Angular-Momentum Extrapolations to the Complete Basis Set Limit: Why and When They Work.
Angular-Momentum Extrapolations to the Complete Basis Set Limit: Why and When They Work.
复制标题
角动量外推至完整基组极限：为什么以及何时起作用。
DOI：
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发表时间：
2021
影响因子：
5.5
通讯作者：
K. Strasburger
中科院分区：
文献类型：
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作者：
J. Cioslowski;K. Strasburger
对于具有任意偶数个电子的线性分子和分子离子的1 π态，严格证明了用核心基组计算的能量误差与角动量不超过L的函数的领先L-3依赖性。这个主要的扩展域的适用性所提供的经常引用的希尔渐近表达式，这是有效的，只为氦等电子系列，是完成了一个形式主义，其中的非对角尖点条件的一个和两个电子约化密度矩阵发挥了核心作用。尽管这些结果提供了比以往任何时候都更坚实的理论基础，角动量外推到完整的基组极限似乎更多的是偶然的，而不是数学上的严格性，因为前因子乘以L-3项的可预测性很差，而且涉及L-1的更高次幂的项的贡献远非可以忽略。
The leading L-3 dependence of the errors in the energies computed with nuclei-centered basis sets comprising functions with angular momenta not exceeding L is rigorously proven for the 1Σ states of linear molecules and molecular ions with arbitrary even numbers of electrons. This major expansion of the domain of applicability over that offered by the routinely cited Hill asymptotic expression, which is valid only for the helium isoelectronic series, is accomplished with a formalism in which the off-diagonal cusp conditions for the one- and two-electron reduced density matrices play the central role. Despite being provided by these results with theoretical foundations more solid than ever before, the angular-momentum extrapolations to the complete basis set limit appear to work more by happenstance than mathematical rigor due to the poorly predictable variability in the prefactor multiplying the L-3 term and the far from negligible contributions from the terms involving higher powers of L-1.