Bond-alternation Defects Research Articles

Spin current in the Möbius cyclacene belts

We report on density functional theory studies of the electronic structure and magnetic properties of Möbius-[ n]cyclacenes. The geometry of Möbius bands presents a modulation of bond lengths that is needed to accommodate the twist. This modulation takes the form of bond alternation defects analogous to those of solitons in polyacetylene. The ground state of all Möbius bands is a triplet, with a spin density distribution that follows the bond length modulation. A molecular dynamics simulation of the Möbius cyclacene at 300 K shows that the twist travels around the belt inducing a magnetic current.

Electronic properties of acenes: Oligomer to polymer structure

The conformations and electronic structures of long oligoacenes [${\mathrm{C}}_{2}{\mathrm{H}}_{2}{({\mathrm{C}}_{4}{\mathrm{H}}_{2})}_{n}$, $20\ensuremath{\leqslant}n\ensuremath{\leqslant}23$] and polyacene $[{({\mathrm{C}}_{8}{\mathrm{H}}_{4})}_{x}]$ were theoretically investigated through density functional theory adopting the hybrid B3LYP/6-31G(d) functional. The long oligoacenes present a cis conformation and solitonlike distortions along the chain. The defective regions having uniform bond lengths produce localized states on the top of the oligomer valence band. The spontaneous creation of bond alternation defects leads to high-spin magnetic ground states. The nonmagnetic state of polyacene presents a Peierls-distorted trans conformation which is lower in energy by a few meV per unit cell from the symmetric (nonalternating) state. The lowest-energy structure is predicted to present a cis pattern of bonds with alternation defects and a triplet state per unit cell.

Molecular orbital study of pyrolytic carbons based on small cluster models

Molecular orbital calculations are applied to the Raman scattering and ESR of pyrolytic carbons on the basis of small cluster models. The E 2 g and A 1 g modes of C-C stretching vibrations of coronene, hexabenzocoronene, and circumcoronene, which belong to D 6 h carbon clusters, are shown to appear around the 1550 cm −1 and 1360 cm −1 bands, respectively. The unpaired electrons observed in pyrolytic carbons are attributed to the bond-alternation defects on odd-numbered carbon clusters that are more easily mobile than those of trans-polyacetylene.

Torsional Defects and Photoinduced Charge Transfer in Ring-Containing Polymers

Abstract The importance of ring torsion angle for photoinduced charge generation and transfer in phenyl-ring-containing polymers such as polyaniline and polyparaphenylene sulfide is discussed. The magnitude of the ground state ring torsion angle in these materials is determined by the competition between electron delocalization, favoring planar rings, and the steric repulsion between rings, favoring rings twisted far out of the plane. Upon photoinduced charge transfer, the hole formed upon removal of an electron from the valence band becomes self-localized into a polaronic state in part through changes in ring torsion angle; the effective mass of this defect is estimated to be at least an order of magnitude greater than that of bond-alternation defects. The existence of these ring-torsional defects is borne out by the experimental observation of large effective masses, long relaxation times, and weak photoconductivity for photoexcited defects, as well as by x-ray structural evidence of the dependence of t...

Ring-rotational defects in polyaniline

The effects of electron-lattice coupling via ring rotation on the electronic structure of leucoemeraldine base (LB) and its charged defects are investigated. We suggest that in LB and other phenyl-ring-containing polymers the charged defect states, particularly hole polarons, are associated with localized distortions of the ground state ring torsion angles toward a planar conformation, in contrast with the bond-alternation defects present in conducting polymers. The relevance of these defects to recent photoinduced optical experiments is discussed.

Investigation of soliton-like excitations in t r a n s-polyacetylene

In the study reported here, unrestricted Hartree–Fock calculations were performed on the ground state and several soliton-like defect states of the model large polyene, trans-polyacetylene. The calculations included the use of the random phase approximation to obtain screened electron repulsion integrals and projection of the UHF eigenfunctions to obtain pure spin states. The trans-polyacetylene ground state geometry is characterized here by alternating double and single bonds with lengths of 1.456 and 1.369 Å, respectively. Calculations on model soliton-like defect states yielded functional forms for the bond alternation, spin density, and charge density defects which are consistent with the soliton model for trans-polyacetylene and are similar to those reported elsewhere. The average positive and average negative spin density on chains containing neutral kink defects are 0.045 and −0.011, respectively. These values are in fair agreement with the best experimental estimates of 0.06 and −0.02.

