Pressure-Dependent Rate Rules for Intramolecular H‑Migration Reactions of Hydroperoxyalkylperoxy Radicals in Low Temperature

Intramolecular H-migration reaction of hydroperoxyalkylperoxy radicals (•O2QOOH) is one of the most important reaction families in the low-temperature oxidation of hydrocarbon fuels. This reaction family is first divided into classes depending upon H atom transfer from -OOH bonded carbon or non-OOH bonded carbon, and then the two classes are further divided depending upon the ring size of the transition states and the types of the carbons from which the H atom is transferred. High pressure limit rate rules and pressure-dependent rate rules for each class are derived from the rate constants of a representative set of reactions within each class using electronic structure calculations performed at the CBS-QB3 level of theory. For the intramolecular H-migration reactions of •O2QOOH radicals for abstraction from an -OOH substituted carbon atom (-OOH bonded case), the result shows that it is acceptable to derive the rate rules by taking the average of the rate constants from a representative set of reactions with different sizes of the substitutes. For the abstraction from a non-OOH substituted carbon atom (non-OOH bonded case), rate rules for each class are also derived and it is shown that the difference between the rate constants calculated by CBS-QB3 method and rate constants estimated from the rate rules may be large; therefore, to get more reliable results for the low-temperature combustion modeling of alkanes, it is better to assign each reaction its CBS-QB3 calculated rate constants, instead of assigning the same values for the same reaction class according to rate rules. The intramolecular H-migration reactions of •O2QOOH radicals (a thermally equilibrated system) are pressure-dependent, and the pressure-dependent rate constants of these reactions are calculated by using the Rice–Ramsberger–Kassel–Marcus/master-equation theory at pressures varying from 0.01 to 100 atm. The impact of molecular size on the pressure-dependent rate constants of the intramolecular H-migration reactions of •O2QOOH radicals has been studied, and it is shown that the pressure dependence of the rate constants of intramolecular H-migration reactions of •O2QOOH radicals decreases with the molecular size at low temperatures and the impact of molecular size on the pressure-dependent rate constants decreases as temperature increases. It is shown that it is acceptable to derive the pressure-dependent rate rules by taking the average of the rate constants from a representative set of reactions with different sizes of the substitutes. The barrier heights follow the Evans–Polanyi relationship for each type of intramolecular hydrogen-migration reaction studied. All calculated rate constants are fitted by a nonlinear least-squares method to the form of a modified Arrhenius rate expression at pressures varying from 0.01 to 100 atm and at the high-pressure limit. Furthermore, thermodynamic parameters for all species involved in these reactions are calculated by the composite CBS-QB3 method and are given in NASA format.氢过氧烷基过氧自由基（hydroperoxyalkylperoxy radicals，•O2QOOH）的分子内氢迁移反应是烃类燃料低温氧化过程中最重要的反应家族之一。该反应家族首先依据氢原子转移的位点分为两类——从连有-OOH的碳原子转移，或是从未连-OOH的碳原子转移；随后两类又可分别根据过渡态的环尺寸以及氢原子转移所涉及的碳原子类型进一步细分。本研究针对每一类反应，基于CBS-QB3理论级别下的电子结构计算结果，通过该类内一组代表性反应的速率常数，推导得到了高压极限速率规则与压力依赖速率规则。针对从连有-OOH的碳原子上夺氢的•O2QOOH自由基分子内氢迁移反应（即-OOH成键情况），研究结果表明，通过取一组具有不同取代基尺寸的代表性反应的速率常数平均值来推导速率规则是可行的。而对于从未连-OOH的碳原子上夺氢的情况（非-OOH成键情况），本研究同样推导了各类反应的速率规则，结果显示，CBS-QB3方法计算得到的速率常数与基于速率规则估算的速率常数之间可能存在较大偏差；因此，为了在烷烃低温燃烧模拟中获得更可靠的结果，相较于依据速率规则为同一反应类统一赋值，为每个反应单独赋予CBS-QB3计算得到的速率常数更为合适。•O2QOOH自由基的分子内氢迁移反应（属于热平衡体系）具有压力依赖性，本研究通过Rice–Ramsberger–Kassel–Marcus/主方程理论，在0.01至100 atm的压力范围内计算得到了这类反应的压力依赖速率常数。本研究还探讨了分子尺寸对•O2QOOH自由基分子内氢迁移反应压力依赖速率常数的影响，结果表明，在低温条件下，•O2QOOH自由基分子内氢迁移反应速率常数的压力依赖性随分子尺寸增大而减弱，且分子尺寸对压力依赖速率常数的影响随温度升高而降低。研究结果证实，通过取一组具有不同取代基尺寸的代表性反应的速率常数平均值来推导压力依赖速率规则是可行的。在所研究的各类分子内氢迁移反应中，反应势垒均符合Evans–Polanyi关系。本研究通过非线性最小二乘法，将0.01至100 atm压力范围及高压极限下的所有计算速率常数拟合为修正的阿伦尼乌斯速率表达式形式。此外，本研究通过复合CBS-QB3方法计算得到了这些反应涉及的所有物种的热力学参数，并以NASA格式给出。