Excited-state symmetry breaking: from fundamental photophysics to asymmetrical photochemistry
Excited-state symmetry breaking in multipolar organic molecules is extensively investigated here. First unambiguous experimental observation of this phenomenon by using femtosecond time-resolved infrared spectroscopy (TRIR) is presented. This photophysical phenomenon originates from the fluctuations and rearrangement of solvent molecules around the electronically excited chromophore. Non-specific quadrupolar and dipolar, as well as specific H-bonding and non-orthodox X-bonding solute-solvent interactions can induce symmetry breaking, whereas dispersion and intramolecular distortions/asymmetric vibrations cannot.
The effect of intramolecular factors, e.g. of the length of charge-transfer branches, is studied.
Symmetry breaking leads to the asymmetrical reactivity of the seemingly identical molecular branches that can be utilized to achieve asymmetrical intra- and intermolecular photochemistry. Additionally, a novel approach to the time-resolved infrared spectroscopy ('solute-pump/solvent-probe') is demonstrated. It is used to decipher the mechanism of H-Bond Induced Nonradiative Deactivation (HBIND) of a quadrupolar [...]
DEREKA, Bogdan. Excited-state symmetry breaking: from fundamental photophysics to asymmetrical photochemistry. Thèse de doctorat : Univ. Genève, 2018, no. Sc. 5177
DOI : 10.13097/archive-ouverte/unige:102503 URN : urn:nbn:ch:unige-1025034
Disclaimer: layout of this document may differ from the published version.
UNIVERSITÉ DE GENÈVE FACULTÉ DES SCIENCES Section de chimie et biochimie
Département de chimie physique Professeur Eric Vauthey
Excited-State Symmetry Breaking:
from Fundamental Photophysics to Asymmetrical Photochemistry
présentée à la Faculté des sciences de l’Université de Genève pour obtenir le grade de Docteur ès sciences, mention chimie
Bogdan DEREKA de
Thèse N° 5177
Genève Atelier ReproMail
Cette thèse a été réalisée au Département de Chimie physique de l’Université de Genève sous la direction du professeur Eric Vauthey. Je tiens à lui exprimer mes plus chaleureux remerciements pour toutes les possibilités, pour les innombrables discussions passionnantes que nous avons eues, et la liberté qu’il ma accordée dans ma recherche. C’était une véritable chance d’avoir l’opportunité d’apprendre d’un mentor aussi enthousiaste.
Je tiens spécialement à remercier les professeurs Peter Hamm (Universität Zürich, Suisse) et Peter Vöhringer (Universität Bonn, Allemagne) pour avoir accepté de s’engager comme experts lors de la soutenance de cette thèse.
Ma gratitude va également aux membres anciens et actuels du groupe Vauthey et aux coauteurs des publications pour avoir su susciter l’inspiration et pour avoir contribué à l’atmosphère chaleureuse et conviviale, que ce soit pendant les travaux de laboratoire ou durant les pauses-thé.
Une personne qui m’a grandement aidé au début de ma thèse est mon collègue Dr. Arnulf Rosspeintner. La qualité des résultats présentés dans ces manuscrits a été possible entre autres grâce à lui et je le remercie chaleureusement pour sa collaboration.
Je remercie également Didier Frauchiger qui s’est occupé de l’équipement nécessaire pour la modification du dispositif expérimental permettant la mesure des spectres vibrationnels infrarouges.
Un merci tout particulier à Sophie Jacquemet pour sa contribution vitale de francophone à la partie quotidienne non-scientifique et administrative de ma thèse. J’ai pu, grâce à elle, me concentrer sur la partie scientifique et consacrer plus de temps à la recherche.
Enfin et surtout, je tiens à remercier ma famille et mes amis qui ont été d’un grand soutien durant ces années.
to my parents Larisa and Andrey
Somewhere, something incredible is waiting to be known.
Peer-reviewed articles presented in this PhD thesis
 B. Dereka, A. Rosspeintner, R. Stężycki, C. Ruckebusch, D. T.
Gryko, E. Vauthey, J. Phys. Chem. Lett. 2017, 8, 6029.
Excited-State Symmetry Breaking in a Quadrupolar Molecule Visualized in Time and Space.
 B. Dereka, D. Svechkarev, A. Rosspeintner, M. Tromayer, R.
Liska, A. Mohs, E. Vauthey, J. Am. Chem. Soc. 2017, 139, 16885.
Direct Observation of a Photochemical Alkyne-Allene Reaction and of a Twisted and Rehybridized Intramolecular Charge-Transfer State in a Donor-Acceptor Dyad.
 B. Dereka, E. Vauthey, J. Phys. Chem. Lett. 2017, 8, 3927.
Solute-Solvent Interactions and Excited-State Symmetry Breaking:
Beyond the Dipole-Dipole and the Hydrogen-Bond Interactions.
 B. Dereka, E. Vauthey, Chem. Sci. 2017, 8, 5057.
Direct Local Solvent Probing by Transient Infrared Spectroscopy Reveals the Mechanism of Hydrogen-Bond Induced Nonradiative Deactivation.
 A. I. Ivanov, B. Dereka, E. Vauthey, J. Chem. Phys. 2017, 146, 164306.
A Simple Model of Solvent-Induced Symmetry-Breaking Charge Transfer in Excited Quadrupolar Molecules.
 B. Dereka, M. Koch, E. Vauthey, Acc. Chem. Res. 2017, 50, 426.
Looking at Photoinduced Charge Transfer Processes in the IR: Answers to Several Long-Standing Questions.
 B. Dereka, A. Rosspeintner, M. Krzeszewski, D. T. Gryko, E.
Vauthey, Angew. Chem. Int. Ed. 2016, 55, 15624; Angew. Chem.
2016, 128, 15853.
Symmetry-Breaking Charge Transfer and Hydrogen Bonding:
Toward Asymmetrical Photochemistry.
 B. Dereka, A. Rosspeintner, Z. Li, R. Liska, E. Vauthey, J. Am.
Chem. Soc. 2016, 138, 4643.
Direct Visualization of Excited-State Symmetry Breaking Using Ultrafast Time-Resolved Infrared Spectroscopy.
Additional peer-reviewed articles composed during the doctoral work
 T. Kumpulainen, A. Rosspeintner, B. Dereka, E. Vauthey, J. Phys.
Chem. Lett. 2017, 8, 4516.
Influence of Solvent Relaxation on Ultrafast Excited-State Proton Transfer to Solvent.
 Q. Sun, B. Dereka, E. Vauthey, L. M. Lawson Daku, A. Hauser, Chem. Sci. 2017, 8, 223.
Ultrafast Transient IR Spectroscopy and DFT Calculations of Ruthenium(II) Polypyridyl Complexes.
 B. Dereka, R. Letrun, D. Svechkarev, A. Rosspeintner, E.
Vauthey, J. Phys. Chem. B 2015, 119, 2434.
