We solve a model of interacting electrons coupled to longitudinal phonons using the density matrix renormalization group method. The model is parametrized for trans-polyacetylene. We calculate the ground state and first excited odd-parity singlet and triplet states. We investigate their energies and geometries for up to 102 sites. The transition energy and the soliton width of the triplet state show significant deviations from the adiabatic approximation for chain lengths larger than the classical soliton size. In contrast, the transition energy of the singlet is close to the adiabatic prediction.
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+) and even-parity singlet
(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+ state lies below that of the $1{}^{1}{B}_{u}^{\ensuremath{-}}$ state. We observe an attraction between the soliton-antisoliton pairs in the
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.
Density matrix renormalization group calculations of a suitably parametrized model of long polyenes (polyacetylene oligomers), which incorporate both long range Coulomb interactions and adiabatic lattice relaxation, are presented. The
13Bu+ and
21Ag+ states are found to have a 2-soliton and a 4-soliton form, respectively, both with large relaxation energies. The ${1}^{1}{B}_{u}^{\ensuremath{-}}$ state forms an exciton polaron and has a very small relaxation energy. The relaxed energy of the
21Ag+ state lies below that of the ${1}^{1}{B}_{u}^{\ensuremath{-}}$ state. The soliton/antisoliton pairs are bound.
We study theoretically polydiacetylene chains diluted in their monomer matrix. We employ the density-matrix renormalisation group method (DMRG) on finite chains to calculate the ground state and low-lying excitations of the corresponding Peierls–Hubbard-Ohno Hamiltonian that is characterised by the electron transfer amplitude t 0 between nearest-neighbours, by electron–phonon coupling constant α, by Hubbard interaction U, and by long-range interaction V. We treat lattice relaxation in the adiabatic limit, i.e., we calculate the polaronic lattice distortions for each excited state. We present accurate DMRG results for the single-particle gap, the singlet exciton, the triplet ground state and its optical excitation, and find a good agreement with experimental data for PDA–3BCMU chains. Using a fairly stiff spring constant, the length of our unit cell is about 1% larger than observed in experiment.
We use the density matrix renormalization group method to investigate the role of gapless, dispersive quantized phonons on the Peierls transition in the extended Hubbard-Peierls model. We calculate the staggered phonon order parameter as a function of the Coulomb interaction and the phonon frequency. For all parameter ranges we show that the staggered phonon order parameter scales as $\sqrt{\ensuremath{\lambda}}$ (and the dimerized bond order scales as $\ensuremath{\lambda}$) as $\ensuremath{\lambda}\ensuremath{\rightarrow}0$ (where $\ensuremath{\lambda}$ is the electron-phonon interaction). We also show that the quantum phonon predictions for the bond order follow the classical (adiabatic) predictions as a function of inverse chain size for small $\ensuremath{\lambda}$. We thus conclude that quantum fluctuations in the nuclear degrees of freedom do not destroy the Peierls state for this model.
We study theoretically polydiacetylene chains diluted in their monomer matrix. We employ the density matrix renormalization group method on finite chains to calculate the ground state and low-lying excitations of the corresponding Peierls--Hubbard-Ohno Hamiltonian which is characterized by the electron transfer amplitude
t0 between nearest neighbors, by the electron-phonon coupling constant $\ensuremath{\alpha}$, by the Hubbard interaction
U, and by the long-range interaction
V. We treat the lattice relaxation in the adiabatic limit, i.e., we calculate the polaronic lattice distortions for each excited state. Using chains with up to 102 lattice sites, we can safely perform the extrapolation to the thermodynamic limit for the ground-state energy and conformation, the single-particle gap, and the energies of the singlet exciton, the triplet ground state, and the optical excitation of the triplet ground state. The corresponding gaps are known with high precision from experiments. We determine a coherent parameter set $({t}_{0}^{*}=2.4\phantom{\rule{0.16em}{0ex}}\mathrm{eV},{\ensuremath{\alpha}}^{*}=3.4\phantom{\rule{0.16em}{0ex}}\mathrm{eV}/\text{\AA{}},{U}^{*}=6\phantom{\rule{0.16em}{0ex}}\mathrm{eV},{V}^{*}=3\phantom{\rule{0.16em}{0ex}}\mathrm{eV})$ from a fit of the experimental gap energies to the theoretical values which we obtain for 81 parameter points in the four-dimensional search space $({t}_{0},\ensuremath{\alpha},U,V)$. We identify dark in-gap states in the singlet and triplet sectors as seen in experiments. Using a fairly stiff spring constant, the length of our unit cell is about 1
larger than its experimental value.