Total photoionization cross-sections of excited electronic states by the algebraic diagrammatic construction-Stieltjes-Lanczos method

Here, we extend the L2 ab initio method for molecular photoionization cross-sections introduced in Gokhberg et al. [J. Chem. Phys. 130, 064104 (2009)] and benchmarked in Ruberti et al. [J. Chem. Phys. 139, 144107 (2013)] to the calculation of total photoionization cross-sections of molecules in electronically excited states. The method is based on the ab initio description of molecular electronic states within the many-electron Green’s function approach, known as algebraic diagrammatic construction (ADC), and on the application of Stieltjes-Chebyshev moment theory to Lanczos pseudospectra of the ADC electronic Hamiltonian. The intermediate state representation of the dipole operator in the ADC basis is used to compute the transition moments between the excited states of the molecule. We compare the results obtained using different levels of the many-body theory, i.e., ADC(1), ADC(2), and ADC(2)x for the first two excited states of CO, N2, and H2O both at the ground state and the excited state equilibrium or saddle point geometries. We find that the single excitation ADC(1) method is not adequate even at the qualitative level and that the inclusion of double electronic excitations for description of excited state photoionization is essential. Moreover, we show that the use of the extended ADC(2)x method leads to a substantial systematic difference from the strictly second-order ADC(2). Our calculations demonstrate that a theoretical modelling of photoionization of excited states requires an intrinsically double excitation theory with respect to the ground state and cannot be achieved by the standard single excitation methods with the ground state as a reference.