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arXiv:cond-mat/0202520 · Physical review. B, Condensed matter

Large-scale numerical investigation of excited states in poly(para-phenylene)

Robert J. Bursill, William Barford

Published Nov 27, 2002• 20 citations
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Abstract

A density-matrix renormalization group scheme is developed, allowing the essentially exact numerical solutions for the important excited states of a realistic semiempirical model for oligophenylenes. By monitoring the evolution of the energies with chain length and comparing them to the experimental absorption peaks of oligomers and thin films, we assign the four characteristic absorption peaks of phenyl-based polymers. We also determine the position and nature of the nonlinear optical states in this model.

DOI
10.1103/physrevb.66.205112

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A density-matrix renormalization group scheme is developed, allowing the essentially exact numerical solutions for the important excited states of a realistic semiempirical model for oligophenylenes. By monitoring the evolution of the energies with chain length and comparing them to the experimental absorption peaks of oligomers and thin films, we assign the four characteristic absorption peaks of phenyl-based polymers. We also determine the position and nature of the nonlinear optical states in this model.
The Pariser-Parr-Pople model of pi-conjugated electrons is solved by a three-block, symmetry-adapted density matrix renormalization group (DMRG) method for the light emitting polymer, poly(para-phenylene vinylene). The energies of the primary excited states are calculated. There is excellent agreement between theory and experiment when solid state screening is incorporated into the model parameters, enabling us to make an identification of the origin of the key spectroscopic features. Appendices describe important technical aspects of the three-block DMRG approach: Local Hilbert space efficiency and its relation to the matrix product formulation of the DMRG; an efficient computational procedure for constructing symmetry-adapted states for DMRG calculations; and correct superblock state targeting to ensure good convergence of the method.
We report the symmetrized density matrix renormalization group (DMRG) study of neutral and doped oligomers of poly-para-phenylene (PPP) system within an extended Hubbard model. Model parameters are determined by comparing the existing results for an interacting small system. We compute a number of properties in the ground state as well as in the one-photon, two-photon and triplet states to completely characterize these states. Bond-order studies show that the lowest two-photon state corresponds to a localized excitation while one-photon and triplet excitations are extended in nature. The bipolaronic state shows clear evidence for charge separation and disproportionation into two polarons. We find that the extended nature of one-photon and triplet states of the neutral system are very similar to those of the bipolaronic ground states.
We report the symmetrized density matrix renormalization group (DMRG) study of neutral and doped oligomers of PPP system within an extended Hubbard model. Model parameters are determined by comparing the existing results for interacting small system. We compute a number of properties in the ground state as well as in the one-photon, two-photon and triplet states to completely characterize these states. Based on the relative positions of the one-photon and two-photon states in long oligomers, we suggest that invoking interchain interactions is essential for explaining strong fluorescence in this system. Bond-order studies show that the lowest two-photon state corresponds to a localized excitation while one-photon and triplet excitations are extended in nature. The bipolaronic state shows clear evidence for charge separation and disproportionation into two polarons. We find that the extended nature of one-photon and triplet states of neutral system are very similar to those of the bipolaronic ground states.
We present density-matrix renormalization-group calculations of the Pariser-Parr-Pople-Peierls model of linear polyenes within the adiabatic approximation. We calculate the vertical and relaxed transition energies, and relaxed geometries for various excitations on long chains. The triplet (13Bu+)(1{}^{3}{B}_{u}^{+})(13Bu+​) and even-parity singlet (21Ag+)(2{}^{1}{A}_{g}^{+})(21Ag+​) states have a 2-soliton and 4-soliton forms, respectively, both with large relaxation energies. The dipole-allowed $(1{}^{1}{B}_{u}^{\ensuremath{-}})$ state forms an exciton-polaron, and has a very small relaxation energy. The relaxed energy of the 21Ag+2{}^{1}{A}_{g}^{+}21Ag+​ state lies below that of the $1{}^{1}{B}_{u}^{\ensuremath{-}}$ state. We observe an attraction between the soliton-antisoliton pairs in the 21Ag+2{}^{1}{A}_{g}^{+}21Ag+​ state. The calculated excitation energies agree well with the observed values for polyene oligomers; the agreement with polyacetylene thin films is less good, and we comment on the possible sources of the discrepancies. The photoinduced absorption is interpreted. The spin-spin correlation function shows that the unpaired spins coincide with the geometrical soliton positions. We study the roles of electron-electron interactions and electron-lattice coupling in determining the excitation energies and soliton structures. Electronic interactions play the key role in determining the ground-state dimerization and the excited-state transition energies.
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.
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.