Excited-State Dynamics of 3-Hydroxyflavone Anion in Alcohols.
 Time-Resolved Vibrational Spectroscopy (TRVS), 2017, Cambridge, UK.
 Swiss Chemical Society Fall Meeting, 2017, Bern, Switzerland.
 Geneva Chemistry and Biochemistry Days, 2017, Geneva, Switzerland.
 Swiss Chemical Society Fall Meeting, 2016, Zürich, Switzerland.
 Central European Conference on Photochemistry (CECP), 2016, Bad Hofgastein, Austria.
 Swiss Chemical Society Fall Meeting, 2015, Lausanne, Switzerland.
 Gordon Research Conference on Vibrational Spectroscopy, 2016, Biddeford, ME, USA.
 Gordon Research Seminar on Vibrational Spectroscopy, 2016, Biddeford, ME, USA.
 Time-Resolved Vibrational Spectroscopy (TRVS), 2015, Madison, WI, USA.
 XXV IUPAC Symposium on Photochemistry, 2014, Bordeaux, France.
 Swiss Chemical Society Fall Meeting, 2014, Zürich, Switzerland.
Other Oral Contributions
 ACS Active Slides Video Presentation (JACS), October 2017.
 Invited seminar (Sheffield University, UK), September 2017.
 Invited lecture (Kharkov University, Ukraine), December 2016.
 ACS Active Slides Video Presentation (JACS), March 2016.
Table of Contents
Remerciements ... 3
Publication list ... 8
Peer-reviewed articles presented in this PhD thesis ... 8
Additional peer-reviewed articles composed during the doctoral work 9 Conference presentations ... 10
Oral Talks ... 10
Posters ... 10
Other Oral Contributions ... 11
Table of Contents ... 12
Preface ... 14
Introduction ... 22
Chapter 1 A Quick Glance at Theory ... 26
1.1 Jablonski Diagram ... 26
1.2 Solvatochromism and Solvation ... 33
1.3 Two-Photon Absorption ... 36
1.4 Painelli-Terenziani Symmetry Breaking Model ... 39
Chapter 2 Ultrafast Spectroscopy in Practice ... 48
2.1 Time-Correlated Single Photon Counting ... 49
2.2 Two-Photon-Excited Fluorescence Spectroscopy ... 52
2.3 UV-Vis Transient Absorption ... 54
2.4 Broadband Fluorescence Upconversion ... 59
2.5 Femtosecond Time-Resolved Infrared ... 66
Chapter 3 Symmetry Breaking: The First Evidence ... 89
Chapter 4 Symmetry Breaking and Hydrogen Bonding: Asymmetrical Reactivity ... 119
Chapter 5 Beyond Dipole-Dipole and Hydrogen Bonding Interactions ... 146
5.1 Ivanov Symmetry-Breaking Model ... 162
Chapter 6 Symmetry Breaking in Time and Space ... 171
Chapter 7 Probing The Solvent ... 193
Chapter 8 A Photochemical Reaction ... 223
Chapter 9 Asymmetrical Photochemistry ... 248
Epilogue ... 265
Appendices ... 270
Appendix 1. Steady-State Methods and Techniques ... 270
Appendix 2. Solvent Properties ... 275
Abbreviations ... 279
Bibliography ... 282
Résumé de la Thèse ... 321
It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair, we had everything before us, we had nothing before us, we were all going direct to Heaven, we were all going direct the other way.
C. Dickens he past four years and four months are filled with some of the most wonderful moments of my life. Now looking back, I am plunging into nostalgia and I realize that I was so fortunate to cross paths with some of the most admirable and fantastic people I will ever meet. This work is the direct product of what I was able to learn from all of them.
This thesis is more than papers on which it is based. I tried to write it in the way that the flow of thoughts that was followed becomes clear. I also tried to devote some space to a number of minor details and my personal reflections that are, probably, not of great importance for the spectroscopic scientific community as a whole, but might be helpful for the current and future members of the group. It does not contain everything that I was doing during the conduction of my doctoral work, but instead I tried to present a single coherent story from the very beginning of the symmetry breaking idea as a curious photophysical process up to its implementation for achieving asymmetrical photochemistry.
I am deeply indebted to my supervisor Eric Vauthey. I remember, it was the end of my second year of the undergraduate studies at Kharkov
University, when Eric came to deliver the lecture about the research on ultrafast photoinduced processes going on in Geneva. Although at that time I had very little appreciation of physical chemistry considering myself primarily an organic chemist, it became very clear that the stuff was too exciting to pass up. And when a couple of years later came an opportunity to take an internship in any research group, anywhere abroad, during my Master’s studies, Eric’s group immediately clicked in my mind. It all started when I came to Geneva for three months with my project and a huge desire to find intermolecular proton transfer from alcohols to the excited-state anion of flavonol. I still remember the very unusually full of snow Geneva winter day of February 11th, 2013, when I came in. The project went on and although we did not find any proton transfer, I’ve got an incredible opportunity to learn a new realm of methods and techniques available in the group. I was hooked almost immediately and there was no other way but to do my post-graduate work in Vauthey group.
Over the past years, I had an incredible opportunity to work on the development of a new direction for the group. Eric’s never-ending scientific curiosity and enthusiasm fostered the atmosphere of excellence and exploration that were my beacons throughout the PhD program. I highly appreciate the freedom that I have been given in exploring my ideas and following the way I felt an inclination towards. Eric was not there to tell me what and how to do, instead he was there to steer me and to encourage trying challenging and interesting things. He was always available to explain, to discuss, to give an advice or even to argue.
Sometimes our discussions proceeded for hours in a row, and I could not acknowledge everything that I was able to learn from him.
But I think one of the most important things I have learned from Eric is the attitude of the true leader. Eric has always been very understanding of the personal issues and circumstances. I owe a lot to his flexibility that allowed me to follow my own schedule of comfort, as I learned that it does not matter when or how you work, but what the end result is. It allowed me to participate at the Johns Hopkins CTY summer program in 2015, write this thesis at home in the other country and try many other things.
During my PhD program, I had many opportunities to present our results
at a number of well-recognized and prestigious conferences, including a bunch of oral talks. I certainly realize that other PhD students anywhere else might only dream about such possibilities. In addition, I was able to travel and participate at new collaborations learning and experimenting in several other research groups throughout Europe. It is the greatest pleasure and a genuine blessing to have such mentor as Eric.
Thanks to Eric’s help I am privileged to have true leaders of the field working at the cutting edge of the vibrational spectroscopy and photochemistry/photophysics as my experts for this PhD thesis. I am hugely grateful to Professor Dr. Peter Hamm (University of Zürich) and Professor Dr. Peter Vöhringer (University of Bonn) for their kind willingness to read and critically assess this PhD thesis and its oral defense.
