不可约表示作为双自由基体系的多参考指示符
Irreducible Representations as Multireference Indicators for Diradicaloid Systems
AI总结：
提出利用不可约表示作为双自由基模型多参考特性的低成本诊断方法，通过对称性分析识别单参考描述的障碍。
摘要：
分子中的多参考行为通常源于前线轨道间小能隙导致闭壳与开壳组态混合。标准的多参考诊断通常依赖于关联波函数、自然轨道占据数或约化密度矩阵。本文研究了一个模型系统中基于对称性的互补判据。对于时间反演不变的哈密顿量，保持对称性的闭壳Slater行列式必须变换为其点群的平凡不可约表示。因此，非平凡的多电子不可约表示排除了这种描述。我们通过同一模型中的两条路径来演示这一点。在控制路径中，前线轨道保持分离，基态在弱到中等相互作用区域保持平凡不可约表示。在阻塞路径中，高对称点产生前线轨道简并，导致具有双组态特征的单重基态和非平凡不可约表示。精确对角化、两态有效模型以及双粒子累积量的Frobenius范数在该区域提供了一致的图像，表明不可约表示可作为双自由基模型多参考特性的低成本诊断。虽然对称性不是关联强度的定量度量，但它提供了一种计算成本低廉的筛选工具，用于识别单参考描述的障碍。
英文摘要：
Multireference behavior in molecules often arises when a small gap between frontier orbitals results in mixing of closed and open-shell configurations. Standard multireference diagnostics of this regime usually rely on correlated wavefunctions, natural-orbital occupations, or reduced density matrices. Here, we examine a complementary, symmetry-based criterion for a model system. For a time-reversal-invariant Hamiltonian, a symmetry-preserving, closed-shell Slater determinant must transform as the trivial irreducible representation of its point group. Therefore, a nontrivial, many-electron irreducible representation excludes such a description. We compare two pathways within the same model to demonstrate this. Along the control pathway, the frontier orbitals remain separated and the ground state retains a trivial irreducible representation over the weak-to-intermediate interaction regime. Along the obstructed pathway, a high-symmetry point produces a frontier-orbital degeneracy, resulting in a singlet ground state with two-configuration character and a nontrivial irreducible representation. Exact diagonalization, a two-state effective model, and the Frobenius norm of the two-particle cumulant provide a consistent picture in this regime, demonstrating that irreducible representations can serve as a low-cost diagnostic of multireference character in diradicaloid models. While symmetry is not a quantitative measure of correlation strength, it does offer a computationally inexpensive screening tool to identify obstructions to a single-reference description.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
