AI 中文总结
研究高度对称系统中基态和激发态的电子结构，统一QSym²和GNOCC理论框架，利用对称轨道和动态关联本征函数，通过研究三个模型系统展示其能针对简并和非简并态，提升数值性能。
AI 中文摘要
高度对称系统中的基态和激发态由于点群对称通常具有高度的空间简并性。然而，许多当前量子化学方法难以准确描述这些态中固有的强关联效应，无法深入了解基础系统的电子结构，许多重要化学和光谱性质也无法可靠计算预测。本文描述了一个新理论框架，统一了QSym²中对非阿贝尔对称的符号处理和广义正规序耦合簇理论（GNOCC），以平衡且有针对性地描述此类基态和激发态。通过QSym²利用对称轨道恢复空间对称性并生成对称适配多行列式波函数的能力，以及GNOCC以尺寸可扩展性和无自旋方式动态关联任意自旋本征函数的能力来确保。通过研究三个模型系统中的几个基态和激发态来展示该框架的能力，结果表明该方法能针对简并和非简并态，且相对于传统单参考耦合簇方法有更好的数值性能。
英文摘要
Ground and excited electronic states in highly symmetric systems typically possess high degrees of spatial degeneracy as a consequence of point-group symmetry. However, many current quantum-chemical methods struggle to accurately describe the strong correlation effects inherently present in these states, thereby precluding the ability to obtain meaningful insights into the electronic structure of the underlying systems. Consequently, many of their important chemical and spectroscopic properties cannot be reliably computed and predicted. In this article, a new theoretical framework is described that unifies the symbolic treatment of non-Abelian symmetry in QSym$^2$ and the recently developed state-specific multi-reference coupled cluster theory termed Generalised Normal Ordered Coupled Cluster (GNOCC) to describe such difficult ground and excited states in a balanced and targeted manner. This is ensured by the ability of QSym$^2$ to exploit symmetry orbits to restore any broken spatial symmetries and generate symmetry-adapted multi-determinantal wavefunctions, as well as the ability of GNOCC to dynamically correlate arbitrary spin eigenfunctions in a size-extensive and spin-free manner. To illustrate the capabilities of this framework, several ground and excited states in three model systems are examined in detail: (i) octahedral $(\textrm{H}_6)^{2+}$, (ii) octahedral $\textrm{H}_6$, and (iii) tetrahedral $\textrm{Li}_4$. The results demonstrate that the proposed method can target both degenerate and non-degenerate states, while delivering improved numerical performance relative to conventional single-reference coupled-cluster approaches.
Comments17 pages, 4 figures
