A linear relation is found between Jaynes entropy and the correlation energy associated with the cumulant for a correlated molecular system, as demonstrated in ${\mathrm{H}}_2$ and a water molecule. The relation modifies the Collins conjecture, in which the correlation energy is defined as the total energy difference with reference to the Hartree-Fock counterpart. The linear behavior is system dependent and shifts slightly on a different basis set. This correlation energy is extensive. For a system whose wave function can be expressed as the antisymmetrized product of orthogonal groups, the correlation energy is just the sum of the individual groups. The finding offers a convenient way to construct an approximate correlation energy functional in reduced density-matrix-functional theory, which may be used in large-scale molecular dynamics simulations and potential energy surface calculations where the molecular geometry needs to be frequently updated.

中文翻译：

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信息熵作为与累积量相关联的相关能量的度量

在 Jaynes 熵和与相关分子系统累积量相关的相关能之间发现线性关系，如 ${\mathrm{H}}_2$和一个水分子。该关系修正了柯林斯猜想，其中相关能量被定义为相对于 Hartree-Fock 对应物的总能量差。线性行为取决于系统，并在不同的基组上略有变化。这种相关能量是广泛的。对于波函数可以表示为正交群的反对称乘积的系统，相关能量就是各个群的总和。该发现提供了一种在简化密度矩阵泛函理论中构建近似相关能量泛函的便捷方法，该方法可用于需要频繁更新分子几何结构的大规模分子动力学模拟和势能面计算。