Thesis
Reference
Photoinduced electron transfer from a fundamental understanding to potential applications
BANERJI, Nathalie Renuka
Abstract
Although the transfer of an electron from a donor to an acceptor after one of them has been electronically excited by the absorption of light appears to be a very simple reaction, there are still many open questions concerning the detailed mechanism of photoinduced electron transfer. It is nevertheless a fascinating and very important reaction, given its key importance in photosynthesis and many modern approaches to solar energy conversion. The objective of this PhD thesis was thus to use ultrafast, femtosecond-resolved spectroscopy in order to gain a better insight to photoinduced electron transfer occuring for closed-shell organic molecules in liquid solution, in particular where the relative geometry of the reaction partners is concerned. The investigations span a large variety of electron donor-acceptor systems, ranging from the intramolecular to the bimolecular case and from simple model systems to complex architectures with potential apllications in solar energy coversion.
BANERJI, Nathalie Renuka. Photoinduced electron transfer from a fundamental
understanding to potential applications . Thèse de doctorat : Univ. Genève, 2009, no. Sc.
4111
URN : urn:nbn:ch:unige-39639
DOI : 10.13097/archive-ouverte/unige:3963
Available at:
http://archive-ouverte.unige.ch/unige:3963
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
Photoinduced Electron Transfer
From a Fundamental Understanding to Potential Applications
THÈSE
présentée à la Faculté des sciences de l’Université de Genève pour obtenir le grade de Docteur ès sciences, mention chimie
par
Natalie Renuka BANERJI
de
Vienne (Autriche)
Thèse N
o4111
GENÈVE
Atelier ReproMail
2009
Ce travail de thèse a été réalisé au sein du Département de Chimie Physique de l’Université de Genève (Suisse) sous la direction du Professeur Dr.
Eric Vauthey. Je tiens à le remercier de m’avoir accueilli dans son groupe et pour l’opportunité d’y mener de stimulantes recherches scientifiques.
Ma gratitude va également au Dr. Dimitra Markovitsi du Laboratoire Francis Perrin de Saclay (France) et au Professeur Dr. Jacques-E. Moser de l’Ecole Polytechnique Fédérale de Lausanne (Suisse), pour avoir accepté de s’engager comme experts lors de la soutenance et à ce titre de lire ce mémoire.
Je tiens à remercier également tout ceux avec qui j’ai pu collaborer pendant cette thèse, en particulier mes collègues de l’Université de Genève et du Max-Born Institut à Berlin. Un grand merci au groupe du Professeur Dr. Stefan Matile pour une collaboration particulièrement enrichissante autour d’un projet fantastique.
J’adresse mes remerciements au Dr. Francine Dreier pour ses précieux conseils lors de la rédaction du mémoire de thèse. Je remercie tout particulièrement tout mes proches dont les conseils et le soutient m’ont guidés tout au long de cette thèse, notamment ma Mère et Pierre-Yves.
To all those who touched my life and left a mark of happiness – in the past, present and future
‘You see Momo,' he (Beppo Roadsweeper) told her one day, 'it's like this. Sometimes, when you've a very long street ahead of you, you think how terribly long it is and feel sure you'll never get it swept.' 'And then you start to hurry,' he went on. 'You work faster and faster, and every time you look up there seems to be just as much left to sweep as before, and you try harder, and you panic, and in the end you're out of breath and have to stop - and still the street stretches away in front of you. That's not the way to do it.'
'You must never think of the whole street at once, understand? You must only concentrate on the next step, the next breath, the next stroke of the broom, and the next, and the next. Nothing else.'
'That way you enjoy your work, which is important, because then you make a good job of it. And that's how it ought to be.'
