Linear, cyclic, and Möbius strip polyacenes: The influence of the topology on the size-dependent HOMO-LUMO energy gap

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Abstract

The electronic structure of finite and infinite linear, cyclic, and Möbius strip polyacenes has been investigated by adopting simple Hückel methodology without and with variable β resonance integrals and the more involved MNDO scheme. Using the Hückel approach, it turns out that the linear polyacenes and the Möbius ladder molecules exhibit HOMO-LUMO gap which monotonously decrease with chain length while their cyclic analogs have a sawtooth behavior. The originality of the approach is to combine band structure and MO approaches to get analytical forms of the energy levels. These results are corroborated at the MNDO levels where the geometry relaxation effects are taken into account. The optimized MNDO structures show that the Möbius defect is localized and extends over approximately one-third of the ladder. Accounting for geometry distortion at the MNDO level results in an increase of the gap of the Möbius strip relative to the linear and cyclic finite size structures, but the similar results for the two methods confirm that the topology is the main factor acting on HOMO-LUMO energy gaps.

Original languageEnglish
Pages (from-to)607-616
Number of pages10
JournalInternational Journal of Quantum Chemistry
Volume84
Issue number6
DOIs
Publication statusPublished - 20 Sep 2001

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Aromatic polymers
Ladders
ladders
strip
Energy gap
topology
Topology
Geometry
geometry
Chain length
Band structure
Electron energy levels
Electronic structure
energy levels
methodology
analogs
electronic structure
Defects
Molecules
defects

Keywords

  • Energy gap
  • Hückel
  • MNDO
  • Möbius
  • Polyacenes

Cite this

@article{949eb9e4402147f2a10ce775bee66000,
title = "Linear, cyclic, and M{\"o}bius strip polyacenes: The influence of the topology on the size-dependent HOMO-LUMO energy gap",
abstract = "The electronic structure of finite and infinite linear, cyclic, and M{\"o}bius strip polyacenes has been investigated by adopting simple H{\"u}ckel methodology without and with variable β resonance integrals and the more involved MNDO scheme. Using the H{\"u}ckel approach, it turns out that the linear polyacenes and the M{\"o}bius ladder molecules exhibit HOMO-LUMO gap which monotonously decrease with chain length while their cyclic analogs have a sawtooth behavior. The originality of the approach is to combine band structure and MO approaches to get analytical forms of the energy levels. These results are corroborated at the MNDO levels where the geometry relaxation effects are taken into account. The optimized MNDO structures show that the M{\"o}bius defect is localized and extends over approximately one-third of the ladder. Accounting for geometry distortion at the MNDO level results in an increase of the gap of the M{\"o}bius strip relative to the linear and cyclic finite size structures, but the similar results for the two methods confirm that the topology is the main factor acting on HOMO-LUMO energy gaps.",
keywords = "Energy gap, H{\"u}ckel, MNDO, M{\"o}bius, Polyacenes",
author = "Jean-Marie Andr{\'e} and Beno{\^i}t Champagne and Perp{\`e}te, {Eric A.} and Maxime Guillaume",
year = "2001",
month = "9",
day = "20",
doi = "10.1002/qua.1415",
language = "English",
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journal = "International Journal of Quantum Chemistry",
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publisher = "John Wiley and Sons Inc.",
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TY - JOUR

T1 - Linear, cyclic, and Möbius strip polyacenes

T2 - The influence of the topology on the size-dependent HOMO-LUMO energy gap

AU - André, Jean-Marie

AU - Champagne, Benoît

AU - Perpète, Eric A.

AU - Guillaume, Maxime

PY - 2001/9/20

Y1 - 2001/9/20

N2 - The electronic structure of finite and infinite linear, cyclic, and Möbius strip polyacenes has been investigated by adopting simple Hückel methodology without and with variable β resonance integrals and the more involved MNDO scheme. Using the Hückel approach, it turns out that the linear polyacenes and the Möbius ladder molecules exhibit HOMO-LUMO gap which monotonously decrease with chain length while their cyclic analogs have a sawtooth behavior. The originality of the approach is to combine band structure and MO approaches to get analytical forms of the energy levels. These results are corroborated at the MNDO levels where the geometry relaxation effects are taken into account. The optimized MNDO structures show that the Möbius defect is localized and extends over approximately one-third of the ladder. Accounting for geometry distortion at the MNDO level results in an increase of the gap of the Möbius strip relative to the linear and cyclic finite size structures, but the similar results for the two methods confirm that the topology is the main factor acting on HOMO-LUMO energy gaps.

AB - The electronic structure of finite and infinite linear, cyclic, and Möbius strip polyacenes has been investigated by adopting simple Hückel methodology without and with variable β resonance integrals and the more involved MNDO scheme. Using the Hückel approach, it turns out that the linear polyacenes and the Möbius ladder molecules exhibit HOMO-LUMO gap which monotonously decrease with chain length while their cyclic analogs have a sawtooth behavior. The originality of the approach is to combine band structure and MO approaches to get analytical forms of the energy levels. These results are corroborated at the MNDO levels where the geometry relaxation effects are taken into account. The optimized MNDO structures show that the Möbius defect is localized and extends over approximately one-third of the ladder. Accounting for geometry distortion at the MNDO level results in an increase of the gap of the Möbius strip relative to the linear and cyclic finite size structures, but the similar results for the two methods confirm that the topology is the main factor acting on HOMO-LUMO energy gaps.

KW - Energy gap

KW - Hückel

KW - MNDO

KW - Möbius

KW - Polyacenes

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U2 - 10.1002/qua.1415

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JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

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