Chem. Soc. Faraday Trans. 1997, 93, 685.
Clary D. C. Science 1998, 279, 1879.
Althorpe S. C. ; Clary D. C. Annu. Rev. Phys. Chem. 2003, 54, 493.
Balint-Kurti G. G. Int. Rev. Phys. Chem. 2008, 27, 507.