Truncated Multipath Variational Transition State Theory and Intramolecular Hydrogen Bond Effect Study for Kinetics of Ethylenediamine Reactions with Nitroglycerin and 1,2,4-Butanetriol Trinitrate

Multipath variational transition state theory (MP-VTST) provides a conformationally complete model for calculating rate constants of gas-phase reactions with multiple transition state structures, which are usually generated by torsional motions around rotatable single bonds and lead to various paths of the same reaction. In general, MP-VTST calculations include the contributions of all of the reaction paths; however, to reduce the computational cost for relatively large molecules, the number of reaction paths is usually truncated according to their electronic barriers. The applicability of this truncation method is unclear for systems with intramolecular hydrogen bonds since hydrogen bonds of species significantly reduce the entropy and increase the Gibbs free energy at combustion temperatures. Therefore, in this work, we analyzed the truncation error for the MP-VTST method with different cutoff energies for the reaction of ethylenediamine (C₂H₄(NH₂)₂) with nitroglycerin (NG). We also proposed a new truncation method, which is called the partition-function cutoff standard, based on the single-structure rovibrational partition function with torsional anharmonicity correction, to reduce the number of reaction paths used in the MP-VTST calculation and applied it to the reactions of C₂H₄(NH₂)₂ with NG and 1,2,4-butanetriol trinitrate (BTTN). The results show that the path dependence of transmission coefficients cannot be ignored and that most transition state structures with hydrogen bonds have relatively low electronic energies but contribute little to the total reaction rate due to the entropy effect. Additionally, we show that both truncation methods can have relatively low truncation error with proper selection of the cutoff parameters, but the truncation method based on the electronic energies may lead to some fluctuations in the uncertainty of the calculated reaction rate, especially at combustion temperatures.