Active-Space Equation-of-Motion Coupled-Cluster Methods through Quadruples for Excited, Ionized, and Electron-Attached States.

Several variants of the equation-of-motion coupled-cluster (EOM-CC) method with singles (one-hole or one-particle), doubles (two-hole-one-particle or two-particle-one-hole), and a selected set of triples (three-hole-two-particle or three-particle-two-hole) and/or quadruples (four-hole-three-particle or four-particle-three-hole) have been implemented by computerized symbolic algebra. They are applicable to excitation energies (EE), ionization potentials (IP), and electron affinities (EA), excited-state dipole moments, and transition dipole moments of both closed- and open-shell species and are abbreviated as EE/IP/EA-EOM-CCSDt, EE/IP/EA-EOM-CCSDtq, and EE/IP/EA-EOM-CCSDTq, where the small letters indicate the use of active-space cluster and EE/IP/EA operators. They are also parallel executable and accelerated by the use of spin, spatial, and permutation symmetries. The remarkable effectiveness of the methods in capturing nondynamical correlation effects has been demonstrated by their applications to the vertical excitation energies of C2, the adiabatic excitation energies and dipole moments of the CH radical, the adiabatic excitation energies of the CH2 diradical, the adiabatic excitation energies and dipole moments of formaldehyde, the vertical ionization energies of N2, and the vertical electron affinities of C2. The effectiveness is found to decline when the basis set is extended, causing the active space to become relatively small and also less well-defined. As a remedy, we propose a composite method that combines higher-rank active-space methods with smaller basis sets for nondynamical correlation and lower-rank nonactive-space methods with larger basis sets for dynamical correlation, which is shown to work well for an excited-state potential energy curve of hydrogen fluoride.