I want to highly acknowledge my senior colleague Ulf who has been immensely helpful since the beginning of my adventures in the ultrafast world. His teachings on everything, from steady-state spectroscopy to minute details of data processing, were of enormous help during the past years. His pickiness, in the best meaning of this word, over the experimental details or data analysis taught me that there is no such thing as too much data or too many solvents used. Sometimes there were hard times: when the physics behind the technical stuff or the volume of the literature was overwhelming, I learned from Ulf how to deal with these things. It is his talent to explain complex things in a simple and accessible language and to separate the essence from the clutter that could not be undervalued. I was so fortunate to work with him in the lab on FLUPS, TA and TPA experiments and learn a multitude of things and tricks both in theory and in practice. It is a particular fun to go through our Skype logs and read the discussions or exchange of ideas that were happening sometimes well over midnight. The quality of the data in this thesis is a direct consequence of Ulf’s philosophy of work and a gigantic zeal in the field of femtochemistry. Besides that, he is a remarkable person and a man of highest dignity.
A great deal of help and support with the transient infrared setup, which is at the core of this thesis, I received from Marius Koch. His fantastic patience and eagerness to explain the tiniest details about optics
and experimental ultrafast spectroscopy, about how to arrange things on the laser table in the best possible layout, allowed me to gain a deep appreciation of the high-quality time-resolved experiment in practice. His good humour and experience were of immense value at the moments when laser did not work or gave us hard times. His persistent striving for excellence allowed me to learn everything I could in lab 115 even after he departed. Until now, I use his approaches toward the experiment and I can only hope to be as instructive and helpful in sharing my skills and knowledge in future as Marius was to me.
Talking about the experiments I should mention Romain Letrun, who was the first person to introduce and walk me in to the ultrafast world back at my internship days as a Master student.
We started our PhD studies with Giuseppe Licari at the same time (and almost on the same day). He is one of the persons whose always positive and optimistic attitude are the life-savers. The past more than four years would have definitely been much less enjoyable if he were not around with his accordion and a contagious smile. I will always very much consider this Sicilian guy as my partner in the spectroscopic crime. I thank Peppe for our awesome gentlemen bets (and for being consistent and losing almost all of them). The office was a brighter place with Giuseppe around.
I am grateful to all previous and present Vauthey group members with whom I was so fortunate to meet, work, learn, laugh or argue. Sandra Mosquera-Vázquez transferred her amazing apartment to me, saving tons of time and nerves in Geneva real estate conditions. Marina Fedoseeva, whose good humour and Russian philosophical attitude toward life were so much helpful during the worst of times and felt like a piece of motherland. I am grateful to Sasha Yushchenko for being a fellow Ukrainian chap and sharing his advice about life in Switzerland. Vesna Markovic, Diego Villamaina, Cho-Shuen Hsieh, Tatu Kumpulainen, Christoph Nançoz, Joe Beckwith, Alex Aster, Magnus Söderberg and Chris Rumble are all greatly acknowledged for the pleasurable discussions and insightful comments and questions as well as tea-times, BBQs, bridge- jumping and lots of other fun outside the lab. Additionally, I would like to mention Julien Christmann who, during his internship, acquired some
preliminary data on double-bonded triazine systems similar to those reported in Chapter 9 that were helpful for comparative purposes.
A special thank you goes to the often-invisible people behind the curtains, but who were helpful for technical questions and support.
Bernhard Lang is acknowledged for his helpful comments on optics, electronics, statistics and data analysis. Didier Frauchiger is a man with golden hands who can create anything one can imagine (and also what one cannot) with steel, glass and plastic. The modification of the TRIR setup would be impossible without his skills and attitude. I sincerely thank to Sophie Jacquemet, without whose patience to my recurrent issues and knowledge of all the peculiarities about how things work and should be arranged at the administrative and everyday level, I would have probably ended up kicked out from the country. Dominique Lovy and Laurent Devenoge are acknowledged for their occasional but very timely technical support with electronics issues, that would have otherwise held me up in the experimental work.
It gives me great pleasure in acknowledging Cyril Ruckebusch (University of Lille) for teaching me about MCR, PCA and giving many tips and tricks on data analysis. I was happy to see his sincere interest in our collaboration and we have more things to follow up with.
I am grateful to Anatoly Ivanov for his interest in symmetry breaking and for providing a simple and robust theoretical model that allows to estimate the degree of asymmetry from easily accessible experimental data.
Besides my main work on the results reported in this thesis, I was involved in several other projects most of which turned out to be successful.
I am eager to acknowledge Andreas Hauser for involving me into the story about ruthenium complexes and for a new perspective on photoinduced processes from the viewpoint of the expert on inorganic not-so-ultrafast photophysics. Qinchao Sun from his group was a pleasure to work with on this story. I thank Tatu Kumpulainen for involving me into his photoacid project and for new insights on the peculiarities of proton transfer. The collaboration with Benedetta Carlotti (University of Perugia) was enjoyable and although we have managed to obtain mainly negative results, I believe that this step was important in my progress of understanding of symmetry
breaking. I wish to say thank you to Petr Sherin (International Tomography Center, Novosibirsk) and his fellow organic chemists for their efforts on synthesis of additional compounds to investigate HBIND process.
Damien Jeannerat’s enthusiasm about the NMR spectroscopy has allowed me to look at the nuclear magnetic resonance with new eyes. He was of great help for our development and constant improvement of the NMR part of the practical laboratory course for undergraduate students that I have been teaching since last three years. Marion Pupier is acknowledged for her help with the NMR DOSY experiments for X- bond-assisted electron transfer project. Théo Berclaz was a great resource to learn about EPR spectroscopy during my very first year of teaching.
Also, people from the departments of physical and organic chemistry with whom it was rewarding to have both fun and argument include in addition Martin Magg, Marta Brucka, Marie Humbert-Droz, Alex Zech, Anna-Bea Bornhof, George Humeniuk and others.
Being nowadays a physical chemist with the past of an organic chemist, I wish to acknowledge the efforts of several groups who worked closely with us to synthesize and modify the molecules that I used throughout this thesis. The group of Robert Liska in Vienna is highly appreciated for their quadrupolar compounds discussed in Chapter 3 and a dipolar double- bonded analogue of the triazine system described in Chapter 8. In addition, I am grateful to Zhiquan Li for the synthesis of DA compound from Chapter 3 that allowed unambiguous interpretation of the data in the first proof-of-principle symmetry breaking infrared experiments. Although the way has not always been smooth, I want to acknowledge the group of Daniel Gryko in Warsaw for the synthesis of ADA and A-p-D-p-A quadrupolar rods that are discussed through the Chapters 4-7. I wish to thank Patric Oulevey and Hans Hagemann for their help with steady-state Raman experiments on ADA reported in Chapter 4.
