Intersystem crossing driven by vibronic spin–orbit coupling: a case study on psoralen

Abstract

For 7H-furo[3,2-g][1]benzopyran-7-one (psoralen), intersystem crossing (ISC) rate constants have been computed. Employing the Fermi golden rule, the harmonic approximation, and a pure-spin Born–Oppenheimer basis, both direct and vibronic spin–orbit (SO) coupling has been taken into account. Necessary data on electronic excitation energies and potential energy hypersurfaces originate from correlated all-electron calculations applying (time-dependent) density functional theory and the density functional theory/multireference configuration interaction approach. SO coupling has been treated by means of the one-center mean-field approximation. Vibronic SO couplings have been evaluated via numerical differentiation of SO matrix elements. Accounting only for direct SO coupling, rate constants of the order of k_ISC ≈ 10¹⁰ s⁻¹ result for S₂(n → π*) T₁(π → π*) ISC, whereas the rates of the channels S₁(π → π*) T_{1,2,3}(π → π*) do not exceed k_ISC ≈ 10⁵ s⁻¹. Including vibronic SO coupling, rate constants of k_ISC ≈ 3 × 10⁸ s⁻¹ are obtained for the S₁(π → π*) T₁(π → π*) ISC. The radiationless transition from the S₁(π → π*) state to the nearly degenerate T₃(π → π*) state has been estimated to be slightly less efficient (k_ISC ≈ 10⁷ s⁻¹). Based on our computed rates of ISC and excited state solvent shifts, we conclude that the experimentally observed appreciable triplet quantum yields of psoralen in polar protic media are primarily due to S₁(π → π*) T(π → π*) channels. For heteroaromatic systems, (π → π*)/(π → π*) ISC driven by vibronic SO coupling is expected to be a common triplet state population mechanism.