### Abstract

The quasiclassical trajectory (QCT) method is an efficient and important tool for studying the dynamics of bimolecular reactions. In this method, the motion of the atoms is simulated classically, and the only quantum effect considered is that the initial vibrational states of reactant molecules are semiclassically quantized. A sensible expectation is that the initial ensemble of classical molecular states generated this way should be stationary, similarly to the quantum state it is supposed to represent. The most widely used method for sampling the vibrational phase space of polyatomic molecules is based on the normal mode approximation. In the present work, it is demonstrated that normal mode sampling provides a nonstationary ensemble even for a simple molecule like methane, because real potential energy surfaces are anharmonic in the reactant domain. The consequences were investigated for reaction CH_{4} + H → CH_{3} + H_{2} and its various isotopologs and were found to be dramatic. Reaction probabilities and cross sections obtained from QCT calculations oscillate periodically as a function of the initial distance of the colliding partners and the excitation functions are erratic. The reason is that in the nonstationary ensemble of initial states, the mean bond length of the breaking C-H bond oscillates in time with the frequency of the symmetric stretch mode. We propose a simple method, one-period averaging, in which reactivity parameters are calculated by averaging over an entire period of the mean C-H bond length oscillation, which removes the observed artifacts and provides the physically most reasonable reaction probabilities and cross sections when the initial conditions for QCT calculations are generated by normal mode sampling.

Original language | English |
---|---|

Article number | 014104 |

Journal | The Journal of Chemical Physics |

Volume | 144 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 7 2016 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*The Journal of Chemical Physics*,

*144*(1), [014104]. https://doi.org/10.1063/1.4939583

**Oscillatory reaction cross sections caused by normal mode sampling in quasiclassical trajectory calculations.** / Nagy, Tibor; Vikár, Anna; Lendvay, G.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 144, no. 1, 014104. https://doi.org/10.1063/1.4939583

}

TY - JOUR

T1 - Oscillatory reaction cross sections caused by normal mode sampling in quasiclassical trajectory calculations

AU - Nagy, Tibor

AU - Vikár, Anna

AU - Lendvay, G.

PY - 2016/1/7

Y1 - 2016/1/7

N2 - The quasiclassical trajectory (QCT) method is an efficient and important tool for studying the dynamics of bimolecular reactions. In this method, the motion of the atoms is simulated classically, and the only quantum effect considered is that the initial vibrational states of reactant molecules are semiclassically quantized. A sensible expectation is that the initial ensemble of classical molecular states generated this way should be stationary, similarly to the quantum state it is supposed to represent. The most widely used method for sampling the vibrational phase space of polyatomic molecules is based on the normal mode approximation. In the present work, it is demonstrated that normal mode sampling provides a nonstationary ensemble even for a simple molecule like methane, because real potential energy surfaces are anharmonic in the reactant domain. The consequences were investigated for reaction CH4 + H → CH3 + H2 and its various isotopologs and were found to be dramatic. Reaction probabilities and cross sections obtained from QCT calculations oscillate periodically as a function of the initial distance of the colliding partners and the excitation functions are erratic. The reason is that in the nonstationary ensemble of initial states, the mean bond length of the breaking C-H bond oscillates in time with the frequency of the symmetric stretch mode. We propose a simple method, one-period averaging, in which reactivity parameters are calculated by averaging over an entire period of the mean C-H bond length oscillation, which removes the observed artifacts and provides the physically most reasonable reaction probabilities and cross sections when the initial conditions for QCT calculations are generated by normal mode sampling.

AB - The quasiclassical trajectory (QCT) method is an efficient and important tool for studying the dynamics of bimolecular reactions. In this method, the motion of the atoms is simulated classically, and the only quantum effect considered is that the initial vibrational states of reactant molecules are semiclassically quantized. A sensible expectation is that the initial ensemble of classical molecular states generated this way should be stationary, similarly to the quantum state it is supposed to represent. The most widely used method for sampling the vibrational phase space of polyatomic molecules is based on the normal mode approximation. In the present work, it is demonstrated that normal mode sampling provides a nonstationary ensemble even for a simple molecule like methane, because real potential energy surfaces are anharmonic in the reactant domain. The consequences were investigated for reaction CH4 + H → CH3 + H2 and its various isotopologs and were found to be dramatic. Reaction probabilities and cross sections obtained from QCT calculations oscillate periodically as a function of the initial distance of the colliding partners and the excitation functions are erratic. The reason is that in the nonstationary ensemble of initial states, the mean bond length of the breaking C-H bond oscillates in time with the frequency of the symmetric stretch mode. We propose a simple method, one-period averaging, in which reactivity parameters are calculated by averaging over an entire period of the mean C-H bond length oscillation, which removes the observed artifacts and provides the physically most reasonable reaction probabilities and cross sections when the initial conditions for QCT calculations are generated by normal mode sampling.

UR - http://www.scopus.com/inward/record.url?scp=84954110117&partnerID=8YFLogxK

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U2 - 10.1063/1.4939583

DO - 10.1063/1.4939583

M3 - Article

VL - 144

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 1

M1 - 014104

ER -