7.10.9 Frozen Natural Orbitals in CC, IP-CC, and SF-CC Calculations

Large computational savings are possible if the virtual space is truncated using the frozen natural orbital (FNO) approach (see Section 6.11). Extension of the FNO approach to ionized states within EOM-CC formalism was recently introduced and benchmarked.⁵²⁶ In addition to ground-state coupled-cluster calculations, FNOs can also be used in EOM-IP-CCSD, EOM-IP-CCSD(dT/fT) and EOM-IP-CC(2,3). In IP-CC the FNOs are computed for the reference (neutral) state and then are used to describe several target (ionized) states of interest. Different truncation scheme are described in Section 6.11.

To reduce the cost of EOM-SF-CCSD calculations, a special variant of FNO—open-shell frozen natural orbital approximation (OSFNO)—has been introduced⁷⁶⁶. This approach is a two-step scheme. First, the open-shell orbitals of the reference are found by singular value decomposition of the overlap matrix of alpha occupied and beta virtual orbitals. These orbitals contain the main amplitudes of the EOM-SF wave functions. Then, after separation of the open-shell orbitals, the rest of the virtual space is transformed through singular value decomposition of the singlet part of the MP2 density matrix (in alpha-beta spinorbital pairs). Benchmarks in Ref. ⁷⁶⁶ show that this scheme achieves speedups similar to FNO, while introducing very small errors to the relative energies of both covalent and ionic EOM-SF states. In particular, the errors in singlet–triplet gaps for single molecule magnets are less than 18 cm${}^{-1}$ for a typical OSFNO truncation at 99% of total population. Properties also show small errors. OSFNO is activated with CC_OSFNO = true rem variable. CC_FNO_THRESH and CC_FNO_USEPOP keywords have the same usage as in conventional FNO.

Because of the limitation of the implementation, point-group symmetry cannot be used with FNO/OSFNO and will be disabled. Please, adjust your input consistently with CC_SYMMETRY = false.

OSFNO can be combined with orbital localization to produce effective Hamiltonians, as described in the Section 13.5.