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.
The dimerization of polyacetylene is studied using a distance-dependent Hubbard Hamiltonian for the valence $\ensuremath{\pi}$ electrons and approximating $\ensuremath{\sigma}$-electron contributions by a sum of pair interactions ${E}_{\ensuremath{\sigma}}{(r}_{\mathrm{ij}})$. The $\ensuremath{\pi}$-electron Coulomb repulsion
U is taken to be independent of the C-C distances
rij and is varied systematically from the uncorrelated or H\"uckel limit all over to the strongly correlated or Heisenberg regime. For each value of
U, ${E}_{\ensuremath{\sigma}}{(r}_{\mathrm{ij}})$, and the $\ensuremath{\pi}$-electron hopping integral
t(rij) are fitted to reproduce ab initio results on the ground-state and first-excited-state energy of the ethylene molecule. The one-dimensional many-body problem is solved numerically by means of the density-matrix renormalization-group (DMRG) method. The ground-state energy
E of the infinite open polymer is obtained by extrapolation considering chains of up to 300 atoms. The dimerization $\ensuremath{\delta}{=(r}_{i,i+1}\ensuremath{-}{r}_{i\ensuremath{-}1,i})/2$ and the average bond length ${R=(r}_{i,i+1}{+r}_{i\ensuremath{-}1,i})/2$ are determined by minimizing
E. While
R is not significantly affected by the value of
U, $\ensuremath{\delta}$ shows a remarkable nonmonotonic behavior. The differences between the delocalized regime, small
U/t, and spin-Peierls behavior, large
U/t, are discussed. The convergence properties of the DMRG algorithm are analyzed as a function of
U, $\ensuremath{\delta}$, and the number states kept at each RG step. Criteria are examined in order to control the accuracy of the DMRG calculations in both weakly and strongly correlated situations.
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.
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 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.