For a long time, performing converged path integral simulations at ultralow but finite temperatures of a few Kelvin has been a nearly impossible task. However, recent developments in advanced colored noise thermostatting schemes for path integral simulations, namely, the Path Integral Generalized Langevin Equation Thermostat (PIGLET) and the Path Integral Quantum Thermal Bath (PIQTB), have been able to greatly reduce the computational cost of these simulations, thus making the ultralow temperature regime accessible in practice. In this work, we investigate the influence of these two thermostatting schemes on the description of hydrogen-bonded systems at temperatures down to a few Kelvin as encountered, for example, in helium nanodroplet isolation or tagging photodissociation spectroscopy experiments. For this purpose, we analyze the prototypical hydrogen bond in the Zundel cation (H₅O₂⁺) as a function of both oxygen–oxygen distance and temperature in order to elucidate how the anisotropic quantum delocalization and, thus, the shape of the shared proton adapts depending on the donor–acceptor distance. The underlying electronic structure of the Zundel cation is described in terms of Behler’s Neural Network Potentials of essentially converged Coupled Cluster accuracy, CCSD(T*)-F12a/AVTZ. In addition, the performances of the PIQTB and PIGLET methods for energetic, structural, and quantum delocalization properties are assessed and directly compared. Overall, our results emphasize the validity and practical usefulness of these two modern thermostatting approaches for path integral simulations of hydrogen-bonded systems even at ultralow temperatures.

中文翻译：

---

耦合簇精度下超低温度Zundel阳离子的聚合有色噪声路径积分分子动力学研究

长期以来，在几个开尔文的超低但有限的温度下执行会聚路径积分模拟几乎是不可能的任务。但是，用于路径积分模拟的高级有色噪声恒温方案的最新发展，即路径积分广义兰文芬方程恒温器（PIGLET）和路径积分量子热浴池（PIQTB），已经能够大大降低这些模拟的计算成本，因此在实践中可以使用超低温条件。在这项工作中，我们研究了这两种温度调节方案对氢键系统在低至几开尔文温度下的描述的影响，例如在氦纳米液滴分离或标记光解离光谱实验中遇到的情况。以此目的，₅ O ₂ ⁺）作为氧-氧距离和温度的函数，以阐明各向异性量子离域以及共享质子的形状如何根据施主-受主距离而变化。Zundel阳离子的基本电子结构是根据Behler的神经网络电势描述的，该电势具有基本收敛的耦合簇精度CCSD（T *）-F12a / AVTZ。另外，评估并直接比较了PIQTB和PIGLET方法在能量，结构和量子离域特性方面的性能。总的来说，我们的结果强调了这两种现代恒温方法即使在超低温下对氢键系统的路径积分模拟的有效性和实用性。