Research Collection Doctoral Thesis Electron delocalization in through and cross conjugated oligomers and its influence on the molecular properties Author(s): Limacher, Peter Andreas Publication Date: 2010 Permanent Link: https://doi.org/10.3929/ethz-a-006234218 Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library Diss. ETH No. 19211 Electron Delocalization in Through and Cross Conjugated Oligomers and its Influence on the Molecular Properties A dissertation submitted to the ETH ZURICH¨ for the degree of Doctor of Sciences presented by PETER ANDREAS LIMACHER Dipl. Chem. ETH born November 15, 1980 citizen of Sch¨upfheim (LU) accepted on the recommendation of PD Dr. Hans Peter L¨uthi, examiner Prof. Dr. Wilfred F. van Gunsteren, Prof. Dr. Markus Reiher, co-examiners 2010 Ach, kein Steg will dahin f¨uhren, Ach, der Himmel ¨uber mir Will die Erde nicht ber¨uhren, Und das Dort ist niemals hier! Friedrich Schiller Acknowledgements First I would like to thank Hans Peter L¨uthi for giving me the op- portunity to work on my PhD studies in his group. He taught me the necessary skills to present and sell dry research data in an at- tractive way, and also gave me profound insight into the community of quantum chemistry. It was also a pleasure to have many scientific and other discussions with him at various places inside and around the ETH. Many thanks also go to Wilfred van Gunsteren and Markus Reiher for their willingness to act as co-examiners at my defense and to critically read and evaluate the content of this work. In addition, I would like to express my appreciation to Wilfred for guaranteeing me a comfortable working and social environment. Thanks should go to both professors and also to their group members for all the nice scientific and mundane interchange we had over the past years. As a ’wanderer between the worlds’, I sort of belong to both groups. I enjoyed many parties, group outings, traveling to conferences, etc. with dedicated people thereof. A special thank goes to Stefano Borini. We had a very fruit- ful collaboration and a great time together. I am also grateful to Kurt Mikkelsen and his group for hosting me and taking care of me during my two scientific visits to Copenhagen. From many of the seminars and colloquia I enjoyed at the ETH, there are two that I especially remember: I owe thanks to Gustavo Scuseria and Daniel Crawford for the fruitful scientific discussions after their talks. Also Martin Br¨andle from the ETH library deserves my grat- vi ACKNOWLEDGEMENTS itude for his always helpful support in the projects we worked on together. Finally I should not forget to mention J¨urg Hutter and Maurizio Bruschi, whom I thank for the scientific collaboration. Besides work, I want to thank all my friends from home for dragging me out of this ’Gehirnfabrik’, as they call it, and letting me enter the real world now and then. I am also grateful to my flat mates for their mental support and the proofreading in the final stages of the thesis writing. And last but not least, a big thank-you to my whole family. Contents Acknowledgements v Summary xi Zusammenfassung xiii Publications xv 1 Introduction 1 1.1 Electron Delocalization . 2 1.2 ConjugatedOligomers . 3 1.3 Structure-Property Relationships . 6 1.4 Computational Aspects . 7 1.5 OutlineoftheThesis. 9 2 Methods and Theory 11 2.1 The H¨uckel Molecular Orbital Method . 12 2.1.1 The H¨uckel Hamiltonian . 12 2.1.2 H¨uckel States and Delocalization Energy . 14 2.1.3 Bond Orders and Orbital Occupation . 15 2.2 Bond Length Alternation . 17 2.3 NBOAnalysis...................... 21 2.3.1 Definition of NAOs and NBOs . 21 2.3.2 Delocalization Energy . 24 2.4 Polarizabilities . 26 2.4.1 Calculating Polarizabilities . 26 viii CONTENTS 2.4.2 The Second Hyperpolarizability in Oligomers 30 2.4.3 Extrapolation Schemes . 31 3 Cross Conjugation 35 3.1 Accounts of Cross Conjugation . 38 3.2 Understanding Cross Conjugation . 41 3.2.1 Results of HMO Theory . 41 3.2.2 BLA in Different Cross Conjugated Systems . 44 3.2.3 Polarizabilities of Cross Conjugated Systems 48 3.2.4 Conclusions . .. .. .. .. .. 49 3.3 Competition among Conjugation Paths . 50 3.3.1 Molecular and Electronic Structure of DPB . 52 3.3.2 Donor-Acceptor Substituted DPB . 55 3.3.3 Conclusions . .. .. .. .. .. 57 4 D-A Substitution 59 4.1 Penetration Depth . 61 4.1.1 Single Substituents . 61 4.1.2 Substituent Combinations . 63 4.2 TheSuperpositionModel . 63 4.2.1 Definitions . 64 4.2.2 Cooperative Effects on Bond Lengths . 65 4.2.3 Cooperative Effects on Polarizabilities . 66 4.3 Property Correlation . 68 5 H¨uckel Polarizabilities 71 5.1 Theoretical Background . 72 5.1.1 Obtaining Atomic Coordinates . 72 5.1.2 Expressions for Polarizabilities . 