Machine Learning Analysis of Direct Dynamics Trajectory Outcomes for Thermal Deazetization of 2,3-Diazabicyclo[2.2.1]hept-2-ene

Experimentally, the thermal gas-phase deazetization of 2,3-diazabicyclo[2.2.1]­hept-2-ene (1) results in the loss of N2 and the formation of bicyclo products 3 (exo) and 4 (endo) in a nonstatistical ratio, with preference for the exo product. Here, we report unrestricted M06-2X quasiclassical trajectories initialized from the concerted N2 ejection transition state that were able to replicate the experimental preference to form 3. We found that the 3:4 ratio results from the relative amounts of very fast (ballistic) exotype trajectories versus trajectories that lead to the 1,3-diradical intermediate 2. These quasiclassical trajectories provided a set of transition-state vibrational, velocity, momenta, and geometric features for the machine learning analysis. A selection of popular supervised classification algorithms (e.g., random forest) provided poor prediction of trajectory outcomes based on only transition-state vibrational quanta and energy features. However, these machine learning models provided more accurate predictions using atomic velocities and atomic positions, attaining ∼70% accuracy using initial conditions and between 85 and 95% accuracy at later reaction time steps. This increased accuracy allowed the feature importance analysis to reveal that, at the later-time analysis, the methylene bridge out-of-plane bending is correlated with trajectory outcomes for the formation of either the exo product or toward the diradical intermediate. Possible reasons for the struggle of machine learning algorithms to classify trajectories based on transition-state features is the heavily overlapping feature values, the finite but very large possible vibrational mode combinations, and the possibility of chaos as trajectories propagate. We examined this chaos by comparing a set of nearly identical trajectories that differed by only a very small scaling of the kinetic energies resulting from the transition-state reaction coordinate.

实验结果表明，2,3-二氮杂双环[2.2.1]庚-2-烯（1）的气相热脱氮反应会脱去N₂，生成双环产物3（exo，外向构型）和4（endo，内向构型），且二者的比例不符合统计分布，更倾向于生成外向型产物3。本研究基于协同脱N₂过渡态初始化了无限制M06-2X准经典轨迹计算，成功复现了实验中倾向生成外向型产物的结果。我们发现，3与4的产率比源于快速（弹道式）外向型轨迹与生成1,3-双自由基中间体2的轨迹的相对占比差异。这些准经典轨迹为机器学习分析提供了一组过渡态的振动、速度、动量及几何特征。多款主流监督分类算法（如随机森林（random forest））仅基于过渡态振动量子数与能量特征对轨迹结果的预测效果较差。但当使用原子速度与原子位置作为特征时，这些机器学习模型的预测准确率显著提升：仅基于初始条件的预测准确率约为70%，而在反应后期时间步的预测准确率可达85%~95%。准确率的提升使得特征重要性分析得以揭示：在后期时间分析中，亚甲基桥的面外弯曲振动与生成外向型产物或双自由基中间体的轨迹结果存在相关性。机器学习算法难以仅基于过渡态特征对轨迹进行分类的潜在原因包括：特征值严重重叠、可能的振动模式组合数量有限但体量极其庞大，以及轨迹传播过程中存在混沌现象。我们通过对比两组仅因过渡态反应坐标对应的动能存在极微小缩放差异的近乎完全相同的轨迹，对该混沌现象进行了考察。