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Communication: Can excitation energies be obtained from orbital energies in a correlated orbital theory?

This work shows that vertical excitation energies (characterized as single-electron processes) can be expressed in terms of one-particle solutions from a self-consistent field problem built by means of correlated operators. There are two alternative ways of enforcing this proposal for i → a transitions in a system (M): (1) by using only eigenvalues obtained for the cationic species reached after the removal of an electron from orbital i (M +) or (2) by combining these quantities with the eigenvalue associated with orbital i from the neutral M system. We demonstrate that those eigenvalues derived from the equation-of-motion formalism in terms of the coupled cluster approach including single and double substitutions for ionization potentials and electron affinities show excellent performance in reproducing these electronic transition energies by either path, with mean absolute deviations (MADs) between 0.02 and 0.06 eV. Moreover, the Kohn-Sham Density Functional Theory (KS-DFT) methods from the Quantum Theory Project (QTP) family provide nice results in terms of the second approach (MADs from 0.21 to 0.47 eV). However, DFT is not as successful as long as one takes into account only the eigenvalues of M +, although the respective excitation energies from QTP functionals are still reasonable (MADs between 0.55 and 0.74 eV). Ultimately, these relations can be used as a new consistency condition to develop KS-DFT approximations to the correlated orbital theory.