[论文解读] Third and fourth density and acoustic virial coefficients of neon from first-principles calculations

Robert Hellmann, Giovanni Garberoglio|arXiv (Cornell University)|Jan 29, 2026

Quantum, superfluid, helium dynamics被引用 0

一句话总结

该论文通过从第一性原理出发，使用含有相对论和后Born–Oppenheimer效应的路径积分蒙特卡洛方法，结合高水平ab initio对成对、三体、四体势进行计算，得到氖的第三、第四密度及声速Virial系数。

ABSTRACT

The third and fourth density and acoustic virial coefficients of neon were determined at temperatures between 10 and 5000 K from first principles employing the path-integral Monte Carlo (PIMC) approach. For these calculations, we used the pair potential of Hellmann $ extit{et al.}$ [J. Chem. Phys. 154, 164304 (2021)], which is based on supermolecular $ extit{ab initio}$ calculations with basis sets of up to octuple-zeta quality and levels of theory up to coupled cluster with single, double, triple, quadruple, and perturbative pentuple excitations [CCSDTQ(P)]. The potential also accounts for relativistic, retardation, and post-Born$-$Oppenheimer effects and is provided with reliable uncertainty estimates. To incorporate nonadditive interactions, we developed a nonadditive three-body potential based on extensive supermolecular CCSD(T), CCSDT, and CCSDT(Q) calculations with basis sets of up to sextuple-zeta quality. This potential also accounts for relativistic effects. The very small nonadditive four-body contributions to the fourth virial coefficients were considered using a relatively simple nonadditive four-body potential based on supermolecular CCSD(T) calculations. We calculated the third and fourth density and third acoustic virial coefficients directly by PIMC and the fourth acoustic virial coefficient indirectly using thermodynamic relations between the density and acoustic virial coefficients. The uncertainties of the pair potential and those estimated for our nonadditive three-body potential were rigorously propagated in the PIMC calculations into uncertainties for the virial coefficients. These uncertainties are distinctly smaller than those of almost all of the corresponding experimental virial coefficient data.

研究动机与目标

• 为气体计量学和多体相互作用的基础测试提供氖的精确热物性建模动机。
• 开发并验证氖的高精度ab initio成对、三体、四体势。
• 在广泛温度范围（10–5000 K）内计算第三、第四密度virial系数和第三、第四声学virial系数。
• 将电子结构的不确定性传播至virial系数并与实验数据比较。

提出的方法

• 使用由Hellmann等人基于CCSDTQ(P)构建、包含相对论、时滞和后Born–Oppenheimer效应的ab initio成对势。
• 基于广泛的CCSD(T)、CCSDT、CCSDT(Q)计算并含有相对论修正，构建非加性三体势。
• 通过简化的CCSD(T)计算势，包含非常小的非加性四体贡献。
• 通过路径积分蒙特卡洛直接计算第三、第四密度virial系数，并通过热力学关系推导第四声学virial系数。
• 拟合ab initio非加性势（三体、四体）的解析形式，以实现高效评估和不确定性传播。
• 提供Fortran 90程序用于评估非加性势及其±不确定性变化（±uncertainty variations）。

实验结果

研究问题

• RQ1 氖在10–5000 K之间的第三、第四密度virial系数分别是多少？
• RQ2 在相同温度范围内，氖的第三、第四声学virial系数分别是多少？
• RQ3 非加性三体和四体相互作用如何贡献于这些高阶virial系数及其不确定性？
• RQ4 第一性原理结果与氖virial系数的实验数据相比如何？
• RQ5 能否将virial系数的不确定性从ab initio势的不确定性中严格传播？

主要发现

• 该研究给出在10–5000 K范围内氖的第三、第四密度virial系数，基于第一性原理计算。
• 第三声学virial系数直接确定；第四声学virial系数通过热力学关系间接获得。
• 非加性三体势对第三、第四virial系数贡献显著，而四体项非常小，采用简化势处理。
• 来自成对势和非加性三体势的不确定性被传播到virial系数，且小于大多数可比实验数据的不确定性。
• 解析形式的非加性势能能再现ab initio结果且便于通过±平移（ΔV123及ΔV123±）实现不确定性传播。
• 对比显示第一性原理结果与先前的理论和实验数据集在氖的virial系数方面的一致性或改进。