发表机构
Arya Vidyapeeth College (A); Gauhati University（阿里亚维迪亚皮特学院; 高哈蒂大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出康奈尔型解析-数值框架，揭示氢键中质子与氘核隧穿劈裂对有效质量平方根的指数标度，并在3D和5D量子模型中验证，为双阱体系提供高效计算方法。
AI 中文摘要
量子隧穿在氢键体系的结构和光谱中起着核心作用，其对同位素取代的敏感性为探测底层势能面提供了严格的探针。尽管已有大量数值研究，许多高水平方法往往掩盖了有效质量、势垒几何和隧穿振幅之间的简单物理关系。在此，我们开发了一个康奈尔型解析-数值框架来描述质子和氘核隧穿，将半解析局域波函数拟设与一维薛定谔方程的数值解相结合。所得的隧穿劈裂表现出对有效同位素质量平方根的指数依赖，即 $\ln(\Delta E)\propto -\sqrt{\mu_{\mathrm{eff}}}$，与半经典Wentzel-Kramers-Brillouin (WKB)理论一致。与甲酸二聚体的多维反应空间计算比较表明，这种标度在完全耦合的3D和5D量子模型中持续存在，得到经验关系 $\ln(\Delta E)= -1.75\sqrt{\mu_{\mathrm{eff}}}+2.60$。本框架为量化氢键及其他双阱体系中的质量标度和隧穿动力学提供了一种透明且计算高效的方法。
英文摘要
Quantum tunnelling plays a central role in the structure and spectroscopy of hydrogen-bonded systems, and its sensitivity to isotopic substitution provides a stringent probe of the underlying potential-energy landscape. Despite extensive numerical studies, many high-level approaches tend to obscure the simple physical relationships linking effective mass, barrier geometry, and tunnelling amplitudes. Here, we develop a Cornell-type analytical--numerical framework to describe proton and deuteron tunnelling, combining a semi-analytical localized wavefunction ansatz with numerical solutions of the one-dimensional Schrödinger equation. The resulting tunnelling splittings exhibit an exponential dependence on the square root of the effective isotope mass,$\ln(ΔE)\propto -\sqrt{μ_{\mathrm{eff}}}$, in agreement with semiclassical Wentzel--Kramers--Brillouin (WKB) theory. Comparison with multidimensional reaction-space calculations for the formic acid dimer shows that this scaling persists in fully coupled 3D and 5D quantum models, yielding an empirical relation $\ln(ΔE)= -1.75\sqrt{μ_{\mathrm{eff}}}+2.60$. The present framework provides a transparent and computationally efficient approach for quantifying mass-scaling and tunnelling dynamics in hydrogen-bonded and other double-well systems.
Comments19 pages, 6 figures, 1 table
Journal refChemical Physics 607 (2026) 113203
DOI：10.1016/j.chemphys.2026.113203
