Structural and electronic instabilities in polyacenes: Density-matrix renormalization group study of a long-range interacting model

Abstract

We have carried out Density Matrix Renormalization Group (DMRG) calculations on the ground state of long polyacene oligomers within a Pariser-Parr-Pople (PPP) Hamiltonian. The PPP model includes long-range electron correlations which are required for physically realistic modeling of conjugated polymers. We have obtained the ground state energy as a function of the dimerization δ and various correlation functions and structure factors for δ = 0. From energetics, we find that while the nature of the Peierls' instability in polyacene is conditional and strong electron correlations enhance the dimerization.The cis form of the distortion is favoured over the trans form. However, from the analysis of correlation functions and associated structure factors, we find that polyacene is not susceptible to the formation of a bond order wave (BOW), spin density wave (SDW) or a charge density wave (CDW) in the ground state. PACS numbers : 31.25.Qm, 71.10.Fd, 71.30.+h, 71.45.-d 1 Introduction The question whether an infinitely long linear polyene (polyacetylene, PA) would have equal bond lengths or not has been debated ever since it was known that benzene has equal bond lengths while 1,3,5-hexatriene has alternating short (double) and long (single) bonds. Addressing this issue, Lennard-Jones [1] and Coulson [2] predicted a ground state with uniform bond lengths. Later work by Labhart [3], Ooshika [4], Longuet-Higgins and Salem [5] established that the ground state would have bond-alternation i.e. the infinite polyene would have alternate long and short bonds. Experimentally, such a dimerization would qualitatively explain the finite optical gap obtained by extrapolation of optical data for linear polyenes [6]. Earlier, Peierls established a more general result, known as the Peierls' instability or Peierls' distortion [7] for a partially filled one-dimensional band. Peierls' demonstrated that lattice vibrations couple to electrons in the band leading to the opening of a gap at the Fermi surface, making the material insulating. The Hückel model solution of Longuet-Higgins and Salem pertain to the specific case of Peierls' distortions in a half-filled extended system. Longuet-Higgins and Salem showed that for an infinite polyene chain, the total electronic energy per carbon atom as a function of the distortion δ in the chain, within a Hückel model [8] is proportional to δ 2 ln |δ| [5].The elastic strain energy of the system is proportional to δ 2 , the proportionality constant depending directly on the lattice stiffness and inversely on the electron-phonon coupling constant. The algebraic forms of the strain and electronic energies guarantee that the gain in electronic energy always exceeds the strain energy and the ground state would correspond to nonzero δ. The distortion of the polyene chain is termed unconditional as the distorted state is always more stable than the undistorted state for any value of the

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

“…͑10͒ and ͑16͒ in Ref. 29, it is clear that the extent of symmetry-breaking complications in unrestricted treatments will smoothly increase with increasing system size, and decreasing band gap thereby, to reach asymptotically its climax at the polymer limit, where the band gap and the lowest excitation energies are expected to vanish in the absence of Peierls distorsions, 9 a ͑metallic͒ scenario which the present contribution seems to confirm. Indeed, the T1 diagnostics and the energy-based %TAE͑HF͒ and %TAE͓͑T͔͒ criteria corroborate the idea that multireference effects very slowly increase with system size.…”

“…7 Among all known PAH compounds, polyacenes probably aroused the greatest fantasies since they were predicted to behave as one-dimensional organic conductors with a zero-band gap, and to be subject to an opening of the bang gap due to Peierls distorsions only if the electron-phonon coupling exceeds the elastic energy strain associated with dimerization of the unit cell in a stiff lattice. 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.…”

“…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.…”

Bonding and Magnetism in High Symmetry Nano-Sized Graphene Molecules: Linear Acenes C<SUB>4<I>m</I>+2</SUB>H<SUB>2<I>m</I>+4</SUB> (<I>m</I>=2,&hellip;25); Zigzag Hexangulenes C<SUB>6<I>m</I><SUP>**</SUP>2</SUB>H<SUB>6<I>m</I></SUB> (<I>m</I>=2,&hellip;10); Crenelated Hexangulenes C<SUB>6(3<I>m</I><SUP>**</SUP>2&minus;3<I>m</I

“…35) In this state the spin ''up'' and spin ''down'' electrons occupy different sites with an anti-ferromagnetic pattern. There have been other recent studies of this effect, [36][37][38][39][40] some overlapping the time frame of this present study. The existence of a singlet or a higher spin ground state (radical) phase in the long acenes is connected to the influence of geometry of the perimeter on bipartite lattices.…”

Role of impurities on the optical properties of rectangular graphene flakes

“…We model the p z electrons in the GFs using the Pariser-Parr-Pople (PPP) Hamiltonian [41][42][43][47][48][49] :…”