Pair Natural Orbitals for Coupled Cluster Quadratic Response Theory

Reduced-scaling approaches have yielded significant improvements in the computational efficiency of coupled cluster methods, making them more feasible for studying large molecules. In this work, we extend the use of pair natural orbitals (PNOs) to frequency-dependent quadratic response properties. We evaluate the performance of PNOs alongside methods optimized for response properties that derive from an approximate field-perturbed density matrix known as perturbation-aware PNOs (PNO++). Additionally, we concatenate the PNO and PNO++ spaces to obtain the combined-PNO++ method, which is tailored to simultaneously maintain the accuracy of the CCSD correlation energies and response properties. We analyze the truncation errors associated with these methods using first electric dipole hyperpolarizability - specifically the average second-harmonic generation and optical refractivity, using canonical coupled cluster singles and doubles (CCSD) as a reference. The performance analysis of the PNO family provides valuable insights into the viability of implementing CCSD quadratic response properties at a full-production level, highlighting which techniques may yield the most successful results.