Linear Response pCCD-Based Methods: LR-pCCD and LR-pCCD plus S Approaches for the Efficient and Reliable Modeling of Excited State Properties

In this work, we derive working equations for the linear response pair coupled cluster doubles (LR-pCCD) ansatz and its extension to singles (S), LR-pCCD+S. These methods allow us to compute electronic excitation energies and transition dipole moments based on a pCCD reference function. We benchmark the LR-pCCD+S model against the linear response coupled-cluster singles and doubles method for modeling electronic spectra (excitation energies and transition dipole moments) of the BH, H2O, H2CO, and furan molecules. We also analyze the effect of orbital optimization within pCCD on the resulting LR-pCCD+S transition dipole moments and oscillator strengths and perform a statistical error analysis. We show that the LR-pCCD+S method can correctly reproduce the transition dipole moments features, thus representing a reliable and cost-effective alternative to standard, more expensive electronic structure methods for modeling electronic spectra of simple molecules. Specifically, the proposed models require only mean-field-like computational cost, while excited-state properties may approach the CCSD level of accuracy. Moreover, we demonstrate the capability of our model to simulate electronic transitions with non-negligible contributions of double excitations and the electronic spectra of polyenes of various chain lengths, for which standard electronic structure methods perform purely.