I owe my deepest gratitude to Denis Svechkarev. He synthesized the molecules discussed at the very end of the thesis, in Chapters 8 and 9. But it is not only due to that. During my earliest days of the first year as an undergraduate student, I started working in the lab under his leadership and he became my role model in research. It was his curiosity-driven love
of science that engaged me into scholarly endeavors. He was wholeheartedly devoting his time and knowledge to nurture a potentially perspective scientist from a kid who was motivated to learn chemistry. I am happy to keep our friendship throughout the years and I hope to continue our conjoint endeavors for many years to come.
I owe a special thank you to Chris Rumble who painstakingly went through majority of this thesis giving his valuable remarks and corrections.
Ulf provided insightful remarks about the bits and pieces of the thesis. Denis Svechkarev’s and Christoph Nançoz’s francophone skills made possible the translation, editing and proofreading of the Résumé de la Thèse.
At the conferences, I have met many brilliant and fun people from all over the world with whom it was both enriching to discuss science or to relax in the pub. In no particular order, I wish to mention Joe Fournier, Memo Carpenter, Jiawang Zhou, James Gaynor, Milan Delor, Joseph Mastron, Baxter Abraham, Layla Qasim, Ivan Spector, Rebika Shrestha, Chris Elles, Patrick Kearns, Theo Keane, Josh Slocum, Robert Mackin, Mike McAnally and Sangha Sengupta.
I want to thank people who showed me that there is a whole new world on the snowy slopes and who were my skiing buddies and teachers: Cédric Huwiler, Artem Borin, Anya Goremykina, Achim Merlo, Nico Eckert, as well as Linghzi, Romaine, Magda, Jana, Marketa and many-many others.
I warmly recall all the people with whom our grand poker tournaments became a real blast. My friends, from Ukraine and beyond, always made the life feel wonderful at our short and not-so-frequent reunions during the holidays.
Last but not least, I am deeply indebted to my family, whose unwavering support and encouragement at every and each moment of my life, kept me going and pushing further. They have shown me that there is no obstacle too big to overcome. To be honest, I don’t even know how to go about everything my parents have done for me, but I know for sure that without their unconditional love and support I would not be who I am.
November 2017 Bogdan Dereka
Funding I would like to thank the University of Geneva and Swiss National Science Foundation for generous funding of the research described in this thesis and for providing the excellent organizational framework and infrastructure. Additionally, I acknowledge the financial support from the Swiss Chemical Society and Société Académique de Genève for my participation to several conferences.
his thesis is dedicated to symmetry-breaking charge transfer phenomena. Specifically, the focus is on conjugated multipolar molecules consisting of multiple electron donors (D) arranged symmetrically around a single electron acceptor (A) or vice versa. Upon photoexcitation in the lowest-energy absorption band, these molecules undergo intramolecular charge transfer between donor and acceptor units.
The simplest representatives of the multipolar architectures are the linear quadrupolar A-(p-D)2 or D-(p-A)2 and star-shaped A-(p-D)3 or D-(p-A)3 octupolar molecules. These are the objects of investigation in this dissertation.
The interest around these molecules originates from their large two- photon absorption cross-sections. Two-photon absorption depends quadratically on the incident light intensity, and it can be achieved only with highly intense laser beams.1 After the advent and technological progress in the generation and compression of ultrashort laser pulses, routine experimental implementation of two-photon absorption processes has become possible. It has a number of advantages compared to its linear (one-photon) absorption counterpart. First of all, it allows achievement of a superior spatial resolution because the process is essentially confined within the focal spot of the pulsed laser beam. Combined with the fact that the photon energy is twice lower for the two-photon absorption, this allows to use longer-wavelength and less energetic light to excite chromophores at precise location in the sample.
This characteristic is of great value for fluorescence imaging applications in biological and living samples.2–6 The longer-wavelength light has a larger penetration depth in tissues and causes considerably less degradation on its path.7 Another important practical application of the
two-photon absorption process lies in the realm of photopolymerization and microfabrication processes.8–11 The great virtue of two-photon induced photopolymerization compared to one-photon or electron beam lithography is in its three-dimensional capabilities. Subdiffraction-limit spatial resolution could be achieved due to the nonlinear nature of the two- photon process.8 The three-dimensional spatial control of the two-photon absorption is highly advantageous for 3D optical data storage.12–14 It allows hundreds of layers to be recorded within a standard optical disk thus increasing the information content from many terabytes to petabytes per disk. Additionally, the use of two-photon dyes is promising for photodynamic therapy15 and controlled uncaging during drug delivery.16
For successful implementation of all these processes and techniques, the primary event of the simultaneous absorption of two photons should be highly efficient. It has been demonstrated that large two-photon cross- section is associated with significant changes of electric quadrupolar and octupolar moments upon excitation, which are achieved in multibranched molecules.17–21 Significant progress has been achieved during the last two decades in the development and synthesis of efficient two-photon absorbers.22–26 A generally good understanding of the properties of these multipolar donor-acceptor systems in the electronic ground state has been achieved thanks to numerous investigations on the relationship between the cross-section and multipolar character, their symmetry and one- photon absorption spectra.25,27–32 However, the same cannot be said about their excited-state behavior: whereas the electronic absorption spectra of multibranched molecules generally do not present a significant solvent dependence, as expected for a purely quadrupolar or octupolar ground state, the fluorescence spectra exhibit a strong solvatochromism indicative of a dipolar S1 state.28–30,33–35 Breakup of the symmetry of the excited state was invoked in order to explain this striking behavior.36–40 However, there was no real-time experimental observation of this process and the model was largely theoretical and based on steady-state data. Time-resolved experiments were carried out in order to give a firm ground to the symmetry-breaking hypothesis and to unveil the origin of the process.
However, time-resolved electronic spectroscopy (transient absorption and
fluorescence upconversion) did not provide direct insight into symmetry- breaking phenomena as, in the reported experiments, the excited-state dynamics of multibranched molecules was found to be alike that of their single-branch analogues.33–35,41–45
In this thesis, efforts to obtain a direct and unambiguous picture of intramolecular symmetry breaking processes in multipolar compounds using mainly femtosecond time-resolved infrared spectroscopy are presented. The focus is on the investigation of local vibrational modes located at different positions in the quadrupolar or octupolar molecules and their dynamics upon electronic photoexcitation. A wealth of experimental material is presented and the rationalization of why the particular approaches succeed or fail is discussed. The current experimental work has spurred substantial interest toward understanding of symmetry-breaking processes in these types of molecules.42,44,46–52
The relevance of symmetry-breaking phenomena discussed throughout this dissertation goes far beyond the simple quadrupolar rods and octupolar ‘stars’ described here. The exciton length, or simply the extent of the excitation delocalization and its temporal evolution, is a highly debated topic in conjugated polymers,53,54 supramolecular systems,55–57 macrocyclic arrays,58,59 dendrimers60–62 and biological photosystems.63–68 In all these cases, the question whether the delocalization of the excited state persists long enough to be harnessed or whether it collapses into a localized state due to disorder and fluctuating interactions depends on particular molecular and environmental conditions.
