Density matrix renormalization group calculations of the low-lying excitations and non-linear optical properties of poly(<i>para</i>-phenylene)

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

doi:10.1088/0953-8984/10/28/021

Cited by 26 publications

(30 citation statements)

References 33 publications

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“…Similar studies by Barford on polyenes have found that the relaxation energies of the 1B u and 2A g can be reduced by as much as 0.3 and 1.0 eV, respectively [48]- [49]. Thus, including lattice relaxation in the Pariser-Parr-Pople-Peierls model is expected to bring the 2A g state below the 1B u in agreement with experiment.…”

Section: B Vertical Excitation Energiessupporting

confidence: 83%

Low-lying excitations of polydiacetylene

2001

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The Pariser-Parr-Pople Hamiltonian is used to calculate and identify the nature of the low-lying vertical transition energies of polydiacetylene. The model is solved using the density matrix renormalisation group method for a fixed acetylenic geometry for chains of up to 102 atoms. The non-linear optical properties of polydiacetylene are considered, which are determined by the third-order susceptibility. The experimental 1B u data of Giesa and Schultz are used as the geometric model for the calculation.For short chains, the calculated E(1B u ) agrees with the experimental value, within solvation effects (∼ 0.3 eV). The charge gap is used to characterise bound and unbound states. The nB u is above the charge gap and hence a continuum state; the 1B u , 2A g and mA g are not and hence are bound excitons. For large chain lengths, the nB u tends towards the charge gap as expected, strongly suggesting that the nB u is the conduction band edge. The conduction band edge for PDA is agreed in the literature to be ∼ 3.0 eV. Accounting for the strong polarisation effects of the medium and polaron formation gives our calculated E ∞ (nB u ) ∼ 3.6 eV, with an exciton binding energy of ∼ 1.0 eV. The 2A g state is found to be above the 1B u , which does not 1 agree with relaxed transition experimental data. However, this could be resolved by including explicit lattice relaxation in the Pariser-Parr-Pople-Peierls model. Particlehole separation data further suggest that the 1B u , 2A g and mA g are bound excitons, and that the nB u is an unbound exciton. I INTRODUCTIONPolymers, and other molecular materials, that exhibit non-linear optical properties and electroluminescence have attracted much interest amongst theorists and experimentalists, owing to their possible use in organic technology [1]- [7]. Poly(diacetylene)s (PDAs) with the general formula shown in Fig. 1. (a) are the π-conjugated organic polymers studied here: they exhibit non-linear optical properties, near-perfect crystal structure and doping-dependent transport properties. These properties make them ideally suited for use in the theorist's calculation. A full characterisation of PDA's electronic properties would mean a better understanding of π-conjugated polymers in general. In PDA with a very low polymer content (x p < 10 −3 in weight), interchain interaction is minimal and thus it can be considered an ideal one-dimensional model system. with 0 < δ < 1. This produces results that are, again, quantitatively too low; however, it does generate an energy difference of 0.48 eV between the butatriene and acetylene structures, in excellent agreement with other calculations and experiment [15]-[16]. In summary, therefore, all these models are seen to give good qualitative predictions for bond alteration, but the 3 data are seen to be consistently red-shifted owing to their single particle picture. First, in polymeric crystal form, the linear absorption spectrum is see to be symmetric and peaks at ∼ 1.8-1.9 eV. However, the onset of photoconduction occurs not at th...

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Section: B Vertical Excitation Energiessupporting

confidence: 83%

Low-lying excitations of polydiacetylene

2001

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“…In the present work values for these parameters have been taken from the literature. [34][35][36][37][38] Since existing parameters have been optimized to optical excitation spectra, an exact agreement with experimental values for the molecular gaps is not to be expected.…”

Section: Pariser-parr-pople Hamiltonianmentioning

confidence: 99%

Benchmarking GW against exact diagonalization for semiempirical models

Kaasbjerg

Thygesen

2010

Phys. Rev. B

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We calculate ground-state total energies and single-particle excitation energies of seven pi-conjugated molecules described with the semiempirical Pariser-Parr-Pople model using self-consistent many-body perturbation theory at the GW level and exact diagonalization. For the total energies GW captures around 65% of the ground-state correlation energy. The lowest lying excitations are overscreened by GW leading to an underestimation of electron affinities and ionization potentials by 0.15 eV on average corresponding to ϳ3%. One-shot G 0 W 0 calculations starting from Hartree-Fock reduce the screening and improve the low-lying excitation energies. The effect of the GW self-energy on the molecular excitation energies is shown to be similar to the inclusion of final-state relaxations in Hartree-Fock theory. We discuss the breakdown of the GW approximation in systems with short-range interactions ͑Hubbard models͒ where correlation effects dominate over screening/ relaxation effects. Finally we illustrate the important role of the derivative discontinuity of the true exchangecorrelation functional by computing the exact Kohn-Sham levels of benzene.

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“…The popular Ohno formula has often been used (more than 270 citations in the last fifteen years, including [14,15]) to parameterize the Coulomb matrix element V jk . However, Eq.…”

Section: Discussionmentioning

confidence: 99%

“…We are hopeful that direct evolution of the photoexcited wavefunction or advances like the DMRG algorithm [27] which allow one to include electron-electron interactions in tight-binding models will permit explicit calculations for realistic [14] and interesting molecules such as those considered here.…”

Section: Discussionmentioning

confidence: 99%

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A vision for ultrafast photoisomerization

Aalberts

Stabenau

2010

Physica A: Statistical Mechanics and its Applications

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We propose a simple physical mechanism to explain the ultrafast first step of vision, a photoinduced cis to trans rotation of retinal. In the ground state, the torsional stability of π bonds is countered by Coulomb interactions acting between the π lobes; the torsional dependence for Coulomb interactions is absent in the often-used Ohno approximation, but restored with our formula. After photoexcitation, the bonding weakens causing the destabilizing terms to dominate. The twist in the ground state due to steric interactions surrounding the 11-cis bond increases the initial torque and thus the speed of the reaction.

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Density matrix renormalization group calculations of the low-lying excitations and non-linear optical properties of poly(para-phenylene)

Cited by 26 publications

References 33 publications

Low-lying excitations of polydiacetylene

Low-lying excitations of polydiacetylene

Benchmarking GW against exact diagonalization for semiempirical models

A vision for ultrafast photoisomerization

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