73 5.1.3 Defining the Perturbation Operator . 74 5.1.4 Units of Polarizabilities . 75 5.2 Algorithmic Implementation . 75 5.3 Applications....................... 77 5.3.1 Bond Strength Alternation . 77 5.3.2 H¨uckel Polarizability . 79 5.3.3 H¨uckel Second Hyperpolarizability . 80 CONTENTS ix 5.3.4 ConcludingRemarks . 81 6 Outlook 83 A SOS Polarizabilities 85 A.1 GeneralSOSExpressions . 85 A.2 Single Determinant Methods . 93 A.3 Interpretation and Remarks . 101 B A H¨uckel Program 103 References 119 Curriculum Vitæ 129 Complete List of Publications 131 x CONTENTS Summary The present thesis is about electron delocalization and its influ- ence on the molecular properties of conjugated oligomers. Neither experiment nor theory are able to determine or uniquely define elec- tron delocalization. On the other hand, many exactly measurable quantities are inherently related to this conceptual quantity. The goal of this thesis is to establish and characterize such relations in view of a better understanding of electron delocalization. To this end, the focus is put on three domains influenced by electron de- localization: the molecular structure, the electronic structure and the molecular properties. The correlation among the observables of these three domains allows for an assessment of the electron delo- calization present in a given molecule. Linearly through and cross conjugated oligomers serve as tunable molecular systems to reveal such correlations. Fundamental differences are found in the electronic structure of these two conjugation types. These are responsible for the only weak electron delocalization in cross conjugated systems. However, it is shown that electron delocalization is significantly enhanced in excited or charged states, which discloses new applications for this neglected type of conjugation. Another peculiarity of cross conju- gation is the presence of steric strain and competing conjugation paths, that may be exploited for the design of functional materials. The investigation of donor-acceptor substituted chains shows that the influence of a substituent on the bond length drops expo- nentially with distance. For the properties of bisubstituted mole- xii SUMMARY cules, a superposition model is proposed which specifically extracts changes related to the conjugation of both substituents. An inves- tigation of these cooperative effects leads to the conclusion that donor-donor and acceptor-acceptor conjugation is equally strong as donor-acceptor conjugation, but with opposite sign. The polarizabilities of conjugated chains are evaluated with sev- eral quantum chemical methods, and problems with current density functional and wave function methods are discussed. Extrapolation schemes are proposed to find reliable values for an infinite polymer chain. The H¨uckel model is extended to calculate polarizabilities of large conjugated oligomers. Its application to systems with de- creasing bond strength alternation reveals a continuous increase in polarizability. In contrast, a maximum value for the second hyper- polarizability is found for a non-vanishing bond strength alterna- tion. Zusammenfassung Die hier vorliegende Dissertation befasst sich mit Elektronendelo- kalisierung und ihrer Auswirkung auf die molekularen Eigenschaf- ten von konjugierten Oligomeren. Weder das Experiment noch die Theorie verm¨ogen die Elektronendelokalisierung genau zu bestim- men oder eine eindeutige Definition zu liefern. Andererseits ex- istieren aber viele exakt messbare Gr¨ossen, die in enger Beziehung zu dieser konzeptuellen Gr¨osse stehen. Das Ziel dieser Dissertation ist es, ebendiese Beziehungen zu erhellen und zu charakterisieren, um so ein besseres Verst¨andnis von Elektronendelokalisierung zu erm¨oglichen. Zu diesem Zweck wird das Augenmerk auf drei Gebie- te gerichtet, die allesamt von Elektronendelokalisierung beeinflusst werden: Die molekulare Struktur, die elektronische Struktur und die molekularen Eigenschaften. Korrelationen unter den Observablen aus diesen drei Gebieten erm¨oglichen es, die Elektronendelokalisie- rung f¨ur ein bestimmtes Molek¨ul einzusch¨atzen. Lineare through- und cross-konjugierte Oligomere dienen dabei als modulierbare Sys- teme um solchen Beziehungen nachzusp¨uren. Es zeigen sich dabei fundamentale Unterschiede in der elektro- nischen Struktur dieser beiden Konjugationsarten. Diese sind ver- antwortlich f¨ur eine nur schwach ausgepr¨agte Elektronendelokali- sierung in cross-konjugierten Systemen. Es wird allerdings gezeigt, dass die Elektronendelokalisierung in angeregten oder ionischen Zu- st¨anden signifikant erh¨oht wird, womit neue Anwendungen f¨ur diese vernachl¨assigte Konjugationsart erschlossen werden. Eine weitere