Energy decomposition analysis for excited states: an extension based on TDDFT

To enhance the understanding of photochemical reactivity and its mechanisms, it is essential to analyze bonding interactions in excited-state reactions. Such insights can aid in optimizing these reactions. This paper presents an energy decomposition analysis method for excited states (exc-EDA), integrating the ground state EDA approach by Morokuma, Ziegler and Rauk with time-dependent density functional theory (TDDFT). The methodology focuses on calculating excitation energies, particularly for the intermediate states of the EDA. We introduce two variants: the first uses non-relaxed excitation coefficients (exc-u-EDA), where the excitation coefficients of the excited fragment are used directly; the second optimizes these coefficients for the intermediate states (exc-r-EDA). Exc-EDA can be applied with various density functionals, but the accuracy depends on the functional's ability to describe the excited state properly. Smaller basis sets result in lower energy values due to fewer virtual orbitals, while larger basis sets produce consistent relative results but may involve different excited states in intermediate steps leading to artificial increase of energy terms in the EDA. The method's convergence behavior resembles that of TDDFT, with a computational cost approximately three times that of the underlying TDDFT calculation. At the current stage, the method requires that the excitation is localized on one of the fragments, but it also enables an analysis of the subsequent charge-transfer effects. Application of exc-EDA to singlet fission in pentacene clusters demonstrates its practical value, offering quantitative insights into excited-state bonding and revealing clear, intuitive trends.