Momo (1973), by Michael Ende
Table of Contents
Table of Contents
1 Introduction ... 2
2 Light, Matter and Electron Transfer ... 8
2.1 Electromagnetic Radiation ... 8
2.1.1 The Nature of Light across History... 8
2.1.2 Light Propagation in Vacuum ... 9
2.1.3 The Electromagnetic Spectrum ... 11
2.1.4 Electromagnetic Propagation in a Dielectric Medium ... 11
2.1.5 Absorption of Electromagnetic Radiation ... 13
2.1.6 Spectroscopy ... 15
2.2 Electronic Absorption Spectroscopy ... 16
2.2.1 Organic Closed-Shell Molecules ... 17
2.2.2 Selection Rules ... 17
2.2.3 Molecules in the Condensed Phase... 19
2.3 Excited State Relaxation ... 21
2.3.1 Vibrational, Geometry and Solvent Relaxation ... 22
2.3.2 Internal Conversion... 24
2.3.3 Fluorescence ... 25
2.3.3.1 The aspect of a fluorescence spectrum ... 25
2.3.3.2 The rate of fluorescence... 26
2.3.4 Intersystem Crossing and Phosphorescence... 29
2.4 Quenching of the Excited State ... 29
2.4.1 Static and Dynamic Quenching... 31
2.4.2 Excitation Energy Transfer... 32
2.4.2.1 The Förster mechanism of EET... 33
2.4.2.2 The Dexter mechanism of EET... 34
2.4.3 Photoinduced Electron Transfer ... 34
2.5 Electron Transfer Theory... 36
2.5.1 Energetics of Photoinduced ET... 36
2.5.2 Adiabaticity of Photoinduced ET ... 38
2.5.3 The Classical Marcus-Hush Theory ... 39
2.5.4 The Semiclassical Marcus Theory... 44
2.5.5 From Non-Adiabatic to Adiabatic ET... 46
2.5.6 Kramers Theory for Adiabatic ET... 49
2.5.7 The Classical Marcus-Sumi Theory... 51
2.5.8 Semiclassical Hybrid Models ... 54
3 Ultrafast Spectroscopy ... 56
3.1 Pulsed Lasers ... 56
3.1.1 Properties of Optical Pulses ... 56
3.1.2 The Laser ... 61
3.1.3 Generation of Optical Pulses... 63
3.2 Nonlinear Optical Effects ... 65
3.2.1 Second Order Nonlinear Effects ... 66
3.2.2 Third Order Nonlinear Effects ... 68
3.3 Steady-State Spectroscopy... 70
3.3.1 Solvatochromism... 72
3.3.2 Fluorescence Quantum Yield Measurements... 73
3.3.3 Stern-Volmer Plots... 74
3.4 Time-Resolved Fluorescence Spectroscopy... 74
3.4.1 Single Photon Counting ... 75
3.4.2 Fluorescence Up-Conversion ... 76
3.4.3 Fluorescence Anisotropy ... 79
3.4.3.1 The temporal decay of anisotropy ... 80
3.4.3.2 The initial anisotropy (r0) ... 81
3.4.3.3 The analysis of fluorescence anisotropy data ... 82
3.5 Transient Absorption Spectroscopy ... 83
3.5.1 The Principle of TA Spectroscopy ... 83
3.5.1.1 Pump-probe spectroscopy ... 83
3.5.1.2 The detection scheme for TA... 84
3.5.1.3 The contributions to ΔA... 87
3.5.2 Experimental Setup for Femtosecond-Resolved TA... 89
3.5.2.1 Generation of tunable 480-700 nm pump pulses... 91
3.5.2.2 Generation of 400 nm pump pulses... 93
3.5.2.3 Generation of white light probe pulses ... 95
Table of Contents
3.5.2.4 Generation of a tunable 480-700 nm probe beam ... 97
3.5.2.5 The pump-probe crossing in the sample ... 99
3.5.2.6 Setup for probing in the IR region ... 100
3.5.3 TA Data Treatment and Analysis... 102
3.5.3.1 Analysis of single wavelength dynamics ... 102
