Frozen natural orbitals for ionized states within equation-of-motion coupled-cluster formalism

The frozen natural orbital (FNO) approach, which has been successfully used in ground-state coupled-cluster calculations, is extended to open-shell ionized electronic states within equation-of-motion coupled-cluster (EOM-IP-CC) formalism. FNOs enable truncation of the virtual orbital space significantly reducing the computational cost with a negligible decline in accuracy. Implementation of the MP2-based FNO truncation scheme within EOM-IP-CC is presented and benchmarked using ionized states of beryllium, dihydrogen dimer, water, water dimer, nitrogen, and uracil dimer. The results show that the natural occupation threshold, i.e., percentage of the total natural occupation recovered in the truncated virtual orbital space, provides a more robust truncation criterion as compared to the fixed percentage of virtual orbitals retained. Employing 99%-99.5% natural occupation threshold, which results in the virtual space reduction by 70%-30%, yields errors below 1 kcal/mol. Moreover, the total energies exhibit linear dependence as a function of the percentage of the natural occupation retained allowing for extrapolation to the full virtual space values. The capabilities of the new method are demonstrated by the calculation of the 12 lowest vertical ionization energies (IEs) and the lowest adiabatic IE of guanine. In addition to IE calculations, we present the scans of potential energy surfaces (PESs) for ionized (H2O)(2) and (H-2)(2). The scans demonstrate that the FNO truncation does not introduce significant nonparallelity errors and accurately describes the PESs shapes and the corresponding energy differences, e.g., dissociation energies.