Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland.
Department of Physical and Quantum Chemistry, Faculty of Chemistry, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland.
J Chem Theory Comput. 2021 Jun 8;17(6):3403-3413. doi: 10.1021/acs.jctc.1c00202. Epub 2021 May 18.
The leading dependence of the errors in the energies computed with nuclei-centered basis sets comprising functions with angular momenta not exceeding is rigorously proven for the Σ 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 term and the far from negligible contributions from the terms involving higher powers of .
对于具有任意偶数电子的线性分子和分子离子的Σ 态，严格证明了由角动量不超过 的原子核中心基组函数组成的计算能量中的误差主要依赖于。这种对通常引用的 Hill 渐近表达式（仅对氦同电子系列有效）的适用范围的重大扩展，是通过一种形式主义实现的，其中一电子和二电子约化密度矩阵的非对角尖点条件起着核心作用。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，但由于 项的前因子的可预测性差以及涉及更高次幂的项的贡献远非微不足道，因此到完全基组极限的角动量外推似乎更多地是偶然的，而不是数学上的严格性。