3.5.3.2 Data acquisition for TA spectra ... 103
3.5.3.3 Data analysis of TA spectra ... 103
3.5.3.4 Determination of the chirp polynomial ... 106
3.5.4 TA and Photoinduced Electron Transfer... 108
3.5.4.1 A simple three-state model for photoinduced ET ... 109
3.5.4.2 Temporal deconvolution of CS and CR dynamics ... 110
3.5.4.3 Spectral TA signatures of the S1 and CS states... 111
3.5.5 Appendices... 112
3.5.5.1 MATLAB Routine 1 ... 112
3.5.5.2 MATLAB Routine 2 ... 115
4 Results I. The Intramolecular Case...120
4.1 Linked Perylene-Dimethylaniline Derivatives... 121
4.1.1 Introduction ... 122
4.1.2 Steady-State Results... 124
4.1.3 Time-Resolved Fluorescence Results ... 129
4.1.3.1 TCSPC experiments ... 129
4.1.3.2 Fluorescence up-conversion experiments... 132
4.1.3.3 Protonation of PeDMA and CNPeDMA... 138
4.1.4 Transient Absorption Results... 140
4.1.4.1 Pe-4C-DMA ... 140
4.1.4.2 PeDMA... 142
4.1.4.3 CNPeDMA ... 149
4.1.5 Discussion... 151
4.1.5.1 Comparison of the CS dynamics in the three compounds.. 151
4.1.5.2 Comparison with Pe and CNPe in pure DMA ... 153
4.1.6 Conclusion... 156
4.2 Linked Porphyrin-NDI Derivatives... 157
4.2.1 Introduction ... 158
4.2.2 Steady-State Absorption Results ... 161
4.2.3 Transient Absorption Results... 164
4.2.3.1 TA spectra of tetra-NDI ...164
4.2.3.2 TA spectra of FbTPP ...170
4.2.3.3 TA spectra of ZnTPP...172
4.2.3.4 TA spectra of FbTPP-NDI in TOL ...174
4.2.3.5 TA spectra of FbTPP-NDI in DCM in BzCN ...181
4.2.3.6 TA spectra of ZnTPP-NDI in TOL and Bz ...185
4.2.3.7 TA spectra of ZnTPP-NDI in DCM ...188
4.2.4 Conclusion ... 192
5 Results II. The Bimolecular Case ... 196
5.1 Introduction ... 197
5.1.1 Photoinduced Bimolecular ET and Diffusion... 197
5.1.1.1 The early Rehm-Weller experiments ...197
5.1.1.2 The hypothesis of long-distance highly exergonic CS ...200
5.1.1.3 The hypothesis of electronically excited CS products ...204
5.1.1.4 The nature of ion pairs formed by bimolecular CS...206
5.1.1.5 Spectroscopic evidence of different ion pairs ...209
5.1.2 Direct CT Excitation of DACs... 211
5.1.2.1 TIP formation in DACs ...212
5.1.2.2 Spectroscopic identification of the TIPs formed in DACs ....213
5.1.2.3 The CR dynamics of DACs...215
5.2 Free Ion Dissociation in the Pe/DCB System... 217
5.2.1 Results and Discussion... 219
5.2.1.1 Identification of the TA-IR bands ...219
5.2.1.2 Time profiles of the TA-IR radical ion band intensity ...221
5.2.1.3 TA-IR band shape analysis ...224
5.2.1.4 Additional results with the Pe/DCE system ...228
5.2.2 Conclusion ... 230
5.3 Different Ion Pairs in the MePe/TCNE System... 230
5.3.1 Results ... 232
5.3.1.1 Steady-state measurements ...232
5.3.1.2 TA-vis measurements ...232
5.3.1.3 TA-IR measurements ...237
5.3.1.4 Polarization-sensitive TA-IR measurements...243
5.3.2 Discussion... 244
Table of Contents
5.3.2.1 Identification of different ion pairs... 244
5.3.2.2 Origin of the spectral differences... 246
5.3.2.3 Interpretation of the anisotropy ... 247
5.3