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Register a new userDMRG Calculations of the Low-lying Excitations and Nonlinear Optical Properties of poly(para-phenylene)
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Added by
Dr Robert J. Bursill
Publication date
1998
fields
Physics
and research's language is
English
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The two state molecular orbital (2-MO) model of the phenyl based semiconductors is used to calculate the low-lying spectra of the Ag and Bu states of poly(para-phenylene) (PPP). The model parameters are determined by fitting its predictions to exact Pariser-Parr-Pople model calculations of benzene and biphenyl, and it is solved using the density matrix renormalisation group method. It is shown that there exists a band of Bu (s-wave) excitons below the band states. In the long chain limit the lowest exciton is situated 3.3 eV above the ground state, consistent with experimental data. The calculated particle-hole separation of these excitons indicates that they are tightly bound, extending over only a few repeat units. The lowest band state is found to be a covalent 2Ag state, whose energy almost coincides with the charge gap Eg. Lying just above the 2Ag state is a band Bu state (the nBu state). The particle-hole separation of the band states scales linearly with oligomer size. The binding energy of the 1Bu exciton is determined rigorously as 0.74 eV. The dipole matrix elements and oscillator strengths for the transitions between the lowest Ag and Bu states are calculated and the NLO properties of PPP, such as electroabsorption (EA) and third harmonic generation, are investigated. A comparison of the EA spectrum with the experimental data shows that the main features of the experimental spectrum are well described by the 2-MO Hamiltonian. Only five states account for most of the calculated EA. These are the 1Ag, 1Bu, 2Ag, nBu and another band Ag state, the kAg, thus confirming the essential states model. An analysis of the particle excitation weight of these states indicates that they are predominately single particle in character.
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The two-state molecular orbital model of the one-dimensional phenyl-based semiconductors is applied to poly(p-phenylene vinylene). The energies of the low-lying excited states are calculated using the density matrix renormalization group method. Calculations of both the exciton size and the charge gap show that there are both Bu and Ag excitonic levels below the band threshold. The energy of the 1Bu exciton extrapolates to 2.60 eV in the limit of infinite polymers, while the energy of the 2Ag exciton extrapolates to 2.94 eV. The calculated binding energy of the 1Bu exciton is 0.9 eV for a 13 phenylene unit chain and 0.6 eV for an infinite polymer. This is expected to decrease due to solvation effects. The lowest triplet state is calculated to be at ca. 1.6 eV, with the triplet-triplet gap being ca. 1.6 eV. A comparison between theory, and two-photon absorption and electroabsorption is made, leading to a consistent picture of the essential states responsible for most of the third-order nonlinear optical properties. An interpretation of the experimental nonlinear optical spectroscopies suggests an energy difference of ca. 0.4 eV between the vertical energy and ca. 0.8 eV between the relaxed energy, of the 1Bu exciton and the band gap, respectively.
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 1Bu data of Giesa and Schultz are used as the geometric model for the calculation. For short chains, the calculated E(1Bu) agrees with the experimental value, within solvation effects (ca. 0.3 eV). The charge gap is used to characterise bound and unbound states. The nBu is above the charge gap and hence a continuum state; the 1Bu, 2Ag and mAg are not and hence are bound excitons. For large chain lengths, the nBu tends towards the charge gap as expected, strongly suggesting that the nBu is the conduction band edge. The conduction band edge for PDA is agreed in the literature to be ca. 3.0 eV. Accounting for the strong polarisation effects of the medium and polaron formation gives our calculated E(nBu) ca. 3.6 eV, with an exciton binding energy of ca. 1.0 eV. The 2Ag state is found to be above the 1Bu, which does not agree with relaxed transition experimental data. However, this could be resolved by including explicit lattice relaxation in the Pariser- Parr-Pople-Peierls model. Particle-hole separation data further suggest that the 1Bu, 2Ag and mAg are bound excitons, and that the nBu is an unbound exciton.
A continuum approach to the three valence-quark bound-state problem in quantum field theory is used to perform a comparative study of the four lightest $(I=1/2,J^P = 1/2^pm)$ baryon isospin-doublets in order to elucidate their structural similarities and differences. Such analyses predict the presence of nonpointlike, electromagnetically-active quark-quark (diquark) correlations within all baryons; and in these doublets, isoscalar-scalar, isovector-pseudovector, isoscalar-pseudoscalar, and vector diquarks can all play a role. In the two lightest $(1/2,1/2^+)$ doublets, however, scalar and pseudovector diquarks are overwhelmingly dominant. The associated rest-frame wave functions are largely $S$-wave in nature; and the first excited state in this $1/2^+$ channel has the appearance of a radial excitation of the ground state. The two lightest $(1/2,1/2^-)$ doublets fit a different picture: accurate estimates of their masses are obtained by retaining only pseudovector diquarks; in their rest frames, the amplitudes describing their dressed-quark cores contain roughly equal fractions of even- and odd-parity diquarks; and the associated wave functions are predominantly $P$-wave in nature, but possess measurable $S$-wave components. Moreover, the first excited state in each negative-parity channel has little of the appearance of a radial excitation. In quantum field theory, all differences between positive- and negative-parity channels must owe to chiral symmetry breaking, which is overwhelmingly dynamical in the light-quark sector. Consequently, experiments that can validate the contrasts drawn herein between the structure of the four lightest $(1/2,1/2^pm)$ doublets will prove valuable in testing links between emergent mass generation and observable phenomena and, plausibly, thereby revealing dynamical features of confinement.
Ground state properties and excited states of ladder-type paraphenylene oligomers are calculated applying semiempirical methods for up to eleven phenylene rings. The results are in qualitative agreement with experimental data. A new scheme to interpret the excited states is developed which reveals the excitonic nature of the excited states. The electron-hole pair of the S1-state has a mean distance of approximately 4 Angstroem.
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.
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