Density functional theory study on the electronic structure and excited-state modulation of naphthalene diimide...

Naphthalene diimide (NDI) derivatives are widely used as n-type organic semiconductors, but quantitative structure-property relationships for this class remain incomplete. Most existing DFT studies map frontier orbital energies without providing bond-level descriptors or predictive models. Here, we combine DFT, TD-DFT, AIM, and hole-electron analysis to study 20 NDI derivatives. First, the LUMO energy follows a linear Hammett relationship with the substituent constant σ_p, providing a simple way to predict electron affinity. Second, AIM analysis shows that electron-withdrawing groups increase the electron density at the CO bond critical point, while electron-donating groups decrease it, directly linking substituent electronics to bond covalency. Third, we identified two distinct mechanisms for long-range charge separation: a bulky substituent creates a near-perpendicular geometry that in acetonitrile gives a long charge-transfer distance (D = 6.04 Å) and a small overlap integral (S = 0.10), while a TEG side chain forms an N → O dative bond yielding an even longer and solvent-independent charge-separated state (D ≈ 13.5 Å). Additionally, amino substituents cause large red shifts (≈22 nm), whereas thiophene derivatives show unexpected blue shifts in acetonitrile. These results provide quantitative design rules for tuning electronic structure and excited-state properties in organic semiconductors.