Accurate method for obtaining band gaps in conducting polymers using a DFT/hybrid approach

DFT calculations on a series of oligomers have been used to estimate band gaps, ionization potentials, electron affinities, and bandwidths for polyacetylene, polythiophene, polypyrrole, polythiazole, and a thiophene - thiazole copolymer. Using a slightly modified hybrid functional, we obtain band gaps within 0.1 eV of experimental solid-state values Calculated bond lengths and bond angles for the central ring of sexithiophene differ by less than 0.026 Å and 0.7° from those of the sexithiopnene crystal structure. IPs and EAs are overestimated by up to 0.77 eV compared to experimental bulk values. Extrapolated bandwidths agree reasonably well with bandwidths from band structure calculations

Comparison of geometries and electronic structures of polyacetylene, polyborole, polycyclopentadiene, polypyrrole, polyfuran, polysilole, polyphosphole, polythiophene, polyselenophene and polytellurophene

Geometries of monomers through hexamers of cylopentadiene, pyrrole, furan, silole, phosphole, thiophene, selenophene and tellurophene, and monomers through nonamers of borole were optimized employing density functional theory with a slightly modified B3P86 hybrid functional. Bandgaps and bandwidths were obtained by extrapolating the appropriate energy levels of trimers through hexamers (hexamers through nonamers for borole) to infinity, Bandgaps increase with increasing π-donor strengths of the heteroatom. In general, second period heteroatoms lead to larger bandgaps than their higher period analogs. Polyborole is predicted to have a very small or no energy gap between the occupied and the unoccupied π-levels. Due to its electron deficient nature polyborole differs significantly from the other polymers. It has a quinoid structure and a large electron affinity. The bandgaps of heterocycles with weak donors (CH 2, SiH 2 and PH) are close to that of polyacetylene. For polyphosphole this is due to the pyramidal geometry at the phosphorous which prevents interaction of the phosphorus lone pair with the π-system. The bandgap of polypyrrole is the largest of all polymers studied. This can be attributed to the large π-donor strength of nitrogen. Polythiophene has the third largest bandgap. The valence bandwidths differ considerably for the various polymers since the avoided crossing between the flat HOMO-1 band and the wide HOMO band occurs at different positions. The widths of the wide HOMO bands are similar for all systems studied. All of the polymers studied have strongly delocalized π-systems. © 1998 Elsevier Science S.A. All rights reserved

Theoretical analysis of effects of π-conjugating substituents on building blocks for conducting polymers

Geometries of 4-dicyanomethylene-4H-cyclopenta[2,1-b:3,4-b'] dithiophene 1 and its C=O, C=S, C=CH2, C=CF2, and C=C(SR)2 analogues were optimized using density functional theory. Three of the above groups, C=C(CN)2, C=O, and C=S, were also examined on dipyrrole, difuran, dicyclopentadiene, and diborole. Electronic structures were analyzed with respect to their suitability as building blocks for conducting polymers with the natural bond orbital (NBO) method. All bridging groups investigated decrease HOMO-LUMO gaps compared to the unsubstituted parent dimers. Substitution affects HOMO and LUMO energies. Energy gap reduction is caused by a stronger decrease of LUMO energies compared to HOMO energies. The C=S group leads to even smaller energy gaps than the dicyanomethylene group since the HOMO is lowered less in energy with C=S. Compared to unsubstituted dimers, the strongest substituent effects are found with pyrroles and furans. Boroles and thiophenes are least affected. The smallest HOMO-LUMO gaps are obtained for electron-poor systems such as boroles followed by cyclopentadienes. This is analogous to the trend for the unsubstituted parent systems. All of the bridging groups are potential π-acceptors due to their low-lying π*-orbitals, and the corresponding polymers are predicted to be n-dopable. In aromatic structures, the LUMO is localized around the bridging substituent and the coefficients at the α-carbon atoms that reflect electron density are small. This might contribute to the poor conductivity of the n-doped form of poly-1. Electron- poor monomers and polymers tend to switch to quinoid structures. In quinoid repeat units, the HOMO is localized but not as strongly as the LUMO in the aromatic repeat units. The LUMO in quinoid repeat units is delocalized with large coefficients at the α-carbon atoms. Quinoid polymers could therefore be good conductors in the n-doped state

Optical absorption in boron clusters B6_{6} and B6+_{6}^{+} : A first principles configuration interaction approach

