## Abstract

This is an updated version of TUMME (Tsinghua University Minnesota Master Equation program), which is a computer program for setting up and solving master equations for chemical kinetics of unimolecular and bimolecular reactions. The master equation is discretized in terms of energy bins, and rate constants are calculated from chemically significant eigenmodes. TUMME has interfaces to Gaussian 16, Polyrate 2023, and MSTor 2023 output files that allow the master equation code to obtain the microcanonical flux coefficients needed for the kernel of the master equation as calculated by conventional transition state theory (TST), variational transition state theory (VTST) with various tunneling methods, or multi-structural or multi-path VTST (MS-VTST or MP-VTST) with various tunneling methods. The tunneling methods supported include zero-curvature tunneling (ZCT), small-curvature tunneling (SCT), large-curvature tunneling (LCT), and microcanonically optimized multidimensional tunneling (μOMT). For mechanisms involving only unimolecular isomerization (no bimolecular pairs), TUMME can set up and solve a conservative master equation for both rate constants and time-dependent energy-bin populations. For mechanisms involving bimolecular pairs, TUMME 2023 can set up and solve two kinds of master equation: (i) a nonconservative master equation for calculating rate constants of bimolecular reactions and (ii) a conservative master equation that includes bimolecular association in the transition matrix and that can be used for calculating the time evolution of the concentration of a pseudo-first-order bimolecular reactant. TUMME is written in double precision with Python 3; quadruple and octuple precision are also available for some subtasks in C++. The Python code can run in serial or parallel (MP or MPI), and C++ code can run on a single processor or on multiple processors with OpenMP. The program includes a manual and a tutorial. New version program summary: Program Title: TUMME 2023 CPC Library link to program files: https://doi.org/10.17632/whcnvm2mc9.2 Developer's repository link: https://doi.org/10.5281/zenodo.7943283 Licensing Provisions: Apache-2.0 for the program and CC-BY-4.0 for the manual Programming languages: Python 3 and C++ Does the new version supersede the previous version?: Yes Journal reference of previous version: Comput. Phys. Commun. 270 (2022) 108140 [1] External libraries: Numpy, Scipy, Numba, mpi4py (optional), modified mpack (optional), qd (optional), omp (optional) Interfaces to other programs: Gaussian 16 [2], Polyrate 2023 [3], and/or MSTor 2023 [4] Nature of problem: Characterize and calculate rate constants for a temperature-dependent and pressure-dependent complex reaction system Solution method: Solve the energy-grained master equation based on the chemically significant eigenmodes to get phenomenological rate constants and time evolutions of the populations [1,5–7]. Reason for new version: The new version increases the functionality and accuracy, and it offers an easier way to run the program. In addition, some bugs have been corrected. Summary of revisions: 1. Added an option (available in high precision) to treat pseudo-first-order bimolecular reactions to obtain the time evolution of the reactants and intermediates. [8] 2. Added an inverse-Laplace-transform option in the REACTION block. 3. Abandoned rounding the sizes of energy bins to an integer wavenumber (ESOT). 4. Changed the way to run TUMME by providing an executable bash script. 5. Slightly adjusted the strategy for eigenmode mergers to deal with some unexpected cases. 6. Adjusted the output for the partition functions. 7. Added options for large-curvature tunneling (LCT) and microcanonically optimized multidimensional tunneling (μOMT). 8. Added the keyword PYRFILE to support a Polyrate 2023 [3] file that ends with a suffix .fu100. 9. Fixed some bugs. 10. Updated the manual and added a tutorial to the program distribution, so the distribution now has both a manual and a tutorial. References: [1] R.M. Zhang, X. Xu, D.G. Truhlar, TUMME: Tsinghua University Minnesota Master Equation program, Comput. Phys. Commun. 270 (2022) 108140, https://doi.org/10.1016/j.cpc.2021.108140. [2] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, G.A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A.V. Marenich, J. Bloino, B.G. Janesko, R. Gomperts, B. Mennucci, H.P. Hratchian, J.V. Ortiz, A.F. Izmaylov, J.L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V.G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J.A. Montgomery, Jr., J.E. Peralta, F. Ogliaro, M.J. Bearpark, J.J. Heyd, E.N. Brothers, K.N. Kudin, V.N. Staroverov, T.A. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A.P. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, J.M. Millam, M. Klene, C. Adamo, R. Cammi, J.W. Ochterski, R.L. Martin, K. Morokuma, O. Farkas, J.B. Foresman, D.J. Fox, Gaussian 16, Gaussian, Inc., Wallingford CT, 2016. [3] R. Meana-Pañeda, J. Zheng, J.L. Bao, S. Zhang, B.J. Lynch, J.C. Corchado, Y.-Y. Chuang, P.L. Fast, W.-P. Hu, Y.-P. Liu, G.C. Lynch, K.A. Nguyen, C.F. Jackels, A. Fernandez Ramos, B.A. Ellingson, V.S. Melissas, J. Villà, I. Rossi, E.L. Coitiño, J. Pu, T.V. Albu, R.M. Zheng, X. Xu, A. Ratkiewicz, R. Steckler, B.C. Garrett, A.D. Isaacson, D.G. Truhlar, Polyrate 2023, University of Minnesota, Minneapolis and Tsinghua University, Beijing, 2023, https://doi.org/10.5281/zenodo.8213313. [4] W. Chen, J. Zheng, J.L. Bao, D.G. Truhlar, and X. Xu, MSTor 2023: A New Version of the Computer Code for Multi-Structural Torsional Anharmonicity, Now with Automatic Torsional Identification Using Redundant Internal Coordinates, Comput. Phys. Commun. 288 (2023) 108740. [5] A. Fernández-Ramos, J.A. Miller, S.J. Klippenstein, D.G. Truhlar, Modeling the Kinetics of Bimolecular Reactions, Chem. Rev. 106 (2006) 4518-4584. [6] Y. Georgievskii, J.A. Miller, M.P. Burke, S.J. Klippenstein, Reformulation and Solution of the Master Equation for Multiple-Well Chemical Reactions, J. Phys. Chem. A 117 (2013) 12146. [7] R.M. Zhang, X. Xu, D.G. Truhlar, Energy Dependence of Ensemble-Averaged Energy Transfer Moments and Its Effect on Competing Decomposition Reactions, J. Phys. Chem. A 125 (2021) 6303-6313. [8] R.M. Zhang, W. Chen, D.G. Truhlar, X. Xu, Master Equation Study of Hydrogen Abstraction from HCHO by OH via a Chemically Activated Intermediate, Faraday Discuss 38 (2022) 431-460.

Original language | English (US) |
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Article number | 108894 |

Journal | Computer Physics Communications |

Volume | 293 |

DOIs | |

State | Published - Dec 2023 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2023 Elsevier B.V.

## Keywords

- Bimolecular reactions
- Chemical kinetics
- Chemically significant eigenmodes
- Master equation
- Torsional anharmonicity
- Tunneling
- Unimolecular reactions
- Variational transition state theory