Open-Shell Ground State of Polyacenes: A Valence Bond Study

Abstract

Applying the density matrix renormalization group (DRMG) method to a nonempirical valence bond (VB) model Hamiltonian, we studied polyacene oligomers of different lengths in the strong electron correlation limit. Geometrical optimizations were performed for the lowest singlet and triplet states of oligomers up to [40]-acene, and a convergence of the bond lengths toward the polymer limit is observed in the interior of the oligomer. For large oligomers, as well as for the polymer, the ground state can be reasonably determined to be a singlet. Furthermore, a high similarity between the singlet geometries and triplet geometries suggests an open-shell character for the singlet ground state. A reasonable speculation of the soliton-antisoliton pair character of the singlet ground state was supported by a spin distribution analysis of the triplet state wave function of large oligomers, with each of the two solitons being broadly delocalized over the upper or bottom edge of the oligomers, respectively.

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

“…8,9 Naphthacene ͑also referred to as tetracene͒, pentacene, and derivative compounds have been used recently to prepare highly ordered conducting organic materials or thin films with particularly large charge carrier mobilities. 10 In contrast with the prevailing view 11 that large acenes have a closed-shell singlet or open-shell triplet electronic ground states, a few groups [12][13][14][15][16] recently conjectured that large acenes such as hexacene, heptacene, or octacene should rather be regarded as open-shell singlet biradical systems, as a result of the instability of unrestricted ͑UBLYP, UB3LYP, UPW91, UBPW91, etc.͒ wave functions, in conjunction with rather modest basis sets ͑STO-3G, 6-31G ‫ء‬ , or cc-pVDZ͒. This in-stability was diagnosed 12 from the fact that in these unrestricted calculations the two outermost singly occupied ␣ and ␤ spin orbitals do not smoothly follow the D 2h symmetry point group imposed by the nuclear frame, but rather reflect an overwhelmingly strong symmetry breaking of the electronic wave function, 12 in the form of a localization of the two frontier electrons on opposite polyacetylenic strands.…”

“…Polyradical antiferromagnetic singlet ground states subject to strong nondynamical electronic correlation and with one unpaired electron spin every five to six rings would eventually be found upon proceeding further to acenes longer than dodecacene. 13,14 These findings are most intriguing, considering that the ionization and electron attachment energies 17,18 of hexacene could be recently recovered within ͑or very near to͒ chemical ͑1 kcal/mol͒ accuracy from an extrapolation of various single-reference symmetry-restricted calculations to the level of coupled cluster theory incorporating single, double, and perturbative triple excitations ͓CCSD͑T͔͒ in the limit of an asymptotically complete basis set ͑CBS͒, by virtue of the principles of a focal point analysis ͑FPA͒ exploiting the faster convergence of the highest-order correlation corrections toward this limit. [19][20][21][22][23][24] In continuation to several studies on many-body quantum mechanical grounds by our group 17,18,25 of the electronic properties, ionization, and shake-up spectra of large PAHs employing the restricted Hartree-Fock ͑RHF͒ wave function as zero-order solution, a first purpose of the present contribution is to assess the extent of multireference effects in the electronic ground state of benzene ͑n =1͒ and n-acenes ͑C 4n+2 H 2n+4 ͒ ranging from naphthalene ͑n =2͒ up to heptacene ͑n =7͒, and to determine whether this state corresponds to a singlet closed-shell or a singlet open-shell wave function.…”

“…36 Heptacene can also be synthesized in the same matrix ͑under an inert atmosphere͒, where it can be maintained only up to 4 h; 37 no one has ever managed to measure the ST gap of this compound so far. Except for multireference MRMP2/cc-pVDZ, 38 CASCI/cc-pVDZ or CASCI/STO-3G studies 13 on systems as large as naphthacene, hexacene, or dodecacene, respectively, most theoretical determinations of oligo-and polyacenes are the result of calculations employing empirical ͑Hückel͒ 8 or semiempirical ͑Parr-Pariser-Pople͒ Hamiltonians, 9,39 Density Functional Theory ͑DFT͒, 12,14 or Time-Dependent DFT ͑TDDFT͒. 40 In spite of the fast convergence of results toward the size of the basis set, the accuracy of DFT or TDDFT calculations of excited states will always necessarily be limited by the approximate nature of the employed exchange-correlation functionals.…”

Nature of ground and electronic excited states of higher acenes

“…Unfortunately, the large system size of higher acenes hinders the use of many accurate but expensive theoretical tools. Empirical or semiempirical studies (42)(43)(44)(45)(46)(47) are inexpensive but also less accurate, and therefore seem to be less widely accepted. One of the most acknowledged theoretical predictions, up to now, is based on the unrestricted density-functional theory (UDFT) calculation performed more than 10 y ago (48).…”

Polarized–unpolarized ground state of small polycyclic aromatic hydrocarbons

“…[1] and their references), and their magnetic properties have motivated the interest in the study of other small polycyclic aromatic hydrocarbons (PAH). Actually, the ground state of n-acenes (n-Ac), n-periacenes (n-PA) and n-circumacenes (n-CA) molecules has been recently studied by using several methods [2][3][4][5][6][7][8][9][10][11][12][13], and the principal conclusion of DFT calculations is that they lead to a spin-polarized (antiferromagnetic) ground state for PAH greater than bysanthene [3] and for polyacenes with n > 7 [2].…”