Calculation of the Hückel parameter β [beta] from the free-electron model

Taubmann, Gerhard

doi:10.1021/ed069p96

Cited by 23 publications

(21 citation statements)

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“…21 Kuhn's equation provides a parallel route to analyze the dependence of band gap of a conjugated polymer upon the length of the conjugated backbone. 22,23 The extrapolation method at B3LYP/6-31G(d) level of theory predicts the band gap of conjugated polymers (polythiophene, polypyrrole, polyfuran, etc.) quite accurately when long conjugated oligomers are used.…”

Section: Introductionmentioning

confidence: 99%

The role of relativity and dispersion controlled inter-chain interaction on the band gap of thiophene, selenophene, and tellurophene oligomers

Chattopadhyaya

Sen²,

Alam

et al. 2012

The Journal of Chemical Physics

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Ab initio relativistic density functional theoretical calculations have been carried out on π-conjugated oligomers of increasing length with S, Se, and Te as heteroatoms. The band gap of the corresponding polymers has been obtained by plotting lowest unoccupied molecular orbital (LUMO)-highest occupied molecular orbital (HOMO)gap against the reciprocal of the number of monomer units (1/N) and extrapolating the curve to 1/N = 0. With B3LYP functional, we predict that role of relativistic correction terms is not very significant in the determination of final band gap of thiophene, selenophene, and tellurophene polymer. The origin of this observation is provided through the density of states (DOS) analysis which manifests that DOS contribution across the Fermi level of these polymers is mostly governed by C atoms and as a consequence relativistic correction terms due to heavy heteroatom remain insignificant to the band gap modification. We also inspected the role of inter-chain interaction in determining the net LUMO-HOMO gap of π-stacked double chain oligomers of increasing length. We have found that due to the exciton splitting in the stacked configurations, the LUMO-HOMO gap decreases steadily. Furthermore, we have noticed that dispersion force has important role in the reduction of the LUMO-HOMO gap of the oligomers studied.

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Section: Introductionmentioning

confidence: 99%

The role of relativity and dispersion controlled inter-chain interaction on the band gap of thiophene, selenophene, and tellurophene oligomers

Chattopadhyaya

Sen²,

Alam

et al. 2012

The Journal of Chemical Physics

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“…We use a value of −0.111 atomic units (derived from experimental properties of C 60 ) for the β parameter in the Hückel method . While we are not aware of a β value determined specifically for graphene, we note that the fullerene value is similar to the estimated ones based on polyenes (−0.096 to −0.124) and the free-electron model (−0.112) . Together with appropriate reference systems, resonance energies ( E R ) can be obtained from the Hückel energies by E R = E Hückel – E ref .…”

Section: Resultsmentioning

confidence: 99%

“…34 While we are not aware of a β value determined specifically for graphene, we note that the fullerene value is similar to the estimated ones based on polyenes (−0.096 to −0.124) 49 and the free-electron model (−0.112). 50 Together with appropriate reference systems, resonance energies (E R ) can be obtained from the Huckel energies by…”

Section: ■ Computational Detailsmentioning

confidence: 99%

A Simple Model for Relative Energies of All Fullerenes Reveals the Interplay between Intrinsic Resonance and Structural Deformation Effects in Medium-Sized Fullerenes

Chan

Kawashima

Dawson

et al. 2019

J. Chem. Theory Comput.

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Fullerenes are sheets of sp 2 carbon atoms wrapped around to form spheres. With this simple consideration, we have in the present study devised and (with over 3600 DFT data points) successfully validated a simple model, termed R+D, for estimating the relative energies of fullerenes. This model contains a resonance component to account for the intrinsic differences between the πenergies of different fullerenes, and a deformation component for treating the distortions from planarity. Notably, we find that both terms (and they alone) are required to obtain good relative energies, which lends support to the formulation of the R+D model. An interesting finding is that for some medium-sized IPR fullerenes, their isomers show similar variations in the two components. We deduce that these fullerenes may represent a good opportunity for tuning molecular properties for practical applications. We hope that the promising results of the present study will encourage further investigations into fullerenes from a fundamental perspective.

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“…By selectively mixing exact exchange, and by explicitly including correlation, the B3LYP gaps come very close to the corresponding optical excitation energy. It is generally accepted that, for conjugated oligomers, extrapolating the linear curve of the HOMO-LUMO gap against the reciprocal of the number of monomer units (1/n) affords a prediction of the band gap for the corresponding polymer [21][22][23][24][25][26][27]. Thus, in this paper the geometries of the oligomers were optimized at an RHF level using a semi-empirical AM1 method [28].…”

Section: Methodsmentioning

confidence: 99%

Theoretical calculation on relationship between molecular structure and band gap of benzo[1,2-b:4,5-b $$'$$ ′ ]dithiophene based homopolymer

et al. 2014

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In order to guide the synthesis of new materials with low band gaps, quantum-chemical methods have been increasingly applied to predict the band gaps of conjugated polymers. Softwares such as Material Studio, Gauss View, Gauss 03 and Gauss 09 calculation program were used in this paper. Semi-empirical AM1 method was applied to calculate the optimal geometric structure of selected three benzo[1,2-b:4,5-b ]dithiophene homopolymers, namely PBDTV, H2 and H3. Using the generalized density function theory based on B3LYP/6-31G*, B3LYP/6-311G* and M062X/6-311G* level calculation of polymers' band gaps. The results indicate that whether there is enough interspace between adjacent subunits, long alkoxy side chain is advantageous to the band gap decrease, and otherwise it will bring steric hindrance to destroy the coplanarity of polymer chain which is disadvantageous to the band gap decrease. The band gaps of polymers mainly depends on the molecular structure, generally speaking, the more coplanarity of main chain, smaller dihedral angle, smaller difference between the bond length of single and double bonds in the main chain, resulting in narrower band gap.

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Calculation of the Hückel parameter β [beta] from the free-electron model

Abstract: It is the goal of this paper to calculate beta from the average bond length between two carbon atoms.

Cited by 23 publications

References 1 publication

The role of relativity and dispersion controlled inter-chain interaction on the band gap of thiophene, selenophene, and tellurophene oligomers

The role of relativity and dispersion controlled inter-chain interaction on the band gap of thiophene, selenophene, and tellurophene oligomers

A Simple Model for Relative Energies of All Fullerenes Reveals the Interplay between Intrinsic Resonance and Structural Deformation Effects in Medium-Sized Fullerenes

Theoretical calculation on relationship between molecular structure and band gap of benzo[1,2-b:4,5-b $$'$$ ′ ]dithiophene based homopolymer

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