中文

Journal of Shanghai University >

2022 , Vol. 28 >Issue 5: 896 - 907

DOI: https://doi.org/10.12066/j.issn.1007-2861.2312

Dynamic calculation method of bimolecular chemical reaction based on real-time path integral

Expand
  • 1. International Center of Quantum and Molecular Structures, College of Sciences, Shanghai University, Shanghai 200444, China
    2. Shanghai Key Laboratory of High Temperature Superconductors, College of Sciences, Shanghai University, Shanghai 200444, China

Received date: 2021-04-21

  Online published: 2021-05-28

Fold

Abstract

The determination of reaction rate coefficients and kinetic isotope effects (KIE) and measurement of cross-section are indispensable to the study of combustion, atmospheric, and interstellar chemical kinetics and dynamics. However, these parameters cannot be accurately and efficiently calculated by common theoretical methods such as quantum scattering, transition state theory (TST), and quasi-classical trajectory. In recent years, the ring-polymer molecular dynamics (RPMD) theory has been successfully applied for the investigation of gas-phase bimolecular reaction dynamics. Driven by modern advances, RPMD can also be implemented in many new applications. This work will review the present challenges of and recent advances in RPMD.

Key words： path integral; rate coefficient; reaction cross-section; semiclassical

Cite this article

LI Yongle, FAN Wenbin, REN Wei . Dynamic calculation method of bimolecular chemical reaction based on real-time path integral[J]. Journal of Shanghai University, 2022 , 28(5) : 896 -907 . DOI: 10.12066/j.issn.1007-2861.2312

