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arXiv:cond-mat/0508433 · Physical Review B

Density matrix renormalization group study of conjugated polymers with transverse π -conjugation

Yan Yan, S. Mazumdar

Published Dec 15, 2005• 3 citations
arXivHTMLPDF

Abstract

We report accurate numerical studies of excited state orderings in long hypothetical $\ensuremath{\pi}$-conjugated oligomers in which the hydrogen atoms of transpolyacetylene are replaced with conjugated side groups, within modified Hubbard models. There exists a range of the bare Coulomb repulsion for which the excited state ordering is conducive to photoluminescence in the substituted systems, even as this ordering is opposite in the unsubstituted polyenes of the same lengths. Our work provides motivation to study real $\ensuremath{\pi}$-conjugated polymers with transverse conjugation and small optical gaps.

DOI
10.1103/physrevb.72.212201

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We report accurate numerical studies of excited state orderings in long hypothetical \ensuremathπ\ensuremath{\pi}\ensuremathπ-conjugated oligomers in which the hydrogen atoms of transpolyacetylene are replaced with conjugated side groups, within modified Hubbard models. There exists a range of the bare Coulomb repulsion for which the excited state ordering is conducive to photoluminescence in the substituted systems, even as this ordering is opposite in the unsubstituted polyenes of the same lengths. Our work provides motivation to study real \ensuremathπ\ensuremath{\pi}\ensuremathπ-conjugated polymers with transverse conjugation and small optical gaps.
We have carried out symmetrized density-matrix renormalization-group calculations to study the nature of excited states of long polyacene oligomers within a Pariser-Parr-Pople Hamiltonian. We have used the C2{C}_{2}C2​ symmetry, the electron-hole symmetry, and the spin parity of the system in our calculations. We find that there is a crossover in the lowest dipole forbidden two-photon state and the lowest dipole allowed excited state with size of the oligomer. In the long system limit, the two-photon state lies below the lowest dipole allowed excited state. The triplet state lies well below the two-photon state and energetically does not correspond to its description as being made up of two triplets. These results are in agreement with the general trends in linear conjugated polymers. However, unlike in linear polyenes wherein the two-photon state is a localized excitation, we find that in polyacenes, the two-photon excitation is spread out over the system. We have doped the systems with a hole and an electron and have calculated the charge excitation gap. Using the charge gap and the optical gap, we estimate the binding energy of the ${1}^{1}{B}^{\ensuremath{-}}$ exciton to be 2.09 eV. We have also studied doubly doped polyacenes and find that the bipolaron in these systems, to be composed of two separated polarons, as indicated by the calculated charge-density profile and charge-charge correlation function. We have studied bond orders in various states in order to get an idea of the excited state geometry of the system. We find that the ground state, the triplet state, the dipole allowed state, and the polaron excitations correspond to lengthening of the rung bonds in the interior of the oligomer while the two-photon excitation corresponds to the rung bond lengths having two maxima in the system.
We apply the Hubbard-Peierls Hamiltonian to study the low-lying excited states of several model conjugated polymers. The calculations employ a numerical renormalization-group method for chains of intermediate length, and a more approximate truncated configuration-interaction scheme to extrapolate the results to longer systems. In the range of on-site Coulomb repulsion strengths of physical interest, we find that a correlated even-parity singlet excited state competes with the odd-parity singlet excitation expected in the U=0 limit of the model, in agreement with previous studies on the Pariser-Parr-Pople model. The lowest electronic excitations in the model are identified as triplet excitations. Self-consistently-relaxed lattice configurations surrounding these electronic excitations are studied. In addition to the stable photoexcitations predicted in the U=0 limit of the theory, we find that the interelectronic repulsive potential leads to a rich spectrum of competing neutral structures, which are studied and characterized. Coulomb correlations provide a mechanism for production of long-lived spin-1/2 neutral excitations for degenerate ground-state systems, and spin-1 neutral excitations for nondegenerate ground-state systems.
