Theory of optical transitions in curved chromophores

Using first order perturbation theory in the Born-Oppenheimer regime of the Frenkel-Holstein model, we develop a theory for the optical transitions in curved chromophores of π-conjugated polymers. Our key results are that for absorption, A, and emission, I, polarized parallel to the 0-0 transition, I⁰¹/I⁰⁰ ≃ A⁰¹/A⁰⁰ = S(N), where S(N) = S(1)/IPR is the effective Huang-Rhys parameter for a chromophore of N monomers and IPR is the inverse participation ratio. In contrast, absorption and emission polarized perpendicular to the 0-0 transition acquires vibronic intensity via the Herzberg-Teller effect. This intensity generally increases as the curvature increases and consequently I⁰¹/I⁰⁰ increases (where I⁰¹ is the total 0-1 emission intensity). This effect is enhanced for long chromophores and in the anti-adiabatic regime. We show via DMRG calculations that this theory works well in the adiabatic regime relevant to π-conjugated polymers, i.e., ħ ω/|J| ≲ 0.2.