Please wait a minute...
Acta Phys. -Chim. Sin.  2018, Vol. 34 Issue (10): 1179-1188    DOI: 10.3866/PKU.WHXB201803161
Special Issue: Molecular Simulations in Materials Science
ARTICLE     
On the Simulation of Complex Reactions Using Replica Exchange Molecular Dynamics (REMD)
Liang XIN1,3,Huai SUN1,2,3,*()
1 School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, P. R. China
2 Materials Genome Initiative Center, Shanghai Jiao Tong University, Shanghai 200240, P. R. China
3 State Key Laboratory of Inorganic Synthesis and Preparative Chemistry, Jilin University, Changchun 130012, P. R. China
Download: HTML     PDF(2347KB) Export: BibTeX | EndNote (RIS)      

Abstract  

A complex reaction, such as combustion, polymerization, and zeolite synthesis, involves a large number of elementary reactions and chemical species. Given a set of elementary reactions, the apparent reaction rates, population of chemical species, and energy distribution as functions of time can be derived using deterministic or stochastic kinetic models. However, for many complex reactions, the corresponding elementary reactions are unknown. Molecular dynamics (MD) simulation, which is based on forces calculated by using either quantum mechanical methods or pre-parameterized reactive force fields, offers a possibility to probe the reaction mechanism from the first principles. Unfortunately, most reactions take place on timescales far above that of molecular simulation, which is considered to be a well-known rare event problem. The molecules may undergo numerous collisions and follow many pathways to find a favorable route to react. Often, the simulation trajectory can be trapped in a local minimum separated from others by high free-energy barriers; thus, crossing these barriers requires prohibitively long simulation times. Due to this timescale limitation, simulations are often conducted on very small systems or at unrealistically high temperatures, which might hinder their validity. In order to model complex reactions under conditions comparable with those of the experiments, enhanced sampling techniques are required. The replica exchange molecular dynamics (REMD) is one of the most popular enhance sampling techniques. By running multiple replicas of a simulation system using one or several controlling variables and exchanging the replicas according to the Metropolis acceptance rule, the phase space can be explored more efficiently. However, most publi`s\vl VE`s\vl Vocuses on the conformational changes of biological molecules or simple reactions that can be described by a reaction coordinate. The optimized parameters of such simulations may not be suitable for simulations of complex reactions, in which the energy changes are much more dramatic than those associated with conformational changes and the hundreds elementary reactions through numerous pathways are unknown prior to the simulations. Therefore, it is necessary to investigate how to use the REMD method efficiently for the simulation of complex reactions. In this work, we examined the REMD method using temperature (T-REMD) and Hamiltonian (H-REMD) as the controlling variable respectively. In order to quantitatively validate the simulation results against direct simulations and analytic solutions, we performed the study based on a simple replacement reaction (A + BC = AB + C) with variable energy barrier heights and reaction energies described using the ReaxFF functional forms. The aim was to optimize the simulation parameters including number, sequence, and swap frequency of the replicas. The T-REMD method was found to be efficient for modeling exothermic reactions of modest reaction energy (< 3 kcal∙mol-1) or activation energy (ca. < 20 kcal∙mol-1). The efficiency was severely impaired for reactions with high activation and reaction energies. The analysis of the simulation trajectory revealed that the problem was intrinsic and could not be solved by adjusting the simulation parameters since the phase space sampled using T-REMD was localized in the region favored by high (artificial for speed-up) temperatures, which is different from the region favored by low (experimental) temperatures. This issue was aggravated in the case of endothermic reactions. On the other hand, the H-REMD run on a series of potential surfaces having different activation energies was demonstrated to be remarkably robust. Since the energy barrier only reduces the reaction rates, while the phase space controlled by the reaction energy differences remains unchanged at a fixed temperature, excellent results were obtained with fewer replicas by using H-REMD. It is evident that H-REMD is a more suitable method for the simulation of complex reactions.



Key wordsReplica exchange      Molecular dynamics      Complex reaction      Temperature      Hamilton     
Received: 08 February 2018      Published: 13 April 2018
MSC2000:  O645  
Fund:  the National Natural Science Foundation of China(21073119);the National Natural Science Foundation of China(21173146);the National Natural Science Foundation of China(21473112);National Basic Research Program of China (973)(2014CB239702)
Corresponding Authors: Huai SUN     E-mail: huaisun@sjtu.edu.cn
Cite this article:

Liang XIN,Huai SUN. On the Simulation of Complex Reactions Using Replica Exchange Molecular Dynamics (REMD). Acta Phys. -Chim. Sin., 2018, 34(10): 1179-1188.