References

[1] Fernández-Ramos A, Miller J A, Klippenstein S J, et al. Modeling the kinetics of bimolecular reactions[J]. Chemical Reviews, 2006, 106(11): 4518-4584.
[2] Barker J R, Golden D M. Master equation analysis of pressure-dependent atmospheric reactions[J]. Chemical Reviews, 2003, 103(12): 4577-4592.
[3] Clary D C. Theoretical studies on bimolecular reaction dynamics[J]. Proceedings of the National Academy of Sciences, 2008, 105(35): 12649-12653.
[4] Lahijani P, Zainal Z A, Mohammadi M, et al. Conversion of the greenhouse gas CO$_{2}$ to the fuel gas CO via the Boudouard reaction: a review[J]. Renewable and Sustainable Energy Reviews, 2015, 41: 615-632.
[5] Laidler K J. Chemical kinetics[M]. San Antonio: Pearson Education Inc, 1987: 59-64.
[6] Tao X, Shushkov P, Miller I T F. Microcanonical rates from ring-polymer molecular dynamics: direct-shooting, stationary-phase, and maximum-entropy approaches[J]. The Journal of Chemical Physics, 2020, 152(12): 124117.
[7] Liu Q, Zhang L, Li Y, et al. Ring polymer molecular dynamics in gas-surface reactions: inclusion of quantum effects made simple[J]. The Journal of Physical Chemistry Letters, 2019, 10(23): 7475-7481.
[8] Marjollet A, Welsch R. Nuclear quantum effects in state-selective scattering from ring polymer molecular dynamics[J]. The Journal of Chemical Physics, 2020, 152(19): 194113.
[9] Durif O, Capron M, Messinger J P, et al. A new instrument for kinetics and branching ratio studies of gas phase collisional processes at very low temperatures[J]. Review of Scientific Instruments, 2021, 92(1): 014102.
[10] Guo H. Quantum dynamics of complex-forming bimolecular reactions[J]. International Reviews in Physical Chemistry, 2012, 31(1): 1-68.
[11] 国家自然科学基金委员会, 中国科学院. 中国学科发展战略理论与计算化学[M]. 北京: 科学出版社, 2016.
[12] Althorpe S C, Clary D C. Quantum scattering calculations on chemical reactions[J]. Annual Review of Physical Chemistry, 2003, 54(1): 493-529.
[13] Zhang D H, Guo H. Recent advances in quantum dynamics of bimolecular reactions[J]. Annual Review of Physical Chemistry, 2016, 67: 135-158.
[14] Manzhos S, Carrington J R T. Neural network potential energy surfaces for small molecules and reactions[J]. Chemical Reviews, 2020, 121(16): 10187-10217.
[15] Jiang B, Li J, Guo H. High-fidelity potential energy surfaces for gas-phase and gas-surface scattering processes from machine learning[J]. The Journal of Physical Chemistry Letters, 2020, 11(13): 5120-5131.
[16] Chen Z, Chen J, Chen R J, et al. Reactivity oscillation in the heavy-light-heavy Cl+CH$_{4}$ reaction[J]. Proceedings of the National Academy of Sciences, 2020, 117(17): 9202-9207.
[17] Chen R J, Shao K J, Fu B N, et al. Fitting potential energy surfaces with fundamental invariant neural network. Ⅱ. Generating fundamental invariants for molecular systems with up to ten atoms[J]. The Journal of Chemical Physics, 2020, 152(20): 204307.
[18] Truhlar D G, Garrett B C, Klippenstein S J. Current status of transition-state theory[J]. The Journal of Physical Chemistry, 1996, 100(31): 12771-12800.
[19] Truhlarg D G, Garrett B C. Variational transition state theory[J]. Annual Review of Physical Chemistry, 1984, 35(1): 159-189.
[20] Shang X, Burd T A H, Clary D C. New developments in semiclassical transition-state theory[J]. The Journal of Physical Chemistry A, 2019, 123(22): 4639-4657.
[21] Nguyen T L, Stanton J F, Barker J R. A practical implementation of semi-classical transition state theory for polyatomics[J]. Chemical Physics Letters, 2010, 499(1/2/3): 9-15.
[22] Nguyen T L, Thorpe J H, Bross D H, et al. Unimolecular reaction of methyl isocyanide to acetonitrile: a high-level theoretical study[J]. The Journal of Physical Chemistry Letters, 2018, 9(10): 2532-2538.
[23] Laude G, Calderini D, Welsch R, et al. Calculations of quantum tunnelling rates for muonium reactions with methane, ethane and propane[J]. Physical Chemistry Chemical Physics, 2020, 22(29): 16843-16854.
