How Does The Variation In The Dihedral Angle Between The Aryl Rings In A Push-pull Substituted Stilbene Molecule Affect The Vibronic Coupling Between The S1 And S2 Electronic States, And What Implications Does This Have For The Interpretation Of Its Dispersed Fluorescence Spectra?

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The variation in the dihedral angle between the aryl rings in a push-pull substituted stilbene significantly influences the vibronic coupling between the S1 and S2 electronic states, with notable implications for the dispersed fluorescence spectra. Here's a structured summary of the analysis:

  1. Dihedral Angle and Conjugation:

    • The dihedral angle affects the conjugation between the aryl rings. A smaller angle (more coplanar) enhances conjugation, delocalizing π-electrons and lowering the energy of excited states, thereby reducing the S1-S2 energy gap.

  2. Vibronic Coupling:

    • A smaller dihedral angle decreases the S1-S2 energy gap, facilitating stronger vibronic coupling. This coupling allows vibrational modes to induce transitions between the states, leading to wavefunction mixing.

  3. Implications for Fluorescence Spectra:

    • Strong Coupling (Small Dihedral Angle): Results in broader or overlapping emission bands due to state mixing. Vibronic progressions may become more complex.
    • Weak Coupling (Large Dihedral Angle): Leads to more resolved spectral features as states are less coupled, with distinct vibrational bands.

  4. Potential Energy Surfaces and Emission:

    • Differences in the potential energy surfaces of S1 and S2 can alter vibrational modes, affecting Franck-Condon factors and thus the relative intensities of fluorescence bands.
    • The possibility of dual fluorescence arises if emission occurs from both S1 and S2, depending on their relative energies and coupling.

  5. Conical Intersections:

    • A small dihedral angle may lead to conical intersections, facilitating non-radiative decay and reducing fluorescence intensity.

In conclusion, the dihedral angle modulates the electronic structure and vibronic interactions, influencing the complexity and resolution of the fluorescence spectra. A smaller angle typically results in more complex spectra due to enhanced coupling, while a larger angle yields simpler, more defined features.