Model calculation of PDA–PA heterostructures: Influence of topological defects on localized states

Model calculations for mixed polydiacetylene (PDA)–polyacetylene (PA) chains are generalized to the inclusion of mobile-soliton-like bond alternation defects. The properties of the midegap state of the solitary defect as well as the influence of the radical electron properties on localized states (‘‘quantum well states’’) of the chain are investigated on the basis of a Hückel band structure calculation. It turns out that the quantum well character of the chain strongly depends on the position of the bond alternation defect, e.g., whether it is located on the PA or PDA part of the chain.

Vibronic states of bond alternation defect in polyacetylene and ESR spectrum

An origin of the temperature dependence of the ESR line shape in trans -(CH) X is investigated on the vibronic structure model of a bond alternation defect in a linear conjugated carbon chain. For this purpose first the vibronic energy levels of a bond alternation defect is calculated from the variational principle for a chain with the odd number of carbon atoms. Secondly the rate of transitions between vibronic levels due to anharmonic terms of the adiabatic potential is calculated. It is shown that these transitions cause the motional narrowing in the ESR spectrum. Finally on the above vibronic structure model the temperature dependence of the ESR line width is calculated from a general formula for the ESR line shape, and a rival effect of transitions between vibronic levels and hyperfine interactions with magnetically inequivalent protons in a vibronic level is clarified. The present theoretical results are in good agreement with experiments.

Continuum model for vibrational excitations of conjugated polymers

The continuum model of the coupled electron-phonon system in conjugated polymers is extended to include the lattice kinetic energy and the coupling of several structural degrees of freedom. The model is used to study defect vibrational spectra for a variety of defects that may occur, e.g., solitons, polarons, and bipolarons, in conjugated polymer systems. In agreement with previous theoretical studies of polyacetylene, a class of infrared-active modes common to all mobile bond-alternation defects is obtained. In addition the study reveals a new class of bound vibrations localized at the defect center of a polaron or a bipolaron. These additional infrared-active modes can be used spectroscopically to identify defect types in conjugated polymers such as polyacetylene or polythiophene. Examples considered include doping and photoinduced defects (solitons and polarons) in both (CH${)}_{\mathrm{x}}$ and (CD${)}_{\mathrm{x}}$ as well as photoinduced defects (bipolarons) in polythiophene.

UHF RPA calculations on large model polyene systems

Unrestricted Hartree-Fock calculations have been performed on even and odd polyenes and both neutral and charged species. The calculations include projection of the pure spin states and the use of the random-phase approximation to obtain screened electron-repulsion integrals. Calculations on even, neutral molecules containing up to seventy-four carbon atoms provide a single-bond length of 1.456 Å and a double-bond length of 1.369 Å for a Δ R∞ value of 0.087 Å, which compares well with experimental data. The functional forms of the bond-alternation, spin-density, and charge-density defects are similar to those reported from earlier treatments. For the odd polyene, the width of the soliton spin-density wave is comparable with the SSH results and the ratio of the total negative spin density to the total positive spin density is 0.25. However, the width of the bond-alternation defect is found to be larger than that found by other investigators.

Lattice dynamics in the continuum model for polyacetylene

The continuum model for the coupled electron-phonon system in (CH) x is generalized by including the coupling of several relevant structural degrees of freedom to the π electron density in the model, and by including a classical lattice kinetic energy so that the lattice dynamics of the model can be studied. The model is used to study the lattice dynamics of the ideal neutral dimerized (CH) x chain and of charged with added carriers trapped at polarons and solitons. The model provides a microscopic theory explaining the appearance of a class of bound modes that are common to any mobile bond alternation defect. The full spectra of localized modes for solitons and polarons are calculated and compared. Various features in the spectra are sensitive to the topological identity and microscopic structure of the defects, and several new experimentally observable features in the spectra are analysed.

A theoretical study of photoluminescence quenching in cis-polyacetylene

The non-radiative decay of photoinduced bond-alternation defects in cis-polyacetylene is considered within the SSH model [18]. The charge-conjugation symmetry of the simplest model Hamiltonian must be violated to explain the low photoluminescent yield (˜ 10-3 %) found experimentally. The simplest such route, that of electron-phonon coupling via second nearest-neighbour hopping is considered. It is found that a multiphonon process is required, the resulting decay rate being very sensitive to the parameters chosen. If this is the dominant non-radiative process, then it gives a potentially highly accurate method of determining the value of α, the nearest-neighbour electron-phonon coupling constant. The results for cis-polyacetylene can be generalized to give a qualitative understanding of photoluminescent properties of more complex conjugated molecules.

