Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA.
J Chem Phys. 2018 Nov 14;149(18):184103. doi: 10.1063/1.5045340.
A low-scaling method is presented for the equation-of-motion coupled-cluster theory with single and double (EOM-CCSD) excitations and its second-order many-body perturbation theory [EOM-MBPT(2)] approximations. For a simple description of an excited state, the particular orbitals, and , are selected from the natural transition orbitals (NTOs, ), where and refer to NTO occupied and virtual orbital indices. They are chosen based on the largest eigenvalues of the transition density matrix. We expect the and pair to be dominant in representing excited states in EOM calculations. Therefore, the double excitation vector, which scale as ∼ , can be modified to keep only a few dominant excitations. Our work indicates that the most important contributions of the vector define smaller subspaces that scale as ∼, ∼ , and ∼ , where and refer to the occupied and virtual orbitals in the NTO basis. Thus, the scaling for the EOM part becomes ∼ . The energy changes due to truncation are small (the mean average deviation from untruncated EOM-CCSD is ∼0.03 eV). We show that this approach works relatively well with various types of NTOs, ranging from configuration singles to time-dependent density functional theory making ∼ scaling calculations possible with the use of MBPT(2) as the reference state.
提出了一种低标度方法，用于单重和双重激发的运动方程耦合簇理论（EOM-CCSD）及其二阶多体微扰理论 [EOM-MBPT(2)] 近似。为了简单描述激发态，选择特定轨道 和 从自然跃迁轨道（NTOs， ）中选择，其中 和 分别指 NTO 占据轨道和虚拟轨道指数。它们是根据跃迁密度矩阵的最大特征值选择的。我们预计 和 对在 EOM 计算中代表激发态起主要作用。因此，标度为 ∼ 的双激发向量 可以进行修改，以仅保留少数主要激发。我们的工作表明， 向量的最重要贡献定义了较小的子空间，其标度为 ∼ ， ∼ ，和 ∼ ，其中 和 分别指 NTO 基中的占据轨道和虚拟轨道。因此，EOM 部分的标度变为 ∼ 。由于 截断引起的能量变化很小（与未截断的 EOM-CCSD 的平均平均偏差约为 0.03 eV）。我们表明，这种方法对于各种类型的 NTO 都相对有效，范围从配置单重态到含时密度泛函理论，从而可以使用 MBPT(2) 作为参考态进行 ∼ 标度计算。
