Low-Lying Excited States of Linear All-Trans Polyenes: Insights from Analytic Gradient and Nonadiabatic Coupling...

Polyenes serve as a rigorous test for theoretical models and electronic structure methods, playing a key role in advancing computational and theoretical chemistry. Here, we present a high-level theoretical investigation of linear, all-trans polyenes using energy gradients and nonadiabatic coupling vectors based on an MR-CISD wave function to describe electronic transitions involving the ground state (1¹A_g^-) and three low-lying excited states (2¹A_g^-, 1¹B_u⁺, and 2¹B_u^-) of hexatriene, octatetraene, and decapentaene. This approach enables accurate evaluation of both adiabatic and vertical excitation and emission energies, yielding results in excellent agreement with experiment, as well as locating minima on the crossing seam between adiabatic states. Our results show that vertical excitation energies to the 1¹B_u⁺ state are blue-shifted by 0.2-0.3 eV relative to the experimental absorption maximum, whereas the vertical emission energy from the 2¹A_g^- state is red-shifted by ∼0.2 eV relative to the experimental emission maximum. Upon relaxation from the Franck-Condon geometry, the 2¹A_g^- state stabilizes by around 1 eV, compared to 0.2-0.3 eV for the 1¹B_u⁺ state. An analysis of the S₁/S₀ crossing seam in hexatriene shows that its minimum involves asymmetric backbone deformations and provides an efficient channel for ultrafast internal conversion to the ground state, consistent with the absence of detectable fluorescence in this molecule. These results demonstrate the power of analytic gradients and nonadiabatic coupling vectors based on an MR-CISD wave function for accurately characterizing the electronic structure and photophysics of polyenes.