Interplay between Electronic Correlation and Metal–Ligand Delocalization in the Spectroscopy of Transition Metal Compounds: Case Study on a Series of Planar Cu2+ Complexes

We present a comprehensive theoretical study of the physical phenomena that determine the relative energies of three of the lowest electronic states of each of the square-planar copper complexes [CuCl4]2–, [Cu­(NH3)4]2+, and [Cu­(H2O)4]2+ and present a detailed analysis of the extent to which truncated configuration interaction (CI) and coupled cluster (CC) theories succeed in predicing the excitation energies. We find that ligand–metal charge transfer (CT) single excitations play a crucial role in the correct determination of the properties of these systems, even though the first impact of these CT on the energetics of these systems appears at fourth-order in perturbation theory. We provide a minimal selected CI space for describing these systems with multireference theories and use a high-order perturbation theory analysis within this space to derive a simple and general physical picture for the LMCT process. We find that coupled cluster singles and doubles (CCSD) energy differences agree very well with near full CI values even though the D1 diagnostics are large, which casts doubt on the usefulness of single-amplitude-based multireference diagnostics. Configuration interaction singles and doubles (CISD) severely underestimates the excitation energies, and the failure is a direct consequence of the size-inconsisency errors in CISD. Finally, we present reference values for the energy differences computed using explicitly correlated CCSD­(T) and BCCD­(T) theory.

本工作针对三种平面正方形铜配合物——四氯合铜(II)配阴离子([CuCl₄]²⁻)、四氨合铜(II)配阳离子([Cu(NH₃)₄]²⁺)与四水合铜(II)配阳离子([Cu(H₂O)₄]²⁺)各自三个最低电子态的相对能量决定因素，开展了全面的理论研究，并详细分析了截断组态相互作用(Configuration Interaction, CI)与耦合簇(Coupled Cluster, CC)理论在激发能预测中的表现优劣。
研究发现，配体-金属电荷转移(Charge Transfer, CT)单激发对这类体系的性质准确描述至关重要，尽管此类电荷转移效应对体系能量的首次显著影响出现在微扰论四阶阶次。
本工作提供了一套适用于多参考态理论描述此类体系的极小选择性组态相互作用空间，并基于该空间开展高阶微扰论分析，为配体-金属电荷转移过程推导得到一套简洁且普适的物理图像。
本研究发现，即便D1诊断量数值较大，耦合簇单双激发(Coupled Cluster Singles and Doubles, CCSD)的能量差值与近乎全组态相互作用结果仍吻合极佳，这一现象对基于单振幅的多参考态诊断方法的实用性提出了质疑。
组态相互作用单双激发(Configuration Interaction Singles and Doubles, CISD)会严重低估激发能，这一失效直接源于CISD存在尺寸不一致性误差。
最后，本工作给出了采用显式关联耦合簇单双激发加微扰三重激发(CCSD(T))与显式关联块相关耦合簇双激发加微扰三重激发(BCCD(T))理论计算得到的能量差值参考值。