This work addresses the question of whether low-lying excitations in conjugated polymers are comprised of free charge carriers or excitons. States are characterized as bound or unbound according to the scaling of the average particle-hole separation with system size. We critically examine other criteria commonly used to characterize states. The polymer is described by an extended Hubbard model with alternating transfer integrals. The model is solved by exact diagonalization and the density-matrix renormalization-group (DMRG) method. We demonstrate that the DMRG accurately determines excitation energies, transition dipole moments and particle-hole separations of a number of dipole-forbidden (Ag){(A}_{g})(Ag​) and dipole-allowed (Bu){(B}_{u})(Bu​) states. Within a parameter regime considered reasonable for polymers such as polyacetylene, it is found that the charge gap, often used to define the exciton binding energy, is not a good criterion by which to decide whether a state is bound or unbound. The essential nonlinear optical state mAg{\mathrm{mA}}_{g}mAg​ is found to mark the onset of unbound excitations in the Ag{A}_{g}Ag​ symmetry sector. In the Bu{B}_{u}Bu​ symmetry sector, on the other hand, it is found that all low-lying states are unbound and that there is no well-defined nBu{\mathrm{nB}}_{u}nBu​ state. That is, the 1Bu{1B}_{u}1Bu​ state marks the onset of unbound excitations in this sector.
The density-matrix renormalization group (DMRG) method is used for a comparative study of low-lying excitations in trans-polyacetylene (t-PA) and transversely substituted t-PA (TS-t-PA). We have employed the Pariser-Parr-Pople model Hamiltonian which incorporates long-range electronic correlations to model these systems. We find some fundamental differences in the excited states of the t-PA and TS-t-PA. We find that the lowest two-photon allowed excited state in TS-t-PA is not made up of two triplet excitons and the gap to this state is nonzero even for undimerized chains in the thermodynamic limit. Contrary to earlier results for the Hubbard model, we find that the lowest two-photon state is always below the first optically allowed state in all the systems studied here making TS-t-PA systems only weakly fluorescent materials. Nonresonant tumbling averaged linear and third harmonic generation optic coefficients of TS-t-PA systems are also much smaller than that of t-PA.
The present thesis deals with a theoretical study of electronic structures in -conjugated molecular materials with focus on their application in organic elec-tronics. We also discuss a modified and efficient symmetrized DMRG algorithm for studying excited states in these systems. In recent times, organic conjugated systems have emerged as potential candidates in a wide range of fascinating fields by virtue of their tunable electronic properties, easy processability and low cost. Tunability in the electronic and optical properties primarily are centered on the or-dering and nature of the low-lying excited states. Probing these important excited states also demands development of efficient and adaptable techniques. Chapter 1 provides a basic overview of conjugated organic polymers which have been utilized over decades in diverse fields as in organic light emitting diodes (OLED), organic solar cells (OSC) and non-linear optical (NLO) devices. These systems also contribute significantly to theoretical understanding as they pro vide important insights of one and quasi-one dimensional systems. In this chapter, we have given basic description of the electronic processes in OLED and OSC along with a brief theoretical description of -conjugated organic systems. Chapter 2 gives an account of the numerical techniques which are necessary for the study of low-dimensional strongly correlated systems like -conjugated sys-tems. For this purpose, effective low-energy model Hamiltonians viz. Huckel,¨ Hubbard and Pariser-Parr-Pople Hamiltonians are discussed. Exact diagonalization technique within the diagrammatic valence bond (DVB) basis and density matrix renormalization group (DMRG) technique are discussed in details. We have also given brief accounts of the methods employed to study real-time dynamics. A short description of different computational techniques for the study of NLO properties in -conjugated systems is also provided. Engineering the position of the lowest triplet state (T1) relative to the first excited singlet state (S1) is of great importance in improving the efficiencies of organic light emitting diodes and organic photovoltaic cells. In chapter 3, we have carried out model exact calculations of substituted polyene chains to understand the fac-tors that affect the energy gap between S1 and T1. The factors studied are backbone dimerization, different donor-acceptor substitutions and twisted backbone geome-try. The largest system studied is an eighteen carbon polyene which spans a Hilbert space of about 991 million in the triplet subspace. We show that for reverse inter-system crossing (RISC) process, the best choice involves substituting all carbon sites on one half of the polyene with donors and the other half with acceptors. Singlet fission (SF) is a potential pathway for significant enhancement of efficiency in OSC. In chapter 4, we study singlet fission in a pair of polyene molecules in two different stacking arrangements employing exact many-body wave packet dy-namics. In the non-interacting model, SF…
We have carried out density-matrix renormalization group 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 $\ensuremath{\delta}$ and various correlation functions and structure factors for $\ensuremath{\delta}=0$. From energetics, we find that the nature of the Peierls' instability in polyacene is conditional and strong electron correlations enhance the dimerization. The cis form of the distortion is favored 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, spin-density wave, or a charge-density wave in the ground state.