Vibronic States of Polyacetylene, (CH)x

Electronic states of π-electrons coupled with lattice vibrations in a linear conjugated carbon chain, are calculated with a particular purpose of clarifiing the vibronic structure of bond alternation defect. First the vibronic Hamiltonian is derived from a general Hamiltonian. It is shown in the adiabatic approximation that the ground state of an odd number of carbon atoms corresponds to the bond alternation defect with an unpaired electron. Then taking account of the kinetic energy of lattice vibrations, the vibronic states of the defect is obtained. It is shown that the unpaired electron moves relatively freely. Finally a method to calculate self-consistently the electronic states and the lattice deformation in the presence of Coulomb interaction is presented. It is shown within the Hartree-Fock approximation that the ground state changes from CDW state to SDWstate with increase of on-site Coulomb interaction.

Magnetic-resonance studies in undopedtrans-polyacetylene(CH)x. II

Magnetic-resonance data in undoped trans-${(\mathrm{CH})}_{x}$, including nuclear relaxation time (${T}_{1}$) measurements versus frequency and ESR linewidth in the temperature range 300---4.2 K, are reported and analyzed. The results are comprehensively explained in terms of highly-one-dimensional diffusive spins which can be trapped in the presence of impurities, or defects, in particular those connected to oxygen contamination. The average number of diffusive spins, as given by the diffusive-spin population at thermal equilibrium, is a function of temperature through two parameters: the trap-site concentration and the trapping energy. Trap-site concentrations of 5% and 25% have been obtained for samples sealed under vacuum and air-contaminated samples, respectively. The trapping energy is found to be distributed, from chain to chain, from a maximum value ${E}_{0}\ensuremath{\simeq}0.06$ eV, which likely corresponds to the chain nearest to ${\mathrm{O}}_{2}$ impurities located at the fibril surface, to about zero for chains far inside the fibril. As the temperature decreases two effects take place, as reflected by the spin-dynamics studies. First, due to the trapping effect, there are fewer and fewer spins in the diffusive state. Second, the diffusion coefficient decreases. Starting from the room-temperature value $\mathcal{D}\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ ${\mathrm{cm}}^{2}$/s, the decrease is slow at first then for $T<100$ K seems to obey a power law $\ensuremath{\propto}{T}^{2}$, similarly to a theoretical result derived by Wada and Schrieffer in the case of Brownian motion of domain walls upon two phonon processes. The spin delocalization has been evaluated for the trapped state from ESR, and for the diffusive state from ${T}_{1}$. In both cases the spin density has been found to be delocalized over 10 to 17 CH units. All characteristics and properties determined from the spins in trans-${(\mathrm{CH})}_{x}$ are consistent with the soliton---bond-alternation defect---picture, provided that the trapping effect is taken into account.

Trapping of phase kinks in polyacetylene

Molecular orbital calculations with full geometry optimization using a semi-empirical tight-binding Hamiltonian for finite molecular models of phase kinks (solitons) in polyacetylene, (CH) X′ were done. This bond alternation defect extends over many atoms from which only ∼30 atoms are energetically important for stabilizing it. The neutral (spin-carying) phase kink is attracted by an energy on the meV scale to carbon atoms joining a non-hydrogen side-group, in contrast to charged phase kinks, where this attraction is estimated to be 100 to 1000 times larger.

Bond alternation defects in long polyene molecules

Recent theoretical work suggests that there is an alternation in carbon-carbon bond lengths throughout a sufficiently long polyene chain. Such alternation implies the possibility of defects in which even-numbered bonds along the chain change over from short to long. In this paper, the electronic properties of such defects are examined by Huckel molecular orbital theory, with the parameters used by Longuet-Higgins and Salem [2]. It is shown that there is a localized non-bonding molecular orbital associated with each defect (if they are well separated). In the neutral molecule, there will be an odd electron in each such molecular orbital, which should be detectable by electron spin resonance. An approximate estimate of the energy required to form a defect suggests that there should be about one per seventy carbon atoms.