Computational Investigations of the Primary Excited States of Poly(para-phenylene vinylene)

The Pariser-Parr-Pople model of pi-conjugated electrons is solved by the density matrix renormalization group method for the light emitting polymer, poly(para-phenylene vinylene). The energies of the primary excited states are calculated. When solid state screening is incorporated into the model parameters there is excellent agreement between theory and experiment, enabling an identification of the origin of the key spectroscopic features.Comment: 6 pages, 3 figure

Quantized Lattice Dynamic Effects on the Spin-Peierls Transition

The density matrix renormalization group method is used to investigate the spin-Peierls transition for Heisenberg spins coupled to quantized phonons. We use a phonon spectrum that interpolates between a gapped, dispersionless (Einstein) limit to a gapless, dispersive (Debye) limit. A variety of theoretical probes are used to determine the quantum phase transition, including energy gap crossing, a finite size scaling analysis, bond order auto-correlation functions, and bipartite quantum entanglement. All these probes indicate that in the antiadiabatic phonon limit a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type is observed at a non-zero spin-phonon coupling, $g_{\text c}$. An extrapolation from the Einstein limit to the Debye limit is accompanied by an increase in $g_{\text c}$ for a fixed optical ($q=\pi$) phonon gap. We therefore conclude that the dimerized ground state is more unstable with respect to Debye phonons, with the introduction of phonon dispersion renormalizing the effective spin-lattice coupling for the Peierls-active mode. We also show that the staggered spin-spin and phonon displacement order parameters are unreliable means of determining the transition.Comment: To be published in Phys. Rev.

Can Quantum Lattice Fluctuations Destroy the Peierls Broken Symmetry Ground State?

The study of bond alternation in one-dimensional electronic systems has had a long history. Theoretical work in the 1930s predicted the absence of bond alternation in the limit of infinitely long conjugated polymers; a result later contradicted by experimental investigations. When this issue was re-examined in the 1950s it was shown in the adiabatic limit that bond alternation occurs for any value of electron-phonon coupling. The question of whether this conclusion remains valid for quantized nuclear degrees of freedom was first addressed in the 1980s. Since then a series of numerical calculations on models with gapped, dispersionless phonons have suggested that bond alternation is destroyed by quantum fluctuations below a critical value of electron-phonon coupling. In this work we study a more realistic model with gapless, dispersive phonons. By solving this model with the DMRG method we show that bond alternation remains robust for any value of electron-phonon coupling

Relaxation energies and excited state structures of poly(para-phenylene)

We investigate the relaxation energies and excited state geometries of the light emitting polymer, poly(para-phenylene). We solve the Pariser-Parr-Pople-Peierls model using the density matrix renormalization group method. We find that the lattice relaxation of the dipole-active $1^1B_{1u}^-$ state is quite different from that of the $1^3B_{1u}^+$ state and the dipole-inactive $2^1A_g^+$ state. In particular, the $1^1B_{1u}^-$ state is rather weakly coupled to the lattice and has a rather small relaxation energy ca. 0.1 eV. In contrast, the $1^3B_{1u}^+$ and $2^1A_g^+$ states are strongly coupled with relaxation energies of ca. 0.5 and ca. 1.0 eV, respectively. By analogy to linear polyenes, we argue that this difference can be understood by the different kind of solitons present in the $1^1B_{1u}^-$, $1^3B_{1u}^+$ and $2^1A_g^+$ states. The difference in relaxation energies of the $1^1B_{1u}^-$ and $1^3B_{1u}^+$ states accounts for approximately one-third of the exchange gap in light-emitting polymers.Comment: Submitted to Physical Review

