Unraveling the Band Gap Trend in the Narrowest Graphene Nanoribbons from the Spin-Adapted Excited-Spectra Reduced Density Matrix Method

Abstract

Polybenzenes as the narrowest graphene nanoribbons with versatile electronic properties are widely studied both theoretically and technologically. Here, we examine the singlet–triplet band gap as a function of length for two members of the oligobenzene family: the acene and phenacene chains. We observe that the prediction of the band gap is highly sensitive to the accurate treatment of the electron correlation. The excited-spectra two-electron reduced density matrix (2-RDM) method, which computes the excited states from a variationally computed ground-state 2-RDM, yields finite band gaps for all finite chain lengths through 10 rings as well as in the extrapolated infinite ring limits of both acenes and phenacenes. In contrast, we find that weakly correlated methods like configuration interaction singles and time-dependent density functional theory predict a crossing of the singlet- and triplet-state energies of the acene chains at a finite ring size, with the triplet becoming the energetically lowest state at longer chain lengths. Recent experiments through decacene and 9-phenacene agree with the correlated 2-RDM calculations, showing that both acene and phenacene chains in the large polymer limit possess finite band gaps.

Remarkable Size Effect on Photophysical and Nonlinear Optical Properties of All‐Carboatomic Rings, Cyclo[18]carbon and Its Analogues

“…[20]), since both hole and electron of corresponding electron excitation are distributed around C−C bond axes. The reason for the red‐shift of maximum absorption of the C 2 N with increasing its size should be closely related to the common phenomenon that as number of repeating units of a π‐conjugated oligomer increases, the energies of HOMO and LUMO rise and drop, respectively, [28,29] implying overall increase of π occupied MOs and decrease of π* unoccupied ones, which in turn result in lowered π‐π* excitation energies. The HOMO‐LUMO gaps and maximum absorption wavelengths of all studied cyclocarbons are collectively plotted in Figure 2, from which it can be seen that the two properties are indeed closely related to each other and share the same variation trend.…”

Pushing the Limits of Acene Chemistry: The Recent Surge of Large Acenes

“…An extrapolation of the pp‐RPA‐B3LYP data to the polyacene limit arrives at an optical gap of 0.85 eV [116] . A larger optical gap of 1.21 eV for polyacene was obtained by extrapolation for values up to 10ac computed with the excited‐spectra two‐electron reduced density matrix (ES‐RDM) method [131] …”

“…[116] Al arger opticalg ap of 1.21 eV for polyacenew as obtained by extrapolation for values up to 10ac computed with the excited-spectra two-electron reduced density matrix (ES-RDM) method. [131] In addition to the singlet-triplet energy gap and singlet-singlet optical gap, the fundamental gap, that is, the difference between the IP and EA, E g = IPÀEA, were evaluated computationally for the acene series.T he gas-phasee xperimental EAs are availableu pt op entacene (Table 3), [19] whereas IPs have been determinede xperimentally up to 6ac (Table 4). [132] The most sophisticated computational evaluation of the IP and EA values was performed by using focal-point analysis and provided data at the CCSD(T)/cc-pV1Zl evel up to 6ac.…”

Dodecacene Generated on Surface: Reopening of the Energy Gap

“…New works published in 2019 are continuing this fundamental discussion, indicating that the debate on the electronic structure of higher acenes is actual and far from being solved 12,15,16 . In particular, the group of Roman Fasel discusses a possible open-shell character of the ground state already for N = 9 (nonacene) on Au(111) 12 .…”