Inverse Relationship of Reorganization Energy to The Number of π Electrons from Perspective of Vibronic Coupling Density

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  • SHIZU Katsuyuki
    Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan
  • SATO Tohru
    Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan Unit of Elements Strategy Initiative for Catalysts & Batteries, Kyoto University, Kyoto 615-8510, Japan
  • TANAKA Kazuyoshi
    Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan

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The 1/Nπ relationship states that the reorganization energy λ of a molecule associated with charge transport is inversely proportional to the number Nπ of sites or π electrons involved in a π state of the molecule: λ∝1/Nπ. We investigated the fundamental question of how λ is influenced by Nπ, from the perspective of the vibronic coupling density. Vibronic coupling density analysis showed that symmetric distribution of the electron-density difference Δρ is essential for this relationship. The relationship can be more precisely rephrased as the size of the vibronic coupling constant is inversely proportional to the square-root of the number of sites over which Δρ is delocalized. Our findings provide not only a fundamental understanding of the 1/Nπ relationship, but also a practical approach to the molecular design of functional materials through controlling Δρ and vibronic couplings.

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