We present a pair natural orbital (PNO)-based implementation of coupled cluster singles and doubles (CCSD) excitation energies that builds upon the previously proposed state-specific PNO approach to the excited state eigenvalue problem. We construct the excited state PNOs for each state separately in a truncated orbital specific virtual basis and use a local density-fitting approximation to achieve an at most quadratic scaling of the computational costs for the PNO construction. The earlier reported excited state PNO construction is generalized such that a smooth convergence of the results for charge transfer states is ensured for general coupled cluster methods. We investigate the accuracy of our implementation by applying it to a large and diverse test set comprising 153 singlet excitations in organic molecules. Already moderate PNO thresholds yield mean absolute errors below 0.01 eV. The performance of the implementation is investigated through the calculations on alkene chains and reveals an at most cubic cost-scaling for the CCSD iterations with the system size.

中文翻译：

---

在线性响应理论框架内基于CCSD激发能的一对自然轨道实现

我们提出了基于成对自然轨道（PNO）的耦合簇单双峰（CCSD）激发能量的实现，该实现基于先前提出的针对激发态特征值问题的特定于状态的PNO方法。我们在截断的轨道特定虚拟基础上分别为每个状态构造激发态PNO，并使用局部密度拟合近似来实现PNO构造的计算成本最多为二次方的缩放比例。对较早报道的激发态PNO的构造进行了概括，以确保对于常规耦合簇方法而言，电荷转移态的结果能够平稳收敛。我们通过将其应用于包含有机分子中的153个单重态激发的大型多样的测试集来研究实现的准确性。中等的PNO阈值已经产生低于0.01 eV的平均绝对误差。通过对烯烃链的计算研究了该实现的性能，并揭示了具有系统大小的CCSD迭代最多具有三次成本定标。