A Novel Expression of Cohesive Energy Contributions to the Highly Compressed Characteristic for Rare-Gas Solids
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摘要: 基于量子理论和原子团簇理论，运用多体展开方法和第一性原理的从头算方法，提出了一种计算稠密惰性元素（氦、氖、氩和氪）原子结合能的新势函数，运用新公式研究了结合能对高压稠密惰性元素高压压缩特性的影响。此公式引入了一个物理参量
$\beta $ （其值为0.5），使得势函数的表达形式更加简单、准确。对比结果表明，结合能的新势函数能够准确地描述多体相互作用对结合能的贡献，且平均相对误差在5%以内。结合能的新势函数对压缩特性的影响在当前实验压强范围内（氦60 GPa、氖238 GPa、氩114 GPa、氪128 GPa）做出了令人满意的描述，且与实验值及理论计算结果基本完全吻合，平均相对误差在3%以内。最后，以固氩的压强数据为例，验证了势函数的准确性。该势函数不仅适用于更宽密度和更高压强范围，而且对所有惰性元素原子各种状态的结合能、高压压缩特性、定容比热容、熔化曲线和弹性模量的研究具有重要的指导意义。Abstract: Based on quantum theory and atomic cluster theory, using many-body expansion method and the ab initio method, a novel expression is presented for calculating the cohesive energy of rare-gas solids (RGS) (RGS=He, Ne, Ar, Kr) and studying the cohesive energy contribution to the highly compressed characteristics for RGS. In this expression, we introduce a new coefficient$\beta $ =0.5, which makes the expression of potential function simple and accurate. Compared with previous results, it is necessary to obtain a new cohesive energy expression that can describe accurately the many-body interaction contribution to cohesive energy, and the mean relative errors are within 5%. The expression can also be applied to calculate the compressibility of solid helium, neon, argon and krypton in the present experimental pressure range (He 60 GPa, Ne 238 GPa, Ar 114 GPa, Kr 128 GPa), and the numerical results are consistent with the recent experiment results and ab initio calculation results with the mean relative errors of no more than 5%. Finally, an application in solid argon verifies the accuracy of the potential expression. The expression not only can be applicable in a wider density and pressure range, but also all rare gas systems. In addition, it has important guiding significance for studying the high-pressure compression, specific heat, melting curve and elastic modulus of rare-gas solids. -
图 1 U2(M)、Vn(M)和E(M)三者的关系（曲线OE表示函数f(x)，虚线OG代表U2(M)x）
Figure 1. The correlations among U2(M), Vn(M), and E(M) (The curve line OE represents function f(x), and the dash line OG describes U2(M)x.)
表 1 固氩的压强分量
Table 1. The pressure components of solid argon
R/Å V/(cm3·mol–1) P/GPa Error/% Exp.[24] Ab initio[11] Eq.(10) 2.40 5.887 237.61 248.95 247.04 3.97 2.45 6.262 194.11 204.44 200.72 3.41 2.50 6.653 158.51 167.59 163.25 3.00 2.55 7.061 129.38 137.12 132.81 2.65 2.60 7.484 105.53 111.96 107.98 2.32 2.65 7.924 86.02 91.23 87.70 1.95 2.70 8.381 70.06 74.18 71.12 1.51 2.75 8.856 57.00 60.20 57.57 1.00 2.80 9.348 46.34 48.75 46.49 0.32 2.85 9.857 37.62 39.41 37.54 –0.21 2.90 10.385 30.51 31.80 30.31 –0.66 2.95 10.932 24.71 25.62 24.65 –0.24 3.00 11.497 19.99 20.60 19.79 –1.00 
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