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物理化学学报  2019, Vol. 35 Issue (2): 145-157    DOI: 10.3866/PKU.WHXB201803281
所属专题: 2017年中国科学院新增院士特刊
综述     
多原子反应体系的高精度拟合势能面
傅碧娜*(),陈俊,刘天辉,邵科杰,张东辉*()
Highly Accurately Fitted Potential Energy Surfaces for Polyatomic Reactive Systems
Bina FU*(),Jun CHEN,Tianhui LIU,Kejie SHAO,Dong H. ZHANG*()
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摘要:

本文介绍了近几年来我们组构建多原子反应体系的高精度拟合势能面的进展。我们基于神经网络(NN)方法,成功构建了多原子气相分子体系和气相分子在金属表面解离的一系列势能面。这些势能面的拟合精度相当高,并且经过了严格的量子动力学测试,能广泛应用到动力学研究中。我们还提出了一种新的置换不变势能面的拟合方法,即基本不变量神经网络方法(FI-NN)。基本不变量的使用极大地减少了神经网络输入层多项式的个数,有效提高了势能面的计算速度。

关键词: 势能面神经网络反应动力学基本不变量从头算    
Abstract:

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.

Key words: Potential energy surface    Neural networks    Reaction dynamics    Fundamental invariants    Ab initio
收稿日期: 2018-03-01 出版日期: 2018-03-28
中图分类号:  O643  
基金资助: 国家自然科学基金(21722307);国家自然科学基金(21673233);国家自然科学基金(21590804);国家自然科学基金(21433009);国家自然科学基金(21688102);中国科学院战略性先导科技专项(B类)(XDB17000000)
通讯作者: 傅碧娜,张东辉     E-mail: bina@dicp.ac.cn;zhangdh@dicp.ac.cn
作者简介: 傅碧娜,1981年生。2004年本科毕业于大连理工大学物理系,2009年博士毕业于中国科学院大连化学物理研究所。现为中科院大连化学物理研究所分子反应动力学国家重点实验室研究员。主要研究方向为气相多原子分子反应以及气相-表面化学反应的势能面构建和动力学研究|张东辉,1967年生。1989年本科毕业于复旦大学物理系,1994年博士毕业于纽约大学。2017年当选中国科学院院士。现为中国科学院大连化学物理研究所分子反应动力学国家重点实验室主任。主要研究方向为气相和表面化学反应动力学理论和计算研究
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傅碧娜,陈俊,刘天辉,邵科杰,张东辉. 多原子反应体系的高精度拟合势能面[J]. 物理化学学报, 2019, 35(2): 145-157, 10.3866/PKU.WHXB201803281

Bina FU,Jun CHEN,Tianhui LIU,Kejie SHAO,Dong H. ZHANG. Highly Accurately Fitted Potential Energy Surfaces for Polyatomic Reactive Systems. Acta Phys. -Chim. Sin., 2019, 35(2): 145-157, 10.3866/PKU.WHXB201803281.

链接本文:

http://www.whxb.pku.edu.cn/CN/10.3866/PKU.WHXB201803281        http://www.whxb.pku.edu.cn/CN/Y2019/V35/I2/145

图1  具有两个隐藏层的前馈型神经网络函数结构示意图; (b)隐藏层中神经元的运算规则
图2  所有用于从头算构型在O-H2和O-H3坐标空间上的分布,并以红色分割线将整体区域分成OH + H2,H + H2O和OH3相互作用区这三个部分36
图3  在NN1,NN2和NN3势能面上所有构型的拟合误差随着相对于OH + H2平衡构型的从头算能量的分布36
图4  用六维含时波包法在NN1、NN2和NN3势能面上,在体系的总角动量Jtot = 0时计算得到的H2 + OH → H2O + H的反应几率36
图5  用六维含时波包法在NN1、NN2和NN3势能面上,在体系的总角动量Jtot = 0时计算得到的H2O + H → H2O + H′的反应几率36
图6  (a) OH + CO → H + CO2反应在2套势能面上的反应几率比较; (b)在其中一套势能面上的反应几率和去掉10%从头算点重新拟合的势能面上计算得到的反应几率37
图7  H + CH4势能面的从头算点空间分布,其中H + CH4,H2 + CH3和CH5相互作用区分别由分割线隔开56
图8  基于所有从头算点拟合的NN势能面和基于90%从头算点拟合的势能面,H + CH4 → H2 + CH3的总反应几率比较56
图9  H2O处于振转基态时,在top位和bridge位的7维解离几率,其中四个势能面从总共的81个势能面随机挑选产生83
图10  在固定位置上,H2O在Cu(111)表面解离吸附的势能面等高线图83
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