Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Density-matrix renormalization-group study of low-lying excitations of polyacene within a Pariser-Parr-Pople model

C. Raghu, Y. Anusooya Pati, S. Ramasesha

Published Jul 29, 2002• 63 citations
Publisher

Abstract

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 ${C}_{2}$ 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.

DOI
10.1103/physrevb.66.035116

Related papers

Structural and electronic instabilities in polyacenes: Density-matrix renormalization group study of a long-range interacting model

C. Raghu, Y. Anusooya Pati, S. Ramasesha

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.

arXiv:cond-mat/0110136•Physical review. B, Condensed matter•Mar 27, 2002•67 citations

Density-matrix renormalization-group calculations of excited states of linear polyenes

William Barford, Robert J. Bursill, M. Yu. Lavrentiev

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 $(1{}^{3}{B}_{u}^{+})$ and even-parity singlet $(2{}^{1}{A}_{g}^{+})$ 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 $2{}^{1}{A}_{g}^{+}$ state lies below that of the $1{}^{1}{B}_{u}^{\ensuremath{-}}$ state. We observe an attraction between the soliton-antisoliton pairs in the $2{}^{1}{A}_{g}^{+}$ 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.

arXiv:cond-mat/0103100•Physical review. B, Condensed matter•Apr 25, 2001•49 citations

Symmetrized density matrix renormalization group studies of the properties of low-lying states of the poly-para-phenylene system

Y. Anusooya, Swapan Kumar Pati, S. Ramasesha

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.

The Journal of Chemical Physics•Jun 22, 1997•35 citations

Symmetrized DMRG studies of the properties of Low-lying states of Poly-para-phenylene (PPP) system

Y. Anusooya, Swapan Kumar Pati, S. Ramasesha

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.

arXiv:cond-mat/9612012•Nov 30, 1996•1 citation

Open-Shell Ground State of Polyacenes: A Valence Bond Study

Zexing Qu, Dawei Zhang, Chungen Liu +1 more

Applying the density matrix renormalization group (DRMG) method to a nonempirical valence bond (VB) model Hamiltonian, we studied polyacene oligomers of different lengths in the strong electron correlation limit. Geometrical optimizations were performed for the lowest singlet and triplet states of oligomers up to [40]-acene, and a convergence of the bond lengths toward the polymer limit is observed in the interior of the oligomer. For large oligomers, as well as for the polymer, the ground state can be reasonably determined to be a singlet. Furthermore, a high similarity between the singlet geometries and triplet geometries suggests an open-shell character for the singlet ground state. A reasonable speculation of the soliton-antisoliton pair character of the singlet ground state was supported by a spin distribution analysis of the triplet state wave function of large oligomers, with each of the two solitons being broadly delocalized over the upper or bottom edge of the oligomers, respectively.

The Journal of Physical Chemistry A•Jun 15, 2009•101 citations

Low-lying states of transverse substitutedtrans-polyacetylene andtrans-polyacetylene: A comparative DMRG study

Manoranjan Kumar, S. Ramasesha

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.

Physical Review B•Jan 25, 2010•5 citations
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 11B\ensuremath−{1}^{1}{B}^{\ensuremath{-}}11B\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 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.
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 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.
Applying the density matrix renormalization group (DRMG) method to a nonempirical valence bond (VB) model Hamiltonian, we studied polyacene oligomers of different lengths in the strong electron correlation limit. Geometrical optimizations were performed for the lowest singlet and triplet states of oligomers up to [40]-acene, and a convergence of the bond lengths toward the polymer limit is observed in the interior of the oligomer. For large oligomers, as well as for the polymer, the ground state can be reasonably determined to be a singlet. Furthermore, a high similarity between the singlet geometries and triplet geometries suggests an open-shell character for the singlet ground state. A reasonable speculation of the soliton-antisoliton pair character of the singlet ground state was supported by a spin distribution analysis of the triplet state wave function of large oligomers, with each of the two solitons being broadly delocalized over the upper or bottom edge of the oligomers, respectively.
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.