从经典熵和量子熵解读流动分子的高阶结构关联
Deciphering High-order Structural Correlations within Fluxional Molecules from Classical and Quantum Configurational Entropy
摘要：
我们采用k次最近邻估计的构型熵，以解码内的无参数的数值方法的复杂的高阶结构的相关性在fluxional分子超出通常的线性，双变量的相关性。这个通用的基于熵的计划，用于确定多体相关性的质子化乙炔，具有大幅度运动的流动分子的原型的复杂的构型合奏。在揭示了这种分子的高阶关联的重要性之后，我们详细分析了相关关联随温度的演化以及核量子效应对1 K超低温区的影响。我们发现，量子离域和零点振动显着降低质子化乙炔在深量子制度的所有相关性。在大约100至800 K的中间温度下，发现量子到经典的交叉机制，其中经典力学开始正确地描述相关性的趋势，而它甚至在100 K以下定性地失败。最后，原子核的经典描述提供的关联只有在温度超过1000 K时才与量子关联在数量上一致。这种数据密集型分析之所以成为可能，是因为最近基于全维度神经网络潜力的机器学习技术的发展，使我们能够以基本收敛的耦合簇精度对质子化乙炔的经典和量子系综进行详尽的采样。所提出的非参数相关性分析，预计将补充和指导实验测量的分析，特别是多维振动光谱，通过揭示各种自由度之间的复杂耦合。
英文摘要：
We employ the k-th nearest-neighbor estimator of configurational entropy in order to decode within a parameter-free numerical approach the complex high-order structural correlations in fluxional molecules going beyond the usual linear, bivariate correlations. This generic entropy-based scheme for determining many-body correlations is applied to the complex configurational ensemble of protonated acetylene, a prototype for fluxional molecules featuring large-amplitude motion. After revealing the importance of high-order correlations beyond the simple two-coordinate picture for this molecule, we analyze in detail the evolution of the relevant correlations with temperature as well as the impact of nuclear quantum effects down to the ultra-low temperature regime of 1 K. We find that quantum delocalization and zero-point vibrations significantly reduce all correlations in protonated acetylene in the deep quantum regime. At intermediate temperatures of approximately 100 to 800 K, a quantum-to-classical cross-over regime is found where classical mechanics starts to correctly describe trends in the correlations whereas it even qualitatively fails below 100 K. Finally, a classical description of the nuclei provides correlations that are in quantitative agreement with the quantum ones only at temperatures exceeding 1000 K. This data-intensive analysis has been made possible due to recent developments of machine learning techniques based on neural network potentials in full dimensionality that allow us to exhaustively sample both, the classical and quantum ensemble of protonated acetylene at essentially converged coupled cluster accuracy. The presented non-parametric analysis of correlations is expected to complement and guide the analysis of experimental measurements, in particular multi-dimensional vibrational spectroscopy, by revealing the complex coupling between various degrees of freedom.
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