For example, the bacterial photosynthetic reaction center possesses a two-fold symmetry comprising two structurally very similar pathways for the electron transfer to proceed from two closely interacting light- harvesting bacteriochlorophyll molecules, called the special pair, to the bacteriopheophytin monomer.69 However, despite the high level of structural similarity between the two branches, the electron transfer proceeds only along a single pathway.70,71 Various attempts to increase the sequence homology between the two protein subunits, and therefore to increase the symmetry of the reaction center, did not produce any evidence
of the deviation from the unidirectional electron transfer.72,73 It was shown that a significant dielectric asymmetry along the two potential electron transfer pathways inhibits the reaction through one of them, making the reaction center functionally asymmetric.71
A recent review discusses how the coherence can be harnessed to enhance function in chemical and biophysical systems.74 In the language of this review, the term quantum mechanical coherence is used in its broadest sense. For example, the delocalization of the electronic wavefunction in a complex molecule can be viewed as a coherence effect arising from strong resonance interactions between its constituting parts. Such coherences are perceived to be robust and decisive in their roles for function because such states are robust and resist disorder and fluctuations. Delocalized excitonic states of multipolar charge-transfer molecules are a manifestation of such kind of coherence. In the ensuing chapters, we will shed some light about how fragile this coherence is and how well it can resist decoherence phenomena such as structural and solvent fluctuations and disorder.
A Quick Glance at Theory
A theory is something nobody believes, except the person who made it. An experiment is something everybody believes, except the person who made it.
A. Einstein ince neither this thesis, nor any other book of a reasonable size could incorporate all the theoretical details and approaches as well as experimental findings and recent advances concerning the processes discussed throughout this chapter, only a brief and concise description of several notions and phenomena, that are most frequently encountered and hence considered most important for the purpose of this work, are presented.
The structure of this chapter is organized as follows. In the first two parts, we will focus on the elementary photophysical processes relevant to the current work, in the third part, we consider two-photon absorption phenomenon and, in the last part, we shall review a theoretical model of symmetry breaking in multipolar molecules.
1.1 Jablonski Diagram
We are going to discuss the processes that an organic molecule undergoes when in an excited state. The Jablonski diagram presented in Figure 1.1 is a convenient way to proceed with introducing elementary radiative (photon absorption and emission) and nonradiative (internal conversion, intersystem crossing and vibrational relaxation) processes of a
photophysical cycle. No explicit photochemical processes are considered here.
Figure 1.1 | Jablonski diagram for a typical organic molecule. Adapted from Ref. 75.
Absorption. Electromagnetic waves can interact with a molecule promoting it to an excited state. Depending on the energy of the light, it might be, among others, an electronic or vibrational excited state.
Electronic excitation is normally achieved with ultraviolet or visible light, while vibrations are excited with less energetic infrared radiation.
Absorption occurs only if the electric field of the electromagnetic wave interacts with a transient molecular charge distribution characterized by the transition dipole moment 𝑀"→$.
𝑀"→$= Ψ" 𝜇 Ψ$ = 𝜒"𝜒$ 𝜓" 𝜇 𝜓$ (1.1) where 𝜇 is the dipole moment operator, Ψ is the total molecular wavefunction, while 𝜒 and 𝜓 are vibrational and electronic wavefunctions respectively. The square modulus of the integral 𝜒"𝜒$ is called the Franck-Condon (FC) factor and is a measure of the overlap between vibrational wavefunctions of initial and final state at the geometry of the initial state.75,76 The separation of the two integrals in (1.1) is valid within
the Born-Oppenheimer approximation. It follows from the Franck- Condon principle stating that electronic transitions occur on a much faster timescale than nuclear motions and thus should be considered vertical, i.e.
occurring without geometrical changes in the molecule.77
The probability of the transition 𝑖 → 𝑓 is determined by the Einstein coefficient for induced absorption 𝐵./ which is related to 𝑀.
3ℏ/ Ψ" 𝑀"→$ Ψ$ / (1.2) The Einstein coefficient of absorption is also proportional to the absorption spectrum divided by the wavenumber:78
𝐵./∝ 𝜈6.𝜀(𝜈) (1.3) Eq. (1.2) and (1.3) lead to:
𝑀"→$ /∝ 𝜈6.𝜀(𝜈) (1.4)
Once the molecule appears on the excited-state potential energy surface various de-excitation processes come into play.
Emission. Emission of a photon is one of the main possible channels of electronic excited-state deactivation. It occurs due to the coupling of the excited state Ψ$ to the ground state Ψ" via the electronic transition dipole moment in analogy with absorption and is related to the Einstein coefficient for spontaneous emission, 𝐴/., which itself is proportional to the Einstein absorption coefficient:
𝑐< 𝐵./ (1.5)
Although Eq. (1.5) rigorously stands for atoms, the cubic frequency factor is also valid for polyatomic molecules.78 There are two different types of emission – fluorescence and phosphorescence – depending on whether the spin multiplicity of the excited state is preserved or altered upon the radiative transition. However, within the scope of this thesis we will encounter only singlet-singlet fluorescence and therefore we discuss only this type of emission hereafter.
The Einstein coefficient for emission is proportional to the fluorescence spectrum:
𝐴/.∝ 𝐹(𝜈) (1.6)
𝑀$→" / = 𝜈6<𝐹(𝜈) (1.7)
leading to the Strickler-Berg equation79 for the intrinsic decay rate of fluorescence:
𝑘@AB = 23038𝜋𝑐𝑛/ 𝑁F
𝐹(𝜈)𝑑𝜈 𝜈6<𝐹 𝜈 𝑑𝜈
𝜈 𝑑𝜈 (1.8)
which is only strictly valid when the ground and excited states possess the same geometry.
In order to represent correctly absorption and emission spectra together, the absorption spectrum has to be divided by the first power of the wavenumber and the emission one by the third. This representation is called the transition dipole moment representation.78
Internal Conversion. Internal conversion (IC) is a nonradiative transition between two electronic states of the same multiplicity. It occurs as an isoenergetic horizontal transition in the Jablonski diagram (Figure 1.1) from a vibrational level of the higher electronic state to a higher vibrational level of the lower electronic state. Internal conversion from the electronic states higher than S1 generally occurs ultrafast leading to the population of the lowest singlet excited state from where the photochemistry and light emission occurs (Kasha’s rule80). However, with the advent of ultrafast spectroscopy, which is able to track the fate of higher excited states down to few fs time resolution, it became evident that this statement is valid statement only in the long-time limit.
