The Evolution of Electronic Structure in Conjugated Molecules Revealed by Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory and Density-Based Analyses: II. Polyacenes

Large conjugated molecules feature small gaps between occupied and virtual orbital spaces, which results in complex electronic structure patterns in their low-lying states. These orbital near-degeneracies also challenge quantum chemistry methods. Mixed-reference spin-flip TDDFT (MRSF-TDDFT) and density-matrix-based analyses provide useful tools to interrogate electronic structure in large conjugated molecules. This paper investigates one such family—polyacenes. Following our recent study of the ground and low-lying excited states of all-trans polyenes, we track this evolution from benzene to dodecacene using MRSF-TDDFT and densitymatrix-based analyses. In polyacenes, the ground state acquires diradical character as the number of rings increases, while the doubly excited state dominated by the HOMO2 → LUMO2 configuration drops steeply in energy and falls below the La state between nonacene and decacene. MRSF-TDDFT reproduces the experimental La/Lb crossing, which standard linear-response TDDFT misses, and gives singlettriplet gaps close to high-level wave-function benchmarks and singlet-fission energetics consistent with experiment. The analyses show that La remains predominantly singly excited throughout the series and we attribute the strong decrease in its oscillator strength to the growing diradical character of the ground state. The doubly excited state evolves from mixed character in naphthalene, similar to the 2 1Ag− state of the polyenes, to a nearly closed-shell doubly excited state in pentacene and hexacene, and finally to a state with natural orbital occupations resembling those of the ground state in the longest acenes. From heptacene onward, doubly excited states