Open-shell frozen natural orbital approach for quantum eigensolvers

We present an open-shell frozen natural orbital (FNO) approach, which utilizes the second-order Z-averaged perturbation theory (ZAPT2), to reduce the restricted open-shell Hartree-Fock virtual space size with controllable accuracy. Our ZAPT2 frozen natural orbital (ZAPT-FNO) selection scheme significantly outperforms the canonical molecular orbital virtual space truncation scheme based on Hartree-Fock orbital energies, especially when using large multiple-polarized and augmented basis sets. We demonstrate that the ZAPT-FNO-selected virtual orbitals lead to a systematic convergence of the correlation energies but, more importantly, to the singlet-triplet T1-S0 energy gaps with respect to the complete active space (CAS) [occupied + virtual] size. We confirm our findings by simulating T1-S0 gaps in H2O2 and O2 molecules using the traditional complete active space configuration interaction (CASCI) approach, as well as in stretched CH2, for which we also employed the iterative qubit coupled cluster (iQCC) method as a quantum eigensolver. Finally, we applied the iQCC method with a ZAPT-FNO-selected active space to the phosphorescent Ir(ppy)3 complex with 260 electrons, where extended basis sets are required to achieve chemical (∼1 mEh) accuracy. In this case, CASCI results are not available; however, the iQCC-computed T1-S0 gaps show robust convergence with an enlarging basis set and CAS size, approaching the experimental value. Thus, the ZAPT-FNO method is very promising for improving the accuracy of quantum chemical modeling in a resource-efficient manner and opens the door to simulating open-shell states of large materials within realistic active space sizes and without compromising on basis-set quality.