From experimental results, it has been concluded that, for example, for aromatic hydrocarbons the radiationless S1→S0 transition is negligible if the energy difference ΔE between S1 and S0 states is larger than 60 kcal/mol but it becomes increasingly more important when the energy
difference decreases.81 These observations were summarized by the relationship
𝑘HI = 10.<𝑒6LMN (1.9) which shows the dependence of the rate constant on the energy gap between lowest singlet excited and ground states and which is referred to as the energy-gap law.82
This law has been successfully applied extensively to the internal conversion of various classes of compounds, e.g. carotenoids,83 xanthene dyes,84 azulene85 and linear polyenes,86 aromatic thiones87 and radicals88 as well as to charge transfer processes of numerous metal complexes89 and in many other systems.90
In addition to the energy gap between electronic states, large displacements between potential energy surfaces lead to large FC factors facilitating an efficient radiationless transition (Figure 1.2).81 In fact, the energy-gap law is not obeyed when the energy surfaces couple strongly or when large rearrangements take place, e.g. in vicinity of state crossings.
Figure 1.2 | Effect of the energy gap and relative displacement of the potential energy surfaces on the Franck-Condon factors for a radiationless transition. Adapted from Ref. 81.
Intersystem Crossing. Intersystem crossing (ISC) is a radiationless process between two isoenergetic vibrational levels of electronic states of different multiplicities. The most encountered scenario for organic molecules is a transition between a molecule in the zero vibrational level of the S1 state to the isoenergetic vibrational level of the Tn triplet state from where vibrational relaxation and internal conversion in the triplet manifold bring it to the zero vibrational level of the T1 state. In principle, such a singlet-triplet transition is forbidden, but if mixing of spin states due to magnetic interactions is available, it might become allowed. An electronic transition that involves a change of spin angular momentum requires some coupling with another source of angular momentum that can both trigger the transition and allow conservation of the total angular momentum and energy of the two interacting systems. For organic molecules, the most important interaction that couples two spin states and that provides a means of conserving the total angular momentum of the system is the coupling of the electron spin with the orbital angular momentum (spin- orbit coupling).77
The rates of the ISC process can be fast enough to compete with other de-excitation pathways, such as fluorescence and internal conversion. The El-Sayed’s rule91 states that the probability and the rate of a spin-forbidden radiationless transition is much larger when it involves two orbital configurations of different type (such as 1p-p* and 3n-p*, for example) when compared to the orbital configurations of the same type (such as
1p-p* and 3p-p*). The spin-orbit coupling increases in the presence of atoms with high nuclear charge (heavy atoms) capable of causing electrons to accelerate strongly and thereby create a large magnetic moment as the result of their orbital motion.77 It causes so called internal and external heavy-atom effects which promote ISC rates.75 Finally, the rate of this process is inversely proportional to the energy gap between the S1 and the triplet state to which intersystem crossing actually occurs (i.e. T1 or some upper triplet Tn).81
Vibrational Relaxation (VR). The Franck-Condon nature of the electronic excitation of a polyatomic molecule dictates that some vibrational modes are excited during the electronic transition thus
imparting it a vibronic character. Since the FC factors differ largely for various normal modes in the molecule, only some – Franck-Condon active – modes end up being populated. These high-frequency modes transfer the energy rather quickly to the low-frequency part of vibrational spectrum through anharmonic coupling. This process is usually very fast taking place on a subpicosecond timescale and is called intramolecular vibrational redistribution (IVR). The population of the intramolecular low-frequency modes (LFM) influences (through anharmonic coupling) the frequencies and intensities of the high-frequency vibrations often leading to their redshift. This gives a characteristic shape (redshift and asymmetrical broadening on the low-frequency side) to a vibrationally hot band (Figure 1.3).92,93
Figure 1.3 | Simulated high-frequency infrared absorption bands of different vibrational temperatures. A. Absorption spectrum A(T). B. Difference spectrum ΔA(T) = A(T) – – A(300 K). The plots are taken from Ref. 92.
This thermalization within the molecule itself leads to the establishment of a Boltzmann distribution of the LFM population and is followed by the vibrational energy transfer to the solvent called vibrational cooling (VC). It is often stated that IVR occurs much faster than VC and
the two are well separated in time.94 In the Landau-Teller description of vibrational energy relaxation in liquids, the rate of relaxation is indeed proportional to the square of the coupling multiplied by the power spectral density of the time correlation function describing the fluctuating forces exerted by solvent molecules on the solute vibration of interest.95,96 The latter term corresponds to friction exerted by the solvent on solute vibrations. Since the spectral density for molecular liquids decreases exponentially with increasing frequency, the friction is the greatest in the low-frequency part of vibrational manifold. This fact underlies the conventional wisdom that VC occurs primarily from the low-frequency modes of solute to the low-frequency modes of solvent. This indeed necessitates IVR to be faster than VC. However, since IVR occurs on a multitude of timescales from tens of femtoseconds97 to 1-2 ps,98 its slower components might overlap with the fastest part of intermolecular vibrational cooling and the two processes might be entangled in time.98 Additionally, in a few studies, solvent was evidenced to facilitate99,100 or to hinder IVR.101 Therefore, the IVR in condensed phase is not necessarily a purely intramolecular process.
1.2 Solvatochromism and Solvation
Photoexcitation of a molecule leads to a redistribution of the electronic density. Quite often, it also leads to the change of its permanent dipole moment µ. In liquid solution, this change might lead to notable effects on its absorption and fluorescence spectra. A comprehensive treatment of this topic is presented in Ref. 102. In polar solvents, the electric field of the local environment interacts with the solute dipole moment and alters the position of the energy levels and therefore the transition frequencies.
The solvatochromic shifts describe how the transition linking a relaxed state (e.g., S0) with a Franck-Condon state (e.g., unrelaxed S1) varies from solvent to solvent. It is essential to split the solvent polarities into two parts (dispersive and dipole-dipole interactions) depending on the timescale of the response to the instantaneous change of the solute dipole moment.
Dispersion solute-solvent interaction depends on the polarizability of the solvent, which is reflected by the refractive index 𝑛. This type of non- specific interaction describes the correlation in the electronic density redistribution in solute and solvent molecules. The electronic polarizability function103
𝑓(𝑛/) = 2(𝑛/− 1)
(2𝑛/+ 1) (1.10)
quantifies the solvent susceptibility to this type of interaction.104 The position of the absorption or emission band plotted versus 𝑓(𝑛/) allows the dispersive stabilization to be estimated.
