A benchmark theoretical study of the electronic ground state and of the singlet-triplet split of benzene and linear acenes

Abstract

A benchmark theoretical study of the electronic ground state and of the vertical and adiabatic singlet-triplet (ST) excitation energies of benzene (n=1) and n-acenes (C4n+2H2n+4) ranging from naphthalene (n=2) to heptacene (n=7) is presented, on the ground of single- and multireference calculations based on restricted or unrestricted zero-order wave functions. High-level and large scale treatments of electronic correlation in the ground state are found to be necessary for compensating giant but unphysical symmetry-breaking effects in unrestricted single-reference treatments. The composition of multiconfigurational wave functions, the topologies of natural orbitals in symmetry-unrestricted CASSCF calculations, the T1 diagnostics of coupled cluster theory, and further energy-based criteria demonstrate that all investigated systems exhibit a (1)A(g) singlet closed-shell electronic ground state. Singlet-triplet (S-0-T-1) energy gaps can therefore be very accurately determined by applying the principles of a focal point analysis 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, 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 infinity Z), the S-0-T-1 vertical excitation energies of benzene (n=1) and n-acenes (n=2-7) amount to 100.79, 76.28, 56.97, 40.69, 31.51, 22.96, and 18.16 kcal/mol, respectively. Values of 87.02, 62.87, 46.22, 32.23, 24.19, 16.79, and 12.56 kcal/mol are correspondingly obtained at the CCSD(T)/cc-pV infinity Z level for the S-0-T-1 adiabatic excitation energies, upon including B3LYP/cc-PVTZ corrections for zero-point vibrational energies. In line with the absence of Peierls distortions, extrapolations of results indicate a vanishingly small S-0-T-1 energy gap of 0 to similar to 4 kcal/mol (similar to 0.17 eV) in the limit of an infinitely large polyacene.