[24] Karplus M, Porter R N, Sharma R D. Exchange reactions with activation energy. Ⅰ. Simple barrier potential for (H, H$_{2}$)[J]. The Journal of Chemical Physics, 1965, 43(9): 3259-3287.
[25] Li J, Xie C J, Ma J Y, et al. Quasi-classical trajectory study of the HO+CO$\to $H+CO$_{2}$ reaction on a new ab initio based potential energy surface[J]. The Journal of Physical Chemistry A, 2012, 116(21): 5057-5067.
[26] Kroes G J, Díaz C. Quantum and classical dynamics of reactive scattering of H$_{2}$ from metal surfaces[J]. Chemical Society Reviews, 2016, 45(13): 3658-3700.
[27] Rodríiguez-Fernández A, Bonnet L, Crespos C, et al. When classical trajectories get to quantum accuracy. Ⅱ. The scattering of rotationally excited H$_{2}$ on Pd (111)[J]. Physical Chemistry Chemical Physics, 2020, 22(39): 22805-22814.
[28] Zhang L, Luo P, Guo K, et al. Theoretical investigation of vibrational relaxation of highly excited O$_{3}$ in collisions with HO$_{2}$[J]. RSC Advances, 2014, 4(19): 9866-9874.
[29] Habershon S, Manolopoulos D E, Markland T E, et al. Ring-polymer molecular dynamics: guantum effects in chemical dynamics from classical trajectories in an extended phase space[J]. Annual Review of Physical Chemistry, 2013, 64: 387-413.
[30] Heller E J. The semiclassical way to dynamics and spectroscopy[M]. Princeton: Princeton University Press, 2018: 133-152.
[31] Craig I R, Manolopoulos D E. Quantum statistics and classical mechanics: real time correlation functions from ring polymer molecular dynamics[J]. The Journal of Chemical Physics, 2004, 121(8): 3368-3373.
[32] Suleimanov Y V, Aoiz F J, Guo H. Chemical reaction rate coefficients from ring polymer molecular dynamics: theory and practical applications[J]. The Journal of Physical Chemistry A, 2016, 120(43): 8488-8502.
[33] Richardson J O, Althorpe S C. Ring-polymer molecular dynamics rate-theory in the deep-tunneling regime: connection with semiclassical instanton theory[J]. The Journal of Chemical Physics, 2009, 131(21): 214106.
[34] Allen J W, Green W H, Li Y, et al. Communication: full dimensional quantum rate coefficients and kinetic isotope effects from ring polymer molecular dynamics for a seven-atom reaction OH+CH$_{4}\!\to $CH$_{3 }$+H$_{2}$O[J]. The Journal of Chemical Physics, 2013, 138(22): 221103.
[35] Fu B, Zhang D H. Ab initio potential energy surfaces and quantum dynamics for polyatomic bimolecular reactions[J]. Journal of Chemical Theory and Computation, 2018, 14(5): 2289-2303.
[36] Miller W H. Quantum mechanical transition state theory and a new semiclassical model for reaction rate constants[J]. The Journal of Chemical Physics, 1974, 61(5): 1823-1834.
[37] Chandler D. Statistical mechanics of isomerization dynamics in liquids and the transition state approximation[J]. The Journal of Chemical Physics, 1978, 68(6): 2959-2970.
[38] Wang H, Fang J, Yang H, et al. Ring-polymer molecular dynamical benchmarks for X+H$_{2}$ insertion reactions[J]. Chemical Physics Letters, 2019, 730: 227-233.
[39] Suleimanov Y V, Allen J W, Green W H. RPMDrate: bimolecular chemical reaction rates from ring polymer molecular dynamics[J]. Computer Physics Communications, 2013, 184(3): 833-840.
[40] Li J, Guo H. Thermal rate coefficients and kinetic isotope effects for the reaction OH+CH$_{4}\!\to $H$_{2}$O+CH$_{3}$ on an ab initio-based potential energy surface[J]. The Journal of Physical Chemistry A, 2018, 122(10): 2645-2652.
[41] Zhang B, Shiu W, Lin J J, et al. Mode correlation of product pairs in the reaction OH+CD$_{4}\!\to $HOD+CD$_{3}$[J]. The Journal of Chemical Physics, 2005, 122(13): 131102.
[42] Zhang B, Shiu W, Liu K. Imaging the reaction dynamics of OH+CD$_{4}$. 2. translational energy dependencies[J]. The Journal of Physical Chemistry A, 2005, 109(40): 8983-8988.
[43] Suleimanov Y V, Espinosa-Garcia J. Recrossing and tunneling in the kinetics study of the OH+CH$_{4\!}\to $H$_{2}$O+CH$_{3}$ reaction[J]. The Journal of Physical Chemistry B, 2016, 120(8): 1418-1428.
