电子相关Electron correlation

动态相关源于电子之间的短程瞬时回避，在所有体系中都存在，可用微扰理论（MP2）或耦合簇（CCSD(T)，被称为量子化学的“黄金标准”）处理。静态（非动态）相关出现在多个电子组态能量相近时，如键解离、双自由基、过渡金属配合物，单行列式描述完全失败，需用多组态方法（CASSCF、MRCI）。哈特里-福克已包含同自旋电子之间的部分相关（费米空穴），但不包含异自旋电子的库仑相关。

Dynamic correlation, the short-range instantaneous avoidance of electrons, is present in every system and is handled by perturbation theory (MP2) or coupled cluster (CCSD(T), the 'gold standard' of quantum chemistry). Static (non-dynamic) correlation arises when several electronic configurations are close in energy, as in bond breaking, diradicals and transition-metal complexes, where a single determinant fails completely and multiconfigurational methods (CASSCF, MRCI) are needed. Hartree–Fock already includes some correlation between same-spin electrons (the Fermi hole) but not the Coulomb correlation of opposite-spin electrons.

1934 年维格纳研究电子气时首先讨论了相关能；1934 年默勒和普莱塞特提出多体微扰理论（MP 理论）。1958 年洛丁正式定义了相关能。1966 年契热克等引入耦合簇理论到量子化学，1989 年拉加瓦查里等提出 CCSD(T)。密度泛函理论把相关效应纳入交换-相关泛函。

Wigner first discussed correlation energy in the electron gas in 1934, the year Møller and Plesset proposed many-body perturbation theory. Löwdin formally defined correlation energy in 1958. Čížek brought coupled-cluster theory into quantum chemistry in 1966, and Raghavachari and colleagues proposed CCSD(T) in 1989. Density functional theory folds correlation into the exchange–correlation functional.

相关能虽只占总能量约 1%，但对化学至关重要：哈特里-福克方法预测 F₂ 不稳定（结合能为负），加入电子相关后才得到正确结合能；色散力（范德华吸引）完全来自电子相关，没有它就无法描述 DNA 碱基堆积、分子晶体和蛋白质-配体结合。

Although correlation energy is only about 1% of the total, it is crucial for chemistry: Hartree–Fock predicts F₂ to be unbound, and only with correlation does the right binding energy appear. Dispersion (van der Waals attraction) arises entirely from correlation, so without it DNA base stacking, molecular crystals and protein–ligand binding cannot be described.