Focal Point Analysis of the Singlet–Triplet Energy Gap of Octacene and Larger Acenes

A benchmark theoretical study of the electronic ground state and of the vertical and adiabatic singlet–triplet (ST) excitation energies of n-acenes (C4n+2H2n+4) ranging from octacene (n = 8) to undecacene (n = 11) is presented. The T1 diagnostics of coupled cluster theory and further energy-based criteria demonstrate that all investigated systems exhibit predominantly a 1Ag singlet closed-shell electronic ground state. Singlet–triplet (S0–T1) energy gaps can therefore be very accurately determined by applying the principle of a focal point analysis (FPA) onto the results of a series of single-point and symmetry-restricted calculations employing correlation consistent cc-pVXZ basis sets (X = D, T, Q, 5) and single-reference methods [HF, MP2, MP3, MP4SDQ, CCSD, and CCSD(T)] of improving quality. According to our best estimates, which amount to a dual extrapolation of energy differences to the level of coupled cluster theory including single, double, and perturbative estimates of connected triple excitations [CCSD(T)] in the limit of an asymptotically complete basis set (cc-pV∞Z), the S0–T1 vertical (adiabatic) excitation energies of these compounds amount to 13.40 (8.21), 10.72 (6.05), 8.05 (3.67), and 7.10 (2.58) kcal/mol, respectively. In line with the absence of Peierls distortions (bond length alternations), extrapolations of results obtained at this level for benzene (n = 1) and all studied n-acenes so far (n = 2–11) indicate a vanishing S0–T1 energy gap, in the limit of an infinitely large polyacene, within an uncertainty of 1.5 kcal/mol (0.06 eV). Lacking experimental values for the S0–T1 energy gaps of n-acenes larger than hexacene, comparison is made with recent optical and electrochemical determinations of the HOMO–LUMO band gap. Further issues such as scalar relativistic, core correlation, and diagonal Born–Oppenheimer corrections (DBOCs) are tentatively examined.