Elucidating the Magnitude of Internal Reorganization Energy of Molecular Excited States from the Perspective of Transition Density

Quantifying vibronic couplings in molecular excited states is crucial for the elucidation of a broad range of photophysical phenomena. In this study, we compare different theoretical approaches for the calculation of reorganization energy, a measure of vibronic coupling strength, and provide a rigorous derivation to show that molecular transition density characterizing electronhole excitation could be used to quantify the magnitude of reorganization energy. The theory enables a descriptor based on molecular-orbital coefficients and atomic transition densities to quantify the magnitude of reorganization energies in molecular excited states. Applying the approach to low-lying excited states of polyacenes, we demonstrate that transition density distribution explains the difference in the magnitude of the reorganization energy of different excited states. Furthermore, to clarify the applicability of the transition density descriptor in molecular design for small-reorganization energy molecules, we investigate a broad range of molecular chromophores to show the effectiveness of the proposed theory. With this perspective on the relationship between reorganization energy and transition density, we successfully provide a quantitative rule to identify pi-conjugated systems with small reorganization energy in the excited state, which should be useful for the development of novel optoelectronic materials.