URL:

http://www.whxb.pku.edu.cn/10.3866/PKU.WHXB201803161     OR     http://www.whxb.pku.edu.cn/Y2018/V34/I10/1179

 
 
 
EAF/ps-1 tc/ns Nex
1 1.00 1, 000
2 0.50 1, 000
4 0.25 1, 000
8 0.25 2, 000
40 0.25 10, 000
 
Activation energy Reaction energy
0 -1.5 -3 -5 -10
MD 15 3.42 2.97 2.46 3.43 2.21
20 2.42 2.83 3.19 2.53 2.50
25 3.95 2.47 2.75 3.31 2.60
30 2.45 2.38 3.22 2.39 4.62
40 3.64 3.29 3.28 2.56 4.99
50 3.21 2.42 3.31 3.42 3.70
T-REMD 15 0.31 0.30 1.51 0.79 0.91
20 0.65 0.39 0.51 0.51 0.69
25 0.31 0.31 0.22 0.36 0.44
30 0.19 0.23 0.30 0.45 0.33
40 0.13 0.21 0.22 0.28 0.44
50 0.13 0.12 0.10 0.10 0.22
 
MD REMD Theo.
T/K lnKs tc/ps T/K lnKs tc/ps lnKr
1000 1.52(0.12) 1000 1000 1.45(0.17) 250 1.41
2000 0.69(0.09) 100 2042 0.74(0.13) 250 0.69
3000 0.40(0.08) 30 2954 0.40(0.08) 250 0.33
4000 0.37(0.07) 10 4000 0.33(0.03) 250 0.26
 
 
T/K T-REMD MD
1000 17.1 16.8
1937 22.8 23.1
2991 26.6 26.5
4000 30.8 30.9
 
 
 
 
i Ea(i)
1 15.0
2 16.1
3 17.8
4 19.9
5 21.6
6 23.7
7 26.0
8 28.5
9 31.2
10 34.0
11 36.9
12 40.0
 
 
Model T-REMD H-REMD Theo.
(-3, 25) 1.45 ± 0.17 1.44 ± 0.15 1.48
(-5, 40) 1.77 ± 0.21 2.40 ± 0.30 2.49
(-10, 50) 1.68 ± 0.20 4.90 ± 0.50 5.01
 
