低温动力学过程由于极易受量子效应（如零点能和量子隧穿效应）的影响，经常表现出与高温动力学过程迥异的动力学特性，探究低温动力学过程中的量子效应有助于人们清晰理解低温下的动力学机理。本论文基于小曲率隧穿修正的正则变分过渡态理论（CVT/SCT）对三种量子效应突出的低温动力学过程进行了理论计算研究，详细分析了其中可能存在的量子效应及其对动力学过程的影响。 现有实验研究发现，甲醇与OH自由基间的反应速率常数在200 K及以下先随温度降低而显著升高，后又趋于平缓。其复杂的低温动力学特性与显著的量子效应密切相关，但具体的动力学机理并不明确。本论文着重分析了该反应的低温动力学过程。我们发现过渡态高频振动的强非简谐性影响了零点能的计算从而对低温速率常数的计算有着明显的影响；低温下量子隧穿效应显著增强，并且低于反应物能量的预反应复合物的稳定程度影响了量子隧穿效应的程度，完全稳定的预反应复合物会导致特别大的隧穿系数从而导致低温下显著的负温度效应；超低温下反应受限于预反应复合物的生成从而趋于平缓。 动力学量子筛分是一种极具前景的同位素混合物分离技术，基于同位素气体混合物由量子效应的不同导致的扩散速度差异进行筛分。目前该方法的量子效应作用机理尚不清晰。本论文以氢气和氘气在RHO沸石中的扩散为例，提出了一种精确且方便的方法用于细致化分析零点能和隧穿效应两种典型的量子效应对动力学量子筛分的单独贡献。我们揭示了零点能和隧穿效应的相反的贡献：氘气的零点能小于氢气，引起了更低的扩散能垒，因此比氢气扩散要快；但是质量轻的氢气比氘气更容易发生隧穿，因此隧穿效应会导致与零点能相反的不可忽视的影响。 μ子素（Mu）质量仅为H的1/9，Mu反应的动力学同位素效应的计算是动力学中的量子效应研究的有效分析手段。其中Mu和丙烷的反应存在着不同寻常的量子效应，已有的理论计算与实验测量存在着显著的差异。我们发现该反应的振动非简谐性沿着反应坐标有明显的变化。这种变化引起了反应的有效势能面上势垒的高度和宽度的同时缩小，前者直接增大反应的速率常数，而后者增大了隧穿系数从而极大地增大了反应的速率常数。
Dynamics process at low temperatures is easily affected by quantum effects such as zero point energy and quantum tunneling effect, and so it often shows different dynamic characteristics from high-temperature dynamics process. It can be helpful to explore the quantum effects in low-temperature dynamics process for understanding the dynamics mechanism of reactions at low temperatures. This thesis focuses on the theoretical investigation of three kinds of low-temperature dynamics processes which are all greatly affected by quantum effects, by using the canonical variational theory (CVT) with small-curvature tunneling (SCT) contributions. We analyze the possible quantum effects and their effects on these dynamics process detailedly. Previous experimental studies have reported the significantly increasing reaction rate constant between methanol and OH with the decrease of temperature when the temperature is below 200 K, which then tends to be a constant at ultralow temperature. This unusual phenomenon has been believed to be related with the large quantum effect, but the dynamic mechanism is still unclear. In this thesis, we mainly concentrate on the low-temperature mechanism of methanol reaction with OH. We find a significant effect of the large anharmonicity of high-frequency modes of transition states on the low-temperature rate constants; the quantum tunneling effect is significantly enhanced at low temperatures, and it depends on the stability of the pre-reaction complex which has a lower energy than the reactants. The completely stablized pre-reaction complex will lead to an extremely large tunneling coefficient, resulting in a significant negative temperature effect at low temperature. At ultralow temperatures, the capture rate for the formation of the complex is the dominant dynamical bottleneck, and therefore the reaction shows weak temperature dependence of the rate constants.Kinetic quantum sieving (KQS) is a promising separation technique for isotopic mixtures based on the difference of diffusion rate constants of isotopes caused by the different quantum effects in microporous materials. The detailed mechanism of how quantum effects affect the diffusion process is unclear yet. We propose an accurate and convenient way to calculate the quantum effects on diffusion with the example of H2 diffusion in zeolite RHO here. We reveal the opposite contribution of zero point energy and quantum tunneling effect. Deuterium has a lower ZPE, which leads to a smaller effective barrier for tunneling because the transition state has a larger ZPE than the precursor stable state; this results in an inverse KIE. However, quantum tunneling would lead to a normal kinetic isotopic sieving effect, in which lighter diprotium diffuses faster than dideuterium. Due to the large mass ratio between muonium (Mu) and H (1:9), calculations of kinetic isotope effects for muonium reactions provide challenging tests of quantum effects on reaction rates. There is a large discrepancy between experiment and theory for the reaction of Mu with C3H8, which reveals the unusual quantum effect mechanism in this reaction system. We find that the vibrational anharmonicity of this muonium reaction is significant and depends greatly on the reaction coordinate, which decreases both the height and width of the vibrationally adiabatic potential barrier, with both effects increasing the rate constants.
