近日，印度理工学院古瓦哈提分校的Ashish Kumar Gupta及其研究团队取得一项新进展。经过不懈努力，他们获得不稳定阴离子的自洽场解。相关研究成果已于2024年12月24日在国际知名学术期刊《物理评论A》上发表。

本文介绍了使用修正的参数化运动方程（PEM）结合核电荷稳定化方法，以获得不稳定阴离子的理想SCF解。首先，以较高核电荷下阴离子的SCF解为起点（此时阴离子是束缚态），然后执行修正的PEM，直到额外的核电荷减至零，最终得到不稳定阴离子的SCF解。

为不稳定阴离子获得有意义SCF解的关键在于，在整个PEM计算过程中，保持对应于单占据分子轨道的轨道占据数固定。通过验证所得解是否为自洽场解，确认了该方法的准确性。为了考虑电子相关性，对阴离子组分进行了MP2计算。

据悉，对于不稳定的阴离子，当使用弥散基组时，自洽场（SCF）解往往会导致一个能量最小的解，其中基组中最弥散的轨道上会多出一个电子。随着弥散函数的增加，这一解最终会收敛到一个中性分子和一个自由电子。因此，任何基于这种解的后续SCF计算都无法得出有意义的物理结果。

附：英文原文

Title: Self-consistent-field solution for unstable anions

Author: Deepak Kumar and Ashish Kumar Gupta

Issue&Volume: 2024-12-24

Abstract: For an unstable anion, when using a diffuse basis set, the self-consistent field (SCF) solution often leads to a minimum energy solution with an additional electron in the most diffuse orbital present in the basis set. Eventually, it converges to a neutral molecule and a free electron with increase in the diffuse functions. Consequently, any post-SCF calculations using this solution do not yield meaningful physical results. This paper introduces the use of modified parametric equation of motion (PEM) in combination with nuclear charge stabilization to obtain a desirable SCF solution for an unstable anion. The SCF solution for an anion at a higher nuclear charge is used as the starting point, where the anion is bound. The modified PEM is then carried out until the additional nuclear charge reaches zero, ultimately producing the SCF solution for the unstable anion. The key to achieving meaningful SCF solutions for temporary anions lies in maintaining a fixed occupation number for the orbital corresponding to the singly occupied molecular orbital throughout the PEM calculation. The solution obtained using the modified PEM is checked for being self-consistent-field solution, confirming the accuracy of the method. To account for electron correlation, MP2 calculations are carried out for anionic species.

DOI: 10.1103/PhysRevA.110.062821

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.062821