Eric E. Moore

Comparison of density matrix renormalization group calculations with electron-hole models of exciton binding in conjugated polymers

By analogy with inorganic semiconductors such as GaAs or Si, electron-hole models may be expected to provide a useful description of the excited states of conjugated polymers. Here, these models are tested against density matrix renormalization group (DMRG) calculations. The DMRG method is used to generate nearly-exact descriptions of the ground state, 11Bu optical gap state, and the band gap of the Pariser-Parr-Pople (PPP) Hamiltonian of polyenes with between 2 and 40 carbon atoms. These are compared with both bare electron-hole (singles configuration interaction theory and the random phase approximation) and dressed electron-hole (second and third order Green’s function) methods. For the optical gap, only second-order Green’s function results were obtained. When an unscreened (Ohno) electron-electron interaction potential is used, the dressed electron-hole methods work well for the band gap. The difference between the band gap predicted by bare and dressed electron-hole methods increases with chain leng...

Coulomb screening and exciton binding energies in conjugated polymers

Hartree–Fock solutions of the Pariser–Parr–Pople and MNDO Hamiltonians are shown to give reasonable predictions for the ionization potentials and electron affinities of gas-phase polyenes. However, the energy predicted for formation of a free electron-hole pair on an isolated chain of polyacetylene is much larger than that seen in the solid state. The prediction is 6.2 eV if soliton formation is ignored and about 4.7 eV if soliton formation is included. The effects of interchain interactions on the exciton binding energy are then explored using a model system consisting of one solute and one solvent polyene, that are coplanar and separated by 4 A. The lowering of the exciton binding energy is calculated by comparing the solvation energy of the exciton state to that of a single hole (a cationic solute polyene) and a single electron (an anionic solute polyene). It is argued that when the relative timescales of charge fluctuations on the solute and solvent chains are taken into account, it is difficult to ra...

Decomposition of Methylbenzyl Radicals in the Pyrolysis and Oxidation of Xylenes

Alkyl benzyl radicals are important initial products in thermal and combustion reactions of substituted aromatic fuels. The decomposition reactions of the three isomeric methylbenzyl radicals, formed as primary products in xylene combustion, are studied theoretically and are shown to be significantly more complex than previously reported. Thermochemical properties are calculated using the G3X and G3SX model chemistries, with isodesmic and atomization work reactions. G3X atomization calculations reproduce heats of formation for the 14 reference species in the work reactions to a mean unsigned error of 0.23 kcal mol(-1), and maximum error of 0.70 kcal mol(-1), slightly outperforming the G3SX method. For the target molecules the isodesmic and atomization heats of formation agree to within 0.20 kcal mol(-1), on average. We posit that this study approaches the crossover point at which atomization calculations offer improved accuracy over isodesmic ones, for these closed-shell hydrocarbons. Our results suggest that m-xylylene is not the decomposition product of m-methylbenzyl, as was previously reported. Instead, the m-methylbenzyl radical decomposes to p-xylylene (and perhaps some of the less stable o-xylylene) via a ring-contraction/methylene-migration (RCMM) mechanism, with activation energy of around 70 kcal mol(-1). At higher temperatures m-methylbenzyl is predicted to also decompose to 2- and 3-methylfulvenallene + H, with activation energy of around 84 kcal mol(-1). The o-methylbenzyl radical is shown to primarily decompose to o-xylylene + H with bond dissociation energy of 67.3 kcal mol(-1), with fulvenallene + CH3 proposed as a minor product set. Finally, the p-methylbenzyl radical decomposes solely to p-xylylene + H with bond dissociation energy 61.5 kcal mol(-1). Rate expressions are estimated for all reported reactions, based on thermochemical kinetic considerations, with further modeling along with detailed experiments needed to better refine rate constants and branching ratios for methylbenzyl radical decomposition. These calculated reaction mechanisms and rate constants for methylbenzyl radical decomposition are consistent with the experimental data. Our results help explain the ignition behavior of the xylenes, and should lead to improved kinetic models for combustion of these and other alkylated aromatic hydrocarbons.

An explicit-solvent dynamic-dielectric screening model of electron-hole interactions in conjugated polymers

The effects of interchain interactions on the exciton-binding energy of conjugated polymers are explored theoretically, using rigid polyacetylene chains as a model system. An explicit quantum chemical description is used to describe the polarization that an electron and hole induce in the surrounding polymer chains. The motivation for explicitly including interchain interactions is to allow the standard parameters of semiempirical quantum chemistry to be used to make predictions for solid-state polymers. The model includes the time scales of both the electron-hole motion and the dielectric polarization. A free electron or hole forms an electronic polaron, in which the bare electron or hole delocalizes over about four unit cells before developing a polarization cloud. In the 1 1Bu exciton state, the time scale for electron-hole motion is comparable to that of the polarization. (If a fast dielectric response is assumed, the polarization energy is overestimated by about 60%.) For the Pariser-Parr-Pople Hamil...

Models of Coulomb screening and exciton binding in conjugated polymers

Abstract The effects of interchain interactions on the exciton binding energy are investigated using a model system consisting of a solvent polyene with 24 carbon atoms and a solute polyene with between 2 and 18 carbon atoms, separated by 4 Angstroms. It is shown that the time scales of electron-hole motion on the solute and the polarization of the solvent chain are such that a separation of time scales, for instance by screening the electron-hole potential, is not valid. Using a model that does not assume a separation of time-scales, interaction with the single solvent chain lowers the exciton binding energy by 0.36eV. Given this large value for a single solvent chain, it seems likely that interchain interactions play an important role in establishing the solid-state exciton binding energy.

Role of electron-electron interactions in the nonresonant nonlinear optical response of conjugated polymers

The origin of the large third-order nonresonant nonlinear optical response of conjugated polymers is explored using single configuration-interaction (S-Cl) theory to solve the Pariser-Parr-Pople (PPP) Hamiltonian of polyacetylene. Both the strength of electron-electron interactions and the degree of bond alternation are treated as free parameters. For a fixed bond alternation, increasing the strength of electron-electron interactions from zero to 150% of that typically used in PPP theory decreases the hyperpolarizability by nearly two orders of magnitude. However, this decrease arises primarily from an increase in the optical gap. When the bond alternation is adjusted such that the optical gap remains fixed, increasing the strength of electron-electron interactions changes the hyperpolarizability by less than 30%. For a wide range of parameters, there is good agreement between Hückel theory and PPP theory, provided the Hückel gap is parameterized to the PPP optical gap. In PPP theory, the hyperpolarizability is nearly proportional to the optical gap raised to the -5.5 power, as compared to the -6 power for Hückel theory. These results suggest that electron-electron interactions need not be explicitly included in a model of the nonresonant response of polymers, but can instead be absorbed into the effective parameters of an independent electron model.