The Complete-Active Space Second-order Perturbation Theory (CASPT2) has been one of the most widely-used methods for reliably calculating electronic structures of multireference systems. Because of its lowest level treatment of dynamic correlation, it has a high computational feasibility; however, its accuracy in some cases falls short of needs. Here, as a simple yet higher-order alternative, we introduce a hybrid theory of the CASPT2 and a multireference variant of the Coupled-Electron Pair Approximation (CEPA), which is a class of high level correlation theory. A central feature of our theory (CEPT2) is to use the two underlying theories for describing different divisions of correlation components based on the full internal contraction framework. The external components, which usually give a major contribution to the dynamic correlation, are intensively described using the CEPA Ansatz, while the rests are treated at the CASPT2 level. Furthermore, to drastically reduce the computational demands, we have incorporated the pair-natural orbital (PNO) method into our multireference implementations. This development, thus, requires highly complex derivations and coding, while it has been largely facilitated with an automatic expression and code generation technique. To highlight the accuracy of the CEPT2 approach and to assess the errors caused by the PNO truncation, benchmark calculations are shown on small- to medium-size molecules, illustrating the high accuracy of the present CEPT2 model. By tightening the truncation thresholds, the PNO-CEPT2 energy converges toward the canonical counterpart and is more accurate than that of PNO-CASPT2 as long as the same truncation thresholds are used.

中文翻译：

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局部对-自然轨道框架中的多参考耦合电子对逼近与完全活动空间摄动理论相结合

完全活动空间二阶摄动理论（CASPT2）是可靠地计算多参考系统电子结构的最广泛使用的方法之一。由于它对动态相关性的最低处理，因此具有很高的计算可行性；但是，在某些情况下其准确性不足。在这里，作为一种简单而又高阶的替代方法，我们介绍了CASPT2的混合理论和耦合电子对近似（CEPA）的多参考变量，它是一类高级相关理论。我们的理论（CEPT2）的主要特征是使用两种基础理论来描述基于完整内部收缩框架的相关成分的不同划分。通常对动态相关性起主要作用的外部组件，Ansatz，其余的则按CASPT2级别处理。此外，为了大大减少计算需求，我们将对自然轨道（PNO）方法纳入了我们的多引用实现中。因此，这种发展需要高度复杂的派生和编码，而自动表达和代码生成技术已大大促进了它的发展。为了突出CEPT2方法的准确性并评估由PNO截短引起的误差，在中小分子上显示了基准计算，这说明了当前CEPT2模型的高精度。通过收紧截断阈值，只要使用相同的截断阈值，PNO-CEPT2能量便会向规范对应点收敛，并且比PNO-CASPT2的能量更准确。