[44] Germann G J, Huh Y D, Valentini J J. State-to-state dynamics of atom+polyatom abstraction reactions. Ⅱ. The H+C$_{2}$H$_{6}$/C$_{3}$H$_{8 }\to $H$_{2}$ (v', J')+C$_{2}$H$_{5}$/C$_{3}$H$_{7}$ reactions[J]. The Journal of Chemical Physics, 1992, 96(8): 5746-5757.
[45] LIN C C, Chen W Y, Matsui H, et al. Direct measurement of site-specific rates of reactions of H with C$_{3}$H$_{8}$, i-C$_{4}$H$_{10}$, and n-C$_{4}$H$_{10}$[J]. The Journal of Chemical Physics, 2017, 147(6): 064304.
[46] Korol R, Bou-Rabee N, Miller I T F. Cayley modification for strongly stable path-integral and ring-polymer molecular dynamics[J]. The Journal of Chemical Physics, 2019, 151(12): 124103.
[47] Korol R, Rosa-Raíices J L, Bou-Rabee N, et al. Dimension-free path-integral molecular dynamics without preconditioning[J]. The Journal of Chemical Physics, 2020, 152(10): 104102.
[48] Liu X, Liu J. Path integral molecular dynamics for exact quantum statistics of multi-electronic-state systems[J]. The Journal of Chemical Physics, 2018, 148(10): 102319.
[49] Zhang Z, Liu X, Yan K, et al. Unified efficient thermostat scheme for the canonical ensemble with holonomic or isokinetic constraints via molecular dynamics[J]. The Journal of Physical Chemistry A, 2019, 123(28): 6056-6079.
[50] Rosa-Raíices J L, Sun J, Bou-Rabee N, et al. A generalized class of strongly stable and dimension-free T-RPMD integrators[J]. The Journal of Chemical Physics, 2021, 154(2): 024106.
[51] Korol R, Bou-Rabee N, Miller I T F. Cayley modification for strongly stable path-integral and ring-polymer molecular dynamics[J]. The Journal of Chemical Physics, 2019, 151(12): 124103.
[52] Collepardo-Guevara R, Suleimanov Y V, Manolopoulos D E. Bimolecular reaction rates from ring polymer molecular dynamics[J]. The Journal of Chemical Physics, 2009, 130(17): 174713.
[53] Marjollet A, Welsch R. Nuclear quantum effects in state-selective scattering from ring polymer molecular dynamics[J]. The Journal of Chemical Physics, 2020, 152(19): 194113.
[54] De Tudela R P, Aoiz F J, Suleimanov Y V, et al. Chemical reaction rates from ring polymer molecular dynamics: zero point energy conservation in Mu+H$_{2}\to $MuH+H[J]. The Journal of Physical Chemistry Letters, 2012, 3(4): 493-497.
[55] Habershon S, Manolopoulos D E. Zero point energy leakage in condensed phase dynamics: an assessment of quantum simulation methods for liquid water[J]. The Journal of Chemical Physics, 2009, 131(24): 244518.
[56] Welsch R, Song K, Shi Q, et al. Non-equilibrium dynamics from RPMD and CMD[J]. The Journal of Chemical Physics, 2016, 145(20): 204118.
[57] Marjollet A, Welsch R. State-selective cross sections from ring polymer molecular dynamics[J]. International Journal of Quantum Chemistry, 2021, 121(3): e26447.
[58] Husch T, Sun J, Cheng L, et al. Improved accuracy and transferability of molecular-orbital-based machine learning: organics, transition-metal complexes, non-covalent interactions, and transition states[J]. The Journal of Chemical Physics, 2021, 154(6): 064108.
[59] Cheng L, Welborn M, Christensen A S, et al. A universal density matrix functional from molecular orbital-based machine learning: transferability across organic molecules[J]. The Journal of Chemical Physics, 2019, 150(13): 131103.
[60] Lee S J R, Husch T, Ding F, et al. Analytical gradients for molecular-orbital-based machine learning[J]. The Journal of Chemical Physics, 2021, 154(12): 124120.
[61] Li Y L, Suleimanov Y V, Guo H. Ring-polymer molecular dynamics rate coefficient calculations for insertion reactions: X+H$_{2 }\!\to $HX+H (X=N, O)[J]. The Journal of Physical Chemistry Letters, 2014, 5(4): 700-705.
[62] Zuo J X, Li Y L, Guo H, et al. Rate coefficients of the HCl+OH$\to $Cl+H$_{2}$O reaction from ring polymer molecular dynamics[J]. The Journal of Physical Chemistry A, 2016, 120(20): 3433-3440.
[63] Yang H, Fan W B, Fang J H, et al. Rate coefficients of roaming reaction H+MgH using ring polymer molecular dynamics[J]. Chinese Journal of Chemical Physics, 2021, 34(2): 149-156.
Options
Outlines

/

〈 〉