 
1 Steinfeld, J. I. ; Francisco, J. S. ; Hase, W. L. Chemical Kinetics and Dynamics; Prentice Hall Englewood Cliffs: Upper Saddle River, NJ, USA, 1989; Vol. 3.
2 érdi, P. ; Tóth, J. Mathematical Models of Chemical Reactions: Theory and Applications of Deterministic and Stochastic Models; Manchester University Press: Oxford Road, Manchester M13 9PL, UK, 1989.
3 Kresse G. ; Hafner J. Phys. Rev. B 1993, 47, 558.
4 Van Duin A. C. T. ; Dasgupta S. ; Lorant F. ; Goddard Ⅲ W. A. J. Phys. Chem. A 2001, 105, 9396.
5 Sugita Y. ; Okamoto Y. Chem. Phys. Lett. 1999, 314, 141.
6 Hukushima K. ; Nemoto K. J. Phys. Soc. Jpn. 1996, 65, 1604.
7 Fukunishi H. ; Watanabe O. ; Takada S. J. Chem. Phys. 2002, 116, 9058.
8 Itoh S. G. ; Okumura H. J. Comput. Chem. 2013, 34, 622.
9 Itoh S. G. ; Okumura H. ; Okamoto Y. J. Chem. Phys. 2010, 132, 134105.
10 Swails J. M. ; Roitberg A. E. J. Chem. Theory Comput. 2012, 8, 4393.
11 Mori T. ; Jung J. ; Sugita Y. J. Chem. Theory Comput. 2013, 9, 5629.
12 Leahy C. T. ; Kells A. ; Hummer G. ; Buchete N. V. ; Rosta E. J. Chem. Phys. 2017, 147, 152725.
13 Stelzl L. S. ; Hummer G. J. Chem. Theory Comput. 2017, 13, 3927.
14 Wallace, A. F. Replica Exchange Methods in Biomineral Simulations. In Methods in Enzymology, De Yoreo, J. J., Ed. ; Academic Press: New York, NY, USA, 2013; Vol. 532, Chapter 4, pp. 71–93.
15 Zhang W. ; Chen J. J. Chem. Theory Comput. 2013, 9, 2849.
16 Bergonzo C. ; Henriksen N. M. ; Roe D. R. ; Swails J. M. ; Roitberg A. E. ; Cheatham T. E. J. Chem. Theory Comput. 2014, 10, 492.
17 Mori Y. ; Okamoto Y. Phys. Rev. E 2013, 87, 023301.
18 Petraglia R. ; Nicola A. ; Wodrich M. D. ; Ceriotti M. ; Corminboeuf C. J. Comput. Chem. 2016, 37, 83.
19 Sato S. J. Chem. Phys. 1955, 23, 592.
20 Plimpton S. J. Comput. Phys. 1995, 117, 1.
21 Shinoda W. ; Shiga M. ; Mikami M. Phys. Rev. B 2004, 69, 134103.
22 Denschlag R. ; Lingenheil M. ; Tavan P. Chem. Phys. Lett. 2009, 473, 193.
23 Bittner E. ; Nu?baumer A. ; Janke W. Phys. Rev. Lett. 2008, 101, 130603.
24 Plattner N. ; Doll J. D. ; Meuwly M. J. Chem. Theory Comput. 2013, 9, 4215.
25 Dupuis P. ; Liu Y. ; Plattner N. ; Doll J. D. Multiscale Model. Simul. 2012, 10, 986.
26 Wolff U. Comput. Phys. Commun. 2004, 156, 143.
27 Flyvbjerg H. ; Petersen H. G. J. Chem. Phys. 1989, 91, 461.
28 Katzgraber H. G. ; Trebst S. ; Huse D. A. ; Troyer M. J. Stat. Mech. Theory Exp. 2006, 03, P03018.
[1] ZHANG Fan, REN Zhe, ZHONG Shenghui, YAO Mingfa, PENG Zhijun. Role of Low-Temperature Fuel Chemistry on Turbulent Flame Propagation[J]. Acta Phys. -Chim. Sin., 2019, 35(2): 158-166.
[2] GUO Junjiang, TANG Shiyun, LI Rui, TAN Ningxin. Mechanism Construction and Simulation for Combustion of Large Hydrocarbon Fuels Applied in Wide Temperature Range[J]. Acta Phys. -Chim. Sin., 2019, 35(2): 182-192.
[3] YANG Huachao, BO Zheng, SHUAI Xiaorui, YAN Jianhua, CEN Kefa. Influence of Wettability on the Charging Dynamics of Electric Double-Layer Capacitors[J]. Acta Phys. -Chim. Sin., 2019, 35(2): 200-207.
[4] Wenqiong CHEN,Yongji GUAN,Xiaoping ZHANG,Youquan DENG. Influence of External Electric Field on Vibrational Spectrum of Imidazolium-Based Ionic Liquids Probed by Molecular Dynamics Simulation[J]. Acta Phys. -Chim. Sin., 2018, 34(8): 912-919.
[5] Marco FRANCO-PÉREZ,José L. GÁZQUEZ,W. AYERS Paul,Alberto VELA. Thermodynamic Dual Descriptor[J]. Acta Phys. -Chim. Sin., 2018, 34(6): 683-391.
[6] Paul W. AYERS,Mel LEVY. Levy Constrained Search in Fock Space: An Alternative Approach to Noninteger Electron Number[J]. Acta Phys. -Chim. Sin., 2018, 34(6): 625-630.
[7] Ágnes NAGY. Phase Space View of Ensembles of Excited States[J]. Acta Phys. -Chim. Sin., 2018, 34(5): 492-496.
[8] Noriyuki YOSHII,Mika KOMORI,Shinji KAWADA,Hiroaki TAKABAYASHI,Kazushi FUJIMOTO,Susumu OKAZAKI. Free Energy Change of Micelle Formation for Sodium Dodecyl Sulfate from a Dispersed State in Solution to Complete Micelles along Its Aggregation Pathways Evaluated by Chemical Species Model Combined with Molecular Dynamics Calculations[J]. Acta Phys. -Chim. Sin., 2018, 34(10): 1163-1170.
[9] Chengzhen SUN,Bofeng BAI. Selective Permeation of Gas Molecules through a Two-Dimensional Graphene Nanopore[J]. Acta Phys. -Chim. Sin., 2018, 34(10): 1136-1143.
[10] Pingying LIU,Chunyan LIU,Qian LIU,Jing MA. Influence of Photoisomerization on Binding Energy and Conformation of Azobenzene-Containing Host-Guest Complex[J]. Acta Phys. -Chim. Sin., 2018, 34(10): 1171-1178.
[11] Fu-Feng LIU,Yu-Bo FAN,Zhen LIU,Shu BAI. Molecular Mechanism Underlying Affinity Interactions between ZAβ3 and the Aβ16-40 Monomer[J]. Acta Phys. -Chim. Sin., 2017, 33(9): 1905-1914.
[12] Xiu-Xiu WANG,Jian-Wei ZHAO,Gang YU. Combined Effects of the Hole and Twin Boundary on the Deformation of Ag Nanowires: a Molecular Dynamics Simulation Study[J]. Acta Phys. -Chim. Sin., 2017, 33(9): 1773-1780.
[13] Xue-Hui HUANG,Xiao-Hui SHANG,Peng-Ju NIU. Surface Modification of SBA-15 and Its Effect on the Structure and Properties of Mesoporous La0.8Sr0.2CoO3[J]. Acta Phys. -Chim. Sin., 2017, 33(7): 1462-1473.
[14] Liao-Ran CAO,Chun-Yu ZHANG,Ding-Lin ZHANG,Hui-Ying CHU,Yue-Bin ZHANG,Guo-Hui LI. Recent Developments in Using Molecular Dynamics Simulation Techniques to Study Biomolecules[J]. Acta Phys. -Chim. Sin., 2017, 33(7): 1354-1365.
[15] Fang CHEN,Yuan-Yuan LIU,Jian-Long WANG,Ning-Ning Su,Li-Jie LI,Hong-Chun CHEN. Investigation of the Co-Solvent Effect on the Crystal Morphology of β-HMX using Molecular Dynamics Simulations[J]. Acta Phys. -Chim. Sin., 2017, 33(6): 1140-1148.