Zhang Chenghao, Sibert Edwin L, Gruebele Martin
Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA.
J Chem Phys. 2021 Mar 14;154(10):104301. doi: 10.1063/5.0043665.
Intramolecular energy flow (also known as intramolecular vibrational redistribution or IVR) is often assumed in Rice-Ramsperger-Kassel-Marcus, transition state, collisional energy transfer, and other rate calculations not to be an impediment to reaction. In contrast, experimental spectroscopy, computational results, and models based on Anderson localization have shown that ergodicity is achieved rather slowly during molecular energy flow. The statistical assumption in rate theories might easily fail due to quantum localization. Here, we develop a simple model for the interplay of IVR and energy transfer and simulate the model with near-exact quantum dynamics for a 10-degree of freedom system composed of two five-mode molecular fragments. The calculations are facilitated by applying the van Vleck transformation to local random matrix models of the vibrational Hamiltonian. We find that there is a rather sharp "phase transition" as a function of molecular anharmonicity "a" between a region of facile energy transfer and a region limited by IVR and incomplete accessibility of the state space (classically, the phase space). The very narrow transition range of the order parameter a happens to lie right in the middle of the range expected for molecular torsion, bending, and stretching vibrations, thus demonstrating that reactive energy transfer dynamics several kT above the thermal energy occurs not far from the localization boundary, with implications for controllability of reactions.
分子内能量流动（也称为分子内振动重新分布或IVR）在赖斯-拉姆齐-卡斯尔-马库斯理论、过渡态理论、碰撞能量转移理论以及其他速率计算中，通常被认为不会对反应造成阻碍。相比之下，实验光谱学、计算结果以及基于安德森局域化的模型表明，在分子能量流动过程中，遍历性的实现相当缓慢。由于量子局域化，速率理论中的统计假设可能很容易失效。在此，我们开发了一个用于IVR与能量转移相互作用的简单模型，并对一个由两个五模分子片段组成的10自由度系统，用近乎精确的量子动力学模拟该模型。通过将范弗莱克变换应用于振动哈密顿量的局部随机矩阵模型，计算得以简化。我们发现，作为分子非谐性“a”的函数，在易于能量转移的区域和受IVR及状态空间（经典地，相空间）不完全可达性限制的区域之间，存在一个相当尖锐的“相变”。序参量a的非常窄的转变范围恰好位于分子扭转、弯曲和拉伸振动预期范围的中间，这表明高于热能几个kT的反应能量转移动力学发生在离局域化边界不远的地方，这对反应的可控性具有重要意义。
