Complex-Variable Equation-of-Motion Coupled-Cluster Singles and Doubles Theory with the Resolution-of-the-Identity Approximation.

We present an implementation of complex-variable equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) theory with the resolution-of-the-identity (RI) approximation. Complex-variable methods are used in the framework of non-Hermitian quantum chemistry to treat electronic resonances. As test cases, we study different types of resonances of N₂ and CO, namely, temporary anions, Stark resonances, autoionizing Rydberg states, and core-ionized states that decay by the Auger-Meitner effect. Temporary anions are treated with the complex basis function (CBF) method and different variants of the complex absorbing potential method. The other resonances are treated only with CBFs. The memory requirements of our implementation are significantly lower than those of canonical EOM-CCSD. We demonstrate that the RI error is smaller than the basis set error for all types of resonances. However, when the size of the decay width approaches the magnitude of the RI error, the width is qualitatively wrong with the RI approximation. In addition, when an adequate auxiliary basis set is not available, i.e., for autoionizing Rydberg states and for core-ionized states, the RI error in the total decay width increases by a factor 10.