Another important type of interaction is the dipole-dipole interaction that is determined by the solvent dipole reorientation function (Onsager dipolar polarizability103):
∆𝑓 = 𝑓 𝜀 − 𝑓 𝑛/ =2(𝜀 − 1)
(2𝜀 + 1)−2(𝑛/− 1)
(2𝑛/+ 1) (1.11)
The difference between absorption (𝜈A) and fluorescence (𝜈$) positions (e.g. spectral maxima or first moments), so-called Stokes shift, due to dipolar interactions can be represented by the Lippert-Mataga equation:102
𝜈A− 𝜈$ = 2 ℎ𝑐
𝑎< ∆𝑓 + 𝑐𝑜𝑛𝑠𝑡 (1.12) where ∆𝜇ST is the magnitude of change of the permanent electric dipole moment between the ground and first singlet excited states, and 𝑎 is the radius of the cavity that a chromophore occupies in the solvent. However, it is strictly valid only for an ideal two-level system. It is usually better to treat the solvatochromism in absorption due to dipole-dipole interactions by
∆𝐸 = −𝜇S(𝜇T− 𝜇S)
𝑎< ∆𝑓 (1.13)
This equation, in principle, allows to determine quantitatively the change of the solute dipole moment upon photoexcitation. However, the slope of this dependence vs. the Onsager function is often more meaningful than
extraction of ∆𝜇ST because the reliable estimation of the cavity radius is not trivial. Although nowadays, it is not a problem to estimate the dimension of the molecule by quantum-chemical calculations, but the solvatochromic model assumes the located solute point dipole in the center of a spherical cavity in solvent continuum. Realistically, very few chromophores have a molecular shape close to spherical and empirically determined correction
‘shape’ factors are necessary.102 Additionally, the off-center position of the dipole in the cavity leads to deviations from the model.105
The dipolar solvation is a dominating interaction for solutes undergoing an appreciable change of the dipole moment in polar solvents.
However, contrary to the dispersive stabilization, which might be considered instantaneous (or at least occurring on the timescale of photon absorption), it involves physical reorientation of the solvent molecules and therefore is much slower. Figure 1.4 illustrates the concept of dynamic solvation for a typical chromophore whose dipole moment enlarges upon absorption. Right after the absorption, the solvent arrangement is identical to the ground state – 𝑃 0 . The solvent dipoles reorient on hundreds of femtoseconds to picoseconds leading to an increasing redshift of the fluorescence band and eventually reach the equilibrium configuration – 𝑃(∞). This time-dependent fluorescence Stokes shift (TDFSS) could be used as a sensitive probe of solvation dynamics. If the fluorescence maximum or first moment is tracked in time from 𝑃 0 to 𝑃(∞) with sufficient time resolution, the solvent correlation function 𝐶(𝑡) can be determined
𝐶(𝑡) = 𝑃 0 − 𝑃(𝑡)
𝑃 0 − 𝑃(∞) (1.14)
The temporal decay of this quantity is a measure of solvation dynamics.
It is a nonexponential function,106,107 however, it is conventionally fit with multiple exponents and a Gaussian.108–110 Appendix 2 (Table A2.6) lists the values extracted from multiexponential fitting for multiple solvents.108,109 These values will be of great use throughout the following chapters.
Typically, for organic solvents at room temperature, an extremely fast (tens of fs) response is observed at the beginning, representing so-called inertial
part of the solvation due to librational motion of solvent molecules in the first few solvation shells, and slower (ps to tens of ps) response represents diffusive solvation due to rotational and translational motion. Since for a typical organic fluorophore the excited-state lifetime is of the order of several nanoseconds, and the reorientation dynamics are few orders of magnitude faster, the steady-state fluorescence spectrum essentially coincides with the fully relaxed emission from 𝑃(∞).
Figure 1.4 | Schematic representation of the time-dependent fluorescence Stokes shift (TDFSS) and the concept of dynamic solvation. Motion of the representative point of the system on the potential energy surfaces (A) and corresponding time-resolved fluorescence spectra (B). The arrows represent dipole moments of the solute and solvent molecules at four limiting time points. The picture is taken from Ref. 111.
1.3 Two-Photon Absorption
Two-photon absorption (TPA) is a third-order nonlinear optical process that involves a simultaneous interaction of a molecule with two photons.112,113 Typically, when TPA occurs, a single photon is nonresonant with any electronic transition in the molecule but the sum of the two is resonant with some available transition. Although the nonresonant condition for a single photon is not mandatory, it is difficult to disentangle
one- and two-photon transitions in this case. The word instantaneous is crucial in the definition above, as it allows to differentiate TPA from excited-state absorption (ESA) that involves sequential absorption of the photons. TPA scales with the square of light intensity in contrast to the linear dependence for one-photon absorption (OPA). Therefore, it occurs at high instantaneous photon densities such as those available in focused femtosecond beams.
The attenuation of a beam of light with intensity 𝐼 over distance 𝑧 in a medium due to two-photon absorption is given by25
𝜕𝑧= −𝑁𝛼/𝐼/= −𝑁𝜎(/)𝐹𝐼 (1.15) where 𝐹 = 𝐼/ℎ𝜈 is the photon flux, 𝑁 is the number of molecules per unit volume, and 𝛼/ is the molecular coefficient for TPA while 𝜎(/) is the molecular TPA cross-section. For a plane-polarized light, the 𝜎(/) value at the maximum of a Lorentzian-shaped band corresponding to the transition between the ground state 𝑔 and a final state 𝑓 is given by1
𝜎dAe(/) =2𝜋ℎ𝜈/(𝑛/+ 2)f 3f𝜀g/𝑛/𝑐/
Γ 𝑆$S (1.16)
where Γ is the half-width at half-maximum of the band, and 𝑆$S is1,114 𝑆$S=1
+ 𝜇S"/ 𝜇"$/ (𝐸S"− ℎ𝜈)/
(1.17) where 𝜇mn is the amplitude of the transition dipole moment induced by the electric field of the wave whose frequency matches the energy gap between any 𝑘 and 𝑙 states, and ∆𝜇S$ is the change in the permanent dipole moment in the 𝑓 state relative to the 𝑔 state. 𝐸S" is the energy gap between the ground state and intermediate state 𝑖. The appearance of the intermediate state 𝑖 in this equation is very important and is explained below.
Two different cases, corresponding to centrosymmetric quadrupolar and non-centrosymmetric dipolar molecules, are considered now (Figure 1.5). For centrosymmetric molecules, the first term in brackets (so- called dipolar term) in Eq. (1.17) disappears since the permanent dipole
moments in both states 𝑔 and 𝑓 equal zero. The TPA cross-section can be approximated by (𝐶 is a constant):
𝜎dAe(/) ≈ 𝐶 𝜇S"/ 𝜇"$/
(𝐸S"/ℎ𝜈 − 1)/Γ (1.18)
Both ground and final states are symmetric with respect to the center of inversion, whereas the intermediate state is antisymmetric. The transitions are one-photon electric-dipole allowed for both 𝑔→𝑖 and 𝑖→𝑓 transitions.
For TPA, the frequency 𝜈 is out of resonance with both these transitions, but it creates a virtual state that is a superposition of |𝑔 and |𝑖 , in which the induced polarization is detuned from that in the intermediate state |𝑖 by a frequency difference that corresponds to the energy ∆ = 𝐸S"− ℎ𝜈.
This virtual state is, of course, a nonstationary state of the system that exists only while the molecule experiences the field of the first photon, but the transient presence of |𝑖 with ungerade parity in the superposition allows the second photon of frequency 𝜈 to induce an electric dipole transition to the final gerade state |𝑓 .25,115 The 𝑔→𝑓 transition is thus allowed in TPA and forbidden in OPA. This reversal of the selection rules in OPA and TPA is general for all centrosymmetric molecules.
