Low scaling EOM-CCSD and EOM-MBPT(2) method with natural transition orbitals.

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, ϕ Ĩ and ϕ à , are selected from the natural transition orbitals (NTOs, ϕ ), where Ĩ and à refer to NTO occupied and virtual orbital indices. They are chosen based on the largest eigenvalues of the transition density matrix. We expect the ϕ Ĩ and ϕ à pair to be dominant in representing excited states in EOM calculations. Therefore, the double excitation vector, R 2 which scale as ∼O 2 V 2, can be modified to keep only a few dominant excitations. Our work indicates that the most important contributions of the R 2 vector define smaller subspaces that scale as ∼OV, ∼O 2 V, and ∼OV 2, where O and V refer to the occupied and virtual orbitals in the NTO basis. Thus, the scaling for the EOM part becomes ∼M 5. The energy changes due to R 2 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 ∼M 5 scaling calculations possible with the use of MBPT(2) as the reference state.