Accurate Core-Level Ionization Energies from an Affordable Second-Order Approach

An approach is proposed for the accurate calculation of core-level ionization potentials (IPs) using second-order methods. The assessed theoretical frameworks are based on the iterative second-order algebraic-diagrammatic construction [ADC(2)] and configuration interaction singles with perturbative second-order correction [CIS(D)] methods. Here, our efficient implementations of IP-ADC(2) and IP-CIS(D) [Mester, D.; Kállay, M. <i>J. Chem. Theory Comput.</i> 2023, 19, 3982-3995] are combined with the core-valence separation (CVS) approximation, thereby enabling ionization from the core region. The approaches exhibit highly favorable scaling behavior: the computational cost is practically cubic, with only a mild prefactor that depends on the number of active core orbitals. Furthermore, the resulting wave function-based methods are combined with spin-scaling techniques and successfully extended to double-hybrid (DH) functionals without any necessary modifications in the implementation of the second-order corrections. The performance of the proposed methods was thoroughly assessed in benchmark calculations. Our results demonstrate that the iterative treatment of double excitations is essential, underscoring the necessity of the more advanced DH ansatz. Moreover, the SOS0-PBE0-2/CVS-IP-ADC(2) approach is highly competitive with more expensive higher-level coupled-cluster methods. Finally, the second-order correction introduces only a negligible overhead in the overall computational time─only about 1 min for a 61-atom azafullerene molecule using triple-ζ basis sets─thereby enabling accurate calculations for extended molecular systems.