Broken-symmetry calculations of diradicals exploit the mean-field energies of determinants that are not eigenfunctions of the ${Ŝ}^2$ operator, the mean value of which is close to 1 for the m_s = 0 solution. This spin contamination must be corrected. Two different contributions affect $⟨{Ŝ}^2⟩$, namely, the mixing between neutral and ionic valence bond components, the so-called kinetic exchange, which decreases $⟨{Ŝ}^2⟩$, and the spin polarization of the supposedly closed shell orbitals, which increases $⟨{Ŝ}^2⟩$. The popular Yamaguchi formula is valid for the first effect but irrelevant for the second one. From a few constrained broken-symmetry calculations, one may treat separately the two contributions and apply their specific spin decontamination correction. This work proposes a consistent spin-decontaminated procedure for the evaluation of singlet–triplet gaps in diradicals.

中文翻译：

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双自由基断裂对称计算的一致自旋去污

双基的不对称对称计算利用不是行列式本征函数的行列式的平均场能量 ${Ŝ}^2$运算符，对于m _s = 0解，其平均值接近1 。这种自旋污染必须得到纠正。两种不同的影响$⟨{Ŝ}^2⟩$即中性和离子价键成分之间的混合，即所谓的动力学交换 $⟨{Ŝ}^2⟩$，以及所谓的闭合壳轨道的自旋极化，这会增加 $⟨{Ŝ}^2⟩$。流行的Yamaguchi公式对第一个效果有效，但对第二个效果无关。从一些受约束的破碎对称性计算中，可以分别处理这两种贡献并应用其特定的自旋去污校正。这项工作提出了一致的自旋去污程序，用于评估双基中的单线态-三重态间隙。