Ionization Potentials at Mean-Field Computational Cost: The Extended Koopmans’ Framework for pCCD

We
introduce a mean-field-like computational model for calculating
ionization potentials (IPs) based on the pair Coupled Cluster Doubles
(pCCD) wave function. Specifically, our model combines the extended
Koopmans’ theorem (EKT) with the advantages of a variationally
orbital-optimized (oo)-pCCD ansatz. The computational cost of the
EKT(pCCD) method is negligible (O(N3)) as the response 1- and 2-particle reduced
density matrices used to construct the generalized Fock matrix are
readily available after an oo-pCCD calculation. We benchmarked our
new computational model for IPs of atoms, small molecules, and a set
of organic acceptor molecules against experimental and theoretical
reference data. The EKT(pCCD) model significantly improves upon the
modified Koopmans’ approach [J. Chem. Phys. 162, 184110 (2025)],
and the obtained IPs are comparable to those of computationally more
expensive IP-EOM-pCCD-based models, approaching CCSD(T) reference
values (with a mean error of 0.05 eV). Most importantly, the EKT(pCCD)
approach is almost independent of the basis set size, and reliable
IPs are already obtained with small basis sets.