Complex-energy second-order approximate coupled-cluster methods for electronic resonances

Electronic resonances are metastable states with finite lifetimes, encountered in processes such as photodetachment, electron transmission spectroscopy, and Auger decay. Resonances appear in Hermitian quantum mechanics as increased density of states in the continuum rather than as discrete energy levels. To describe resonances accurately, including their coupling to the continuum, methods based on non-Hermitian quantum mechanics can be used, which yield complex energies. In this study, we combine the complex absorbing potential and complex basis functions techniques with the RI-CC2 method. The second-order coupled cluster method (CC2) offers a good balance between accuracy and computational cost by approximating equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) theory, making it suitable for studying electronic resonances in larger molecules. The resolution-of-the-identity (RI) approximation further reduces computational demands without significant loss in accuracy. We investigate the numerical performance of the new complex-energy RI-CC2 methods, focusing on temporary anions. Negative electron affinities and decay widths can be computed using the electron-attachment (EA) variant of RI-CC2. For N2, C2H4, CH2O, and HCOOH, EA-CC2 yields electron affinities about 0.1-0.2 eV smaller than EOM-EA-CCSD, while deviations reach 0.5 eV for larger anions such as uracil, naphthalene, cyanonaphthalene, and pyrene. As a result of these trends, EA-CC2 is in better agreement with experiment for the negative electron affinities than EOM-EA-CCSD for all studied anions. The corresponding resonance widths from EA-CC2 calculations are about 0.05-0.25 eV smaller compared to EOM-EA-CCSD. Semi-empirical spin-scaling increases electron affinities by 0.3-0.5 eV and broadens resonance widths, improving the agreement with EOM-EA-CCSD but worsening the agreement with experiment.