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 ͑ST͒ excitation energies of benzene ͑n =1͒ and n-acenes ͑C 4n+2 H 2n+4 ͒ ranging from naphthalene ͑n =2͒ to heptacene ͑n =7͒ 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, 5͒ and single-reference methods ͓HF, MP2, MP3, MP4SDQ, CCSD, CCSD͑T͔͒ 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 ͓CCSD͑T͔͒ in the limit of an asymptotically complete basis set ͑cc-pVϱZ͒, the S 0 -T 1 vertical excitation energies of benzene ͑n =1͒ and n-acenes ͑n =2-7͒ 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 CCSD͑T͒ / cc-pVϱZ 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 ϳ4 kcal/ mol ͑ϳ0.17 eV͒ in the limit of an infinitely large polyacene.

On the Importance of Clar Structures of Polybenzenoid Hydrocarbons as Revealed by the π-Contribution to the Electron Localization Function

“…With B3LYP, the least stable isomer (1) is identified as a singlet biradical (<S 2 > = 0.76), consistent with the earlier study of Bendikov et al [71], although it should be noted that a recent benchmark theoretical study, including a focal point analysis applied onto the results of a series of symmetryrestricted electron correlated calculations of gradually increased sophistication, revealed that 1 has a 1 A g closed-shell singlet ground state [72]. Tetrabenzanthracene (6), having the maximum number of -sextets (five) among the selected heptabenzenoids, is the isomer with the highest thermodynamic stability according to our calculations.…”

Nature of ground and electronic excited states of higher acenes

“…Therefore, the broken-symmetry determinant of UDFT contains limited information of the entire many-electron wave function, and it may not describe the nature of the ground state. In the past 10 y, some accurate but relatively inexpensive theories have been developed and applied to higher acenes (49)(50)(51)(52)(53)(54)(55)(56)(57). Among them, the most widely accepted one seems to be the density matrix renormalization group method in combination with the complete active-space configuration interaction theory (49).…”

Role of exact exchange in thermally-assisted-occupation density functional theory: A proposal of new hybrid schemes

“…Consequently, the experimental singlet-triplet energy gaps (ST gaps) of n-acenes are only available up to pentacene [109][110][111][112]. On the theoretical side, since n-acenes belong to conjugated π-orbital systems, high-level ab initio multi-reference methods, such as the density matrix renormalization group (DMRG) algorithm [115,122], the variational twoelectron reduced density matrix (2-RDM) method [121,124], and other high-level methods [114,[118][119][120], are typically required to capture the essential strong static correlation effects.…”

“…Recently, linear n-acenes (C 4n+2 H 2n+4 ), containing n linearly fused benzene rings (see Figure 10), have attracted considerable interest in the research community owing to their promising electronic properties [20,21,[45][46][47][48][109][110][111][112][113][114][115][116][117][118][119][120][121][122][123][124]. The electronic properties of nacenes have been found to be highly dependent on the chain lengths.…”