The linear optical absorption spectra in neutral boron cluster B$_{6}$ and cationic B$_{6}^{+}$ are calculated using a first principles correlated electron approach. The geometries of several low-lying isomers of these clusters were optimized at the coupled-cluster singles doubles (CCSD) level of theory. With these optimized ground-state geometries, excited states of different isomers were computed using the singles configuration-interaction (SCI) approach. The many body wavefunctions of various excited states have been analysed and the nature of optical excitation involved are found to be of collective, plasmonic type.Comment: 22 pages, 38 figures. An invited article submitted to European Physical Journal D. This work was presented in the International Symposium on Small Particles and Inorganic Clusters - XVI, held in Leuven, Belgiu

Statistical mechanics of semiflexible ribbon polymers

The statistical mechanics of a ribbon polymer made up of two semiflexible chains is studied using both analytical techniques and simulation. The system is found to have a crossover transition at some finite temperature, from a type of short range order to a fundamentally different sort of short range order. In the high temperature regime, the 2-point correlation functions of the object are identical to worm-like chains, while in the low temperature regime they are different due to a twist structure. The crossover happens when the persistence length of individual strands becomes comparable to the thickness of the ribbon. In the low temperature regime, the ribbon is observed to have a novel ``kink-rod'' structure with a mutual exclusion of twist and bend in contrast to smooth worm-like chain behaviour. This is due to its anisotropic rigidity and corresponds to an {\it infinitely} strong twist-bend coupling. The double-stranded polymer is also studied in a confined geometry. It is shown that when the polymer is restricted in a particular direction to a size less than the bare persistence length of the individual strands, it develops zigzag conformations which are indicated by an oscillatory tangent-tangent correlation function in the direction of confinement. Increasing the separation of the confining plates leads to a crossover to the free behaviour, which takes place at separations close to the bare persistence length. These results are expected to be relevant for experiments which involve complexation of two or more stiff or semiflexible polymers.Comment: 20 pages, 11 figures. PRE (in press

Ab initio study of the structure of poly[di(phenoxy)thionylphosphazene]

The stable structure of poly[(diphenoxy)thionylphosphazene] single chains was modeled with a small molecular compound consisting of one repeat unit of the polymer. The geometrical parameters of the nonplanar “trans-cis” conformations of these molecular models were obtained using the ab initio molecular orbital theory. The 3-21G∗ basis set was used in the computation. It was found that the phenoxy groups are positioned approximately parallel to the backbone and the groups located on adjacent phosphorus atoms point in opposite directions. The bonding of the short chain segment exhibits a “single-double” alternating pattern along the backbone. The charge distribution along the backbone is highly polarized. The total dipole moment is oriented parallel to the backbone and is equal to 6.75 debye. The molecular diameter of this compound is estimated to be 13 Å

Ab initio studies on the structure, conformation, and chain flexibility of halogenated poly(thionylphosphazenes)

Ab initio quantum chemical calculations on short-chain model compounds have been used to study the conformation, valence electron density, and chain flexibility of halogen-substituted poly-(thionylphosphazenes) (PTPs) [(NSOX)(NPCl&], (X = F or Cl), which are representatives of a new class of inorganic sulfur(vI)-nitrogen-phosphorus polymers. The calculations were carried out at the closedshell Hartree-Fock level of theory using the Gaussian 92 program package. The electronic wave function was described by the 6-31G* basis set. The results show that model compounds adopt a nonplanar transcis conformation in the minimum-energy state. Based on the stable geometries of the short-chain analogues, the polymer will form a 12/5 helix in its extended conformation. Rigid rotor scans and geometry optimizations of selected rotamers were used in order to investigate the torsional mobility of the main chain of the model compounds. The flexibility of the S-N-P and P-N-P bond angles contributes significantly to the chain flexibility. The torsional barriers for rotations around bonds of the PTP backbone range from 1.5 to 3.5 kcal/mol. A change from chlorine to fluorine as a substituent on sulfur leads to lower torsional barriers and wider minima of the rotational potentials and therefore to an increased torsional mobility of the main chain. The increase in chain flexibility is consistent with trends in glass transition temperatures of the corresponding polymers. The electronic structure of the model compounds, including charge density distributions, is briefly discussed. The results indicate strong charge separations along the backbone of the polymer and in the direction of the substituents bonded to the main chain which are consistent with Dewar’s island delocalization model