It is worth highlighting that this ‘photon’ picture is chosen here because it provides the most intuitive explanation of why the parity of the initial and final states is identical for TPA, whereas they should be of opposite parity for OPA. Rigorously speaking, it is suboptimal to discuss the nonlinear optical phenomena in terms of photons, but rather the sequential interactions between the matter and electric fields should be used.
In dipolar non-centrosymmetric molecules, the 𝑔→𝑓 transition is OPA-allowed and the dipolar term in Eq. (1.17) is not zero. In this case,
|𝑓 plays the role of |𝑖 and the transition is present in both linear and two- photon absorption. The second term in Eq. (1.17) (so called two-photon term) makes a smaller contribution in dipolar chromophores because it relates to higher states (|𝑖 lies above |𝑓 and ∆ > ℎ𝜈). If, however, upper and not the lowest excited states are considered so that there is some state
|𝑖 below |𝑓 , then ∆ < ℎ𝜈, and assuming ∆𝜇S$ = 𝜇S$, which is valid for
chromophores with a substantial charge transfer upon photoexcitation, the dipolar term in Eq. (1.17) is intrinsically smaller than the two-photon term for centrosymmetric systems. This is one of the reasons why dipolar molecular architectures are less efficient two-photon absorbers than their multipolar analogues. The magnitudes 𝜇S"/ and 𝜇S$/ are proportional to the corresponding one-photon oscillator strengths and can be computed from the linear absorption spectrum. However, 𝜇"$/ is rarely determined experimentally and therefore, the approach toward the synthesis of efficient two-photon absorbers is still largely empirical.25 Addition of the donors and acceptor groups to conjugated systems increases the displacement of charge and results in enhanced transition dipole moments.
Multichromophoric and multipolar assemblies also often lead to better efficiency of the TPA process.17,22
Figure 1.5 | Energy level diagrams for the essential states in centrosymmetric quadrupolar and non-centrosymmetric dipolar chromophores. The diagram is general to the lowest TPA transitions in any centrosymmetric or non-centrosymmetric molecule. Adapted from Ref. 25.
1.4 Painelli-Terenziani Symmetry Breaking Model
The concept of symmetry breaking in multipolar compounds was treated theoretically by the group of Prof. Anna Painelli and Prof.
Francesca Terenziani within the essential-state model formalism.36–39 This model is briefly presented below and is referred to as the Painelli- Terenziani SB model hereafter.
Essential-state models offer an efficient theoretical tool to investigate optical properties of conjugated molecules composed of several electron donating (D) and accepting (A) groups linked by p-bridges. These compounds undergo charge-transfer transition(s) upon photoexcitation in the absorption band(s) at low energy. Charge resonance between D and A moieties governs their low-energy physics. In chemical language, this phenomenon is described using several resonating forms as basis states.
Mulliken was the first to apply this formalism116 to describe the optical spectra of dipolar D-p-A chromophores, for which two states are necessary: neutral DA and zwitterionic D+A-.
For quadrupolar chromophores, three resonating states are necessary:
D+A-D⟷DAD⟷DA-D+ (Figure 1.6A). Although we are explicitly considering the DAD structure here and hereafter, the same discussion applies to ADA chromophores as well, provided that the role of D and A is interchanged. The DAD structure is designated as |𝑁 (neutral state), whereas |𝑍. and |𝑍/ are the two degenerate zwitterionic states. The energy difference between the zwitterionic states and the neutral state is defined as 2𝜂, so that for positive 𝜂, the neutral form is lower in energy than zwitterionic ones. The mixing between the states is described by an off-diagonal matrix element of the Hamiltonian 𝑁 𝐻 𝑍. = 𝑁 𝐻 𝑍/ =
= − 2𝑡, that measures the probability of electron transfer from D to A and backward. The direct mixing between 𝑍. and 𝑍/ is set to zero, because represents the hopping between non-nearest neighbor sites. The dipole moments of the two zwitterionic states have the same magnitude 𝜇g, but point in the opposite directions. This is the only matrix element of the dipole moment operator that is considered in the chosen basis.
The zwitterionic states can be combined in the following symmetric and antisymmetric wavefunctions: |𝑍v = 1/ 2 |𝑍. + |𝑍/ and |𝑍6 =
= 1/ 2 |𝑍. − |𝑍/ . Only |𝑁 and |𝑍v can mix with each other since both are even, whereas |𝑍6 is odd. In this symmetrized basis
|𝑁 , |𝑍v , |𝑍6 , the following operators are defined:
𝜌 = 0 0 0 0 1 0 0 0 1
, 𝛿 = 0 0 0 0 0 1 0 1 0
, 𝜎 = 0 1 0 1 0 0 0 0 0
Here, 𝜎 is the mixing operating for the two gerade states, 𝜌 is the iconicity measuring the average charge on the central A site, while 𝛿 measures the unbalance of the charge on the two external D units. The electronic Hamiltonian and dipole operator can be written as:
𝐻Tn= 2𝜂𝜌 − 2𝑡𝜎 (1.20)
𝜇 = 𝜇g𝛿 (1.21)
The eigenstates can be obtained:
|𝑔 = 1 − 𝜌|𝑁 + 𝜌|𝑍v (1.22)
|𝑐 = |𝑍6 (1.23)
|𝑒 = 𝜌|𝑁 − 1 − 𝜌|𝑍v (1.24)
where 𝜌 measures the weight of |𝑍v in the ground state, or equivalently it defines the amount of charge separation in the ground state, and therefore the quadrupolar moment of the molecule. It is determined by the model parameters:
𝜌 = 0.5(1 − 𝜂/ 𝜂/+ 4𝑡/) (1.25) The transition dipole moments and transition frequencies, i.e. the relevant quantities for spectroscopy, can be expressed in terms of 𝜌:
ℏ𝜔S} = 𝐸}− 𝐸S = 2𝑡 1 − 𝜌
𝜌 , 𝜇S} = 𝑔 𝜇 𝑐 = 𝜇g 𝜌 (1.26) ℏ𝜔ST = 𝐸T− 𝐸S = 2𝑡 1
𝜌(1 − 𝜌), 𝜇ST = 𝑔 𝜇 𝑒 = 0 (1.27) ℏ𝜔}T = 𝐸T− 𝐸} = 2𝑡 𝜌
1 − 𝜌, 𝜇}T = 𝑐 𝜇 𝑒 = −𝜇g 1 − 𝜌 (1.28) Figure 1.6 summarizes the electronic three-state model for quadrupolar chromophores. From Eq. (1.26)-(1.28), it follows that odd |𝑐 state is one- photon accessible from the ground state, whereas the transition to the even
|𝑒 state is one-photon forbidden (but two-photon allowed). On the other hand, |𝑒 is one-photon accessible from |𝑐 state.