正则化轨道优化的二阶Møller-Plesset微扰理论：一个可靠的五阶标度电子关联模型
Regularized Orbital-Optimized Second-Order Møller-Plesset Perturbation Theory: A Reliable Fifth-Order Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers
摘要：
我们推导和评估两类新的正则化，以应付在单参考二阶Møller-Plesset微扰理论（MP2）中的违规行为。特别是，我们讨论了使用两种类型的轨道能量依赖正则化，$κ$和$σ$，结合轨道优化的MP2（OOMP 2）。由此产生的五阶标度方法，$κ$ -OOMP 2和$σ$ -OOMP 2，已被检查键断裂，热化学，和biradic问题。具有足够强的正则化的两种方法都恢复受限于不受限制的不稳定性（即Coulson-Fischer点），当$\text{H}_{2}$、$\text{C}_2\text{H}_6$、$\text{C}_2\text{H}_4$和$\text{C}_2\text{H}_2$中的键断裂时，未正则化的OOMP 2缺乏不受限制的不稳定性。使用W 4 -11集进行$κ$和$σ$正则化参数的训练。我们通过在W 4 -11集合的TAE 140子集上训练，进一步开发了缩放相关能量变体$κ$ -S-OOMP 2和$σ$ -S-OOMP 2。这些新的OOMP 2方法在RSE 43集和TA 14集上进行了测试，其中未修改的OOMP 2本身表现非常好。我们所做的修改在这些数据集中被发现是微不足道的。此外，我们测试了新的OOMP 2方法上的单线双radicaloid使用山口的近似自旋投影。不像非正则化的OOMP 2，它无法收敛这些系统由于奇异性，我们表明，正则化的OOMP 2方法成功地捕捉到强大的biradicaloid字符。虽然需要对较大数据集进行进一步评估，但$κ$ -OOMP 2（$κ$ = 1.45 $E_{h}^{-1}$）似乎将Coulson-Fischer点的有利恢复与良好的数值性能相结合。
英文摘要：
We derive and assess two new classes of regularizers that cope with offending denominators in the single-reference second-order Møller-Plesset perturbation theory (MP2). In particular, we discuss the use of two types of orbital energy dependent regularizers, $κ$ and $σ$, in conjunction with orbital-optimized MP2 (OOMP2). The resulting fifth-order scaling methods, $κ$-OOMP2 and $σ$-OOMP2, have been examined for bond-breaking, thermochemistry, and biradical problems. Both methods with strong enough regularization restore restricted to unrestricted instability (i.e. Coulson-Fischer points) that unregularized OOMP2 lacks when breaking bonds in $\text{H}_{2}$, $\text{C}_2\text{H}_6$, $\text{C}_2\text{H}_4$, and $\text{C}_2\text{H}_2$. The training of the $κ$ and $σ$ regularization parameters was performed with the W4-11 set. We further developed scaled correlation energy variants, $κ$-S-OOMP2 and $σ$-S-OOMP2, by training on the TAE140 subset of the W4-11 set. Those new OOMP2 methods were tested on the RSE43 set and the TA14 set where unmodified OOMP2 itself performs very well. The modifications we made were found insignificant in these data sets. Furthermore, we tested the new OOMP2 methods on singlet biradicaloids using Yamaguchi's approximate spin-projection. Unlike the unregularized OOMP2, which fails to converge these systems due to the singularity, we show that regularized OOMP2 methods successfully capture strong biradicaloid characters. While further assessment on larger datasets is desirable, $κ$-OOMP2 with $κ$ = 1.45 $E_{h}^{-1}$ appears to combine favorable recovery of Coulson-Fischer points with good numerical performance.
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