Benchmarking Excited-State Calculations Using Exciton Properties

Benchmarking is an every-day task in computational chemistry, yet making meaningful comparisons between different methods is nontrivial. Benchmark studies often focus on the most obvious quantities such as energy differences. But to gain insight, it is desirable to explain the discrepancies between theoretical methods in terms of underlying wave functions and, consequently, physically relevant quantities. We present a new strategy of benchmarking excited-state calculations, which goes beyond excitation energies and oscillator strengths and involves the analysis of exciton properties based on the one-particle transition density matrix. By using this approach, we compare the performance of many-body excited-state methods (equation-of-motion coupled-cluster and algebraic diagrammatic construction) and time-dependent density functional theory. The selected examples illustrate the utility of different exciton descriptors in assigning state character and explaining the discrepancies among different methods. The examples include Rydberg, valence, and charge-transfer states, as well as delocalized excitonic states in large conjugated systems and states with substantial doubly excited character.