Molecular Orbital Models of Benzene, Biphenyl and the Oligophenylenes

A two state (2-MO) model for the low-lying long axis-polarised excitations of poly(p-phenylene) oligomers and polymers is developed. First we derive such a model from the underlying Pariser-Parr-Pople (P-P-P) model of pi-conjugated systems. The two states retained per unit cell are the Wannier functions associated with the valence and conduction bands. By a comparison of the predictions of this model to a four state model (which includes the non-bonding states) and a full P-P-P model calculation on benzene and biphenyl, it is shown quantitatively how the 2-MO model fails to predict the correct excitation energies. The 2-MO model is then solved for oligophenylenes of up to 15 repeat units using the density matrix renormalisation group (DMRG) method. It is shown that the predicted lowest lying, dipole allowed excitation is ca. 1 eV higher than the experimental result. The failure of the 2-MO model is a consequence of the fact that the original HOMO and LUMO single particle basis does not provide an adequate representation for the many body processes of the electronic system.Comment: LaTeX, 12 pages, 3 eps figures included using epsf. To appear in Chemical Physics, 199

Peierls transition in the quantum spin-Peierls model

We use the density matrix renormalization group method to investigate the role of longitudinal quantized phonons on the Peierls transition in the spin-Peierls model. For both the XY and Heisenberg spin-Peierls model we show that the staggered phonon order parameter scales as $\sqrt{\lambda}$ (and the dimerized bond order scales as $\lambda$) as $\lambda \to 0$ (where $\lambda$ is the electron-phonon interaction). This result is true for both linear and cyclic chains. Thus, we conclude that the Peierls transition occurs at $\lambda=0$ in these models. Moreover, for the XY spin-Peierls model we show that the quantum predictions for the bond order follow the classical prediction as a function of inverse chain size for small $\lambda$. We therefore conclude that the zero $\lambda$ phase transition is of the mean-field type

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

A density matrix renormalisation group scheme is developed, allowing for the first time essentially exact numerical solutions for the important excited states of a realistic semi-empirical model for oligo-phenylenes. 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.Comment: RevTeX, 10 pages, 4 eps figures included using eps

Dynamical model of the dielectric screening of conjugated polymers

A dynamical model of the dielectric screening of conjugated polymers is introduced and solved using the density matrix renormalization group method. The model consists of a line of quantized dipoles interacting with a polymer chain. The polymer is modelled by the Pariser-Parr-Pople (P-P-P) model. It is found that: (1) Compared to isolated, unscreened single chains, the screened 1Bu- exciton binding energy is typically reduced by ca. 1 eV to just over 1 eV; (2) Covalent (magnon and bi-magnon) states are very weakly screened compared to ionic (exciton) states; (3) Screening of the 1Bu- exciton is closer to the dispersion than solvation limit.Comment: 12 pages, 2 figure

Electron-lattice relaxation, and soliton structures and their interactions in polyenes

Density matrix renormalisation group calculations of a suitably parametrised model of long polyenes (polyacetylene oligomers), which incorporates both long range Coulomb interactions and adiabatic lattice relaxation, are presented. The triplet and 2Ag states are found to have a 2-soliton and 4-soliton form, respectively, both with large relaxation energies. The 1Bu state forms an exciton-polaron and has a very small relaxation energy. The relaxed energy of the 2Ag state lies below that of the 1Bu state. The soliton/anti-soliton pairs are bound.Comment: RevTeX, 5 pages, 4 eps figures included using epsf. To appear in Physical Review Letters. Fig. 1 fixed u

Excited states of linear polyenes

We present density matrix renormalisation 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 (3Bu+) and even- parity singlet (2Ag+) states have a 2-soliton and 4-soliton form, respectively, both with large relaxation energies. The dipole-allowed (1Bu-) state forms an exciton-polaron and has a very small relaxation energy. The relaxed energy of the 2Ag+ state lies below that of the 1Bu- state. We observe an attraction between the soliton-antisoliton pairs in the 2Ag+ 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 discrepencies. 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. The electronic interactions play the key role in determining the ground state dimerisation and the excited state transition energies.Comment: LaTeX, 15 pages, 9 figure