Rettig Adam, Shee James, Lee Joonho, Head-Gordon Martin
Department of Chemistry, University of California, Berkeley, California 94720, United States.
Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States.
J Chem Theory Comput. 2022 Sep 13;18(9):5382-5392. doi: 10.1021/acs.jctc.2c00641. Epub 2022 Sep 1.
Optimizing orbitals in the presence of electron correlation, as in orbital-optimized second-order Møller-Plesset perturbation theory (OOMP2), can remove artifacts associated with mean-field orbitals such as spin contamination and artificial symmetry-breaking. However, OOMP2 is known to suffer from divergent correlation energies in regimes of small orbital energy gaps. To address this issue, several approaches to amplitude regularization have been explored, with those featuring energy-gap-dependent regularizers appearing to be most transferable and physically justifiable. For instance, κ-OOMP2 was shown to address the energy divergence issue in, for example, bond-breaking processes while offering a significant improvement in accuracy for the W4-11 thermochemistry data set, and a parameter of κ = 1.45 was recommended. A more recent investigation of regularized MP2 with Hartree-Fock orbitals revealed that stronger regularization (i.e., smaller values of κ) than what had previously been recommended for κ-OOMP2 may offer huge improvements in certain cases such as noncovalent interactions while retaining a high level of accuracy for main-group thermochemistry data sets. In this study, we investigate the transferability of those findings to κ-OOMP2 and assess the implications of stronger regularization on the ability of κ-OOMP2 to diagnose strong static correlation. We found similar results using κ-OOMP2 for several main-group thermochemistry, barrier height, and noncovalent interaction data sets including both closed shell and open shell species. However, stronger regularization yielded substantially higher accuracy for open-shell transition-metal (TM) thermochemistry and is necessary to provide qualitatively correct spin symmetry breaking behavior for several large and electrochemically relevant TM systems. We therefore find a single κ value insufficient to treat all systems using κ-OOMP2.
在存在电子关联的情况下优化轨道，如在轨道优化的二阶莫勒-普莱塞特微扰理论（OOMP2）中，可以消除与平均场轨道相关的伪影，如自旋污染和人为的对称性破缺。然而，已知OOMP2在小轨道能隙区域会出现发散的关联能。为了解决这个问题，人们探索了几种振幅正则化方法，其中那些具有依赖能隙的正则化项的方法似乎最具可转移性且在物理上是合理的。例如，κ - OOMP2被证明可以解决诸如键断裂过程中的能量发散问题，同时在W4 - 11热化学数据集的精度上有显著提高，并推荐了κ = 1.45的参数。最近对用哈特里 - 福克轨道进行正则化的MP2的研究表明，比之前为κ - OOMP2推荐的更强的正则化（即更小的κ值）在某些情况下，如非共价相互作用，可能会带来巨大的改进，同时对主族热化学数据集保持较高的精度。在本研究中，我们研究了这些发现对κ - OOMP2的可转移性，并评估了更强的正则化对κ - OOMP2诊断强静态关联能力的影响。我们发现，对于几个主族热化学、势垒高度和非共价相互作用数据集，包括闭壳层和开壳层物种，使用κ - OOMP2得到了类似的结果。然而，更强的正则化对于开壳层过渡金属（TM）热化学产生了显著更高的精度，并且对于几个大的且与电化学相关的TM系统，提供定性正确的自旋对称性破缺行为是必要的。因此，我们发现使用κ - OOMP2时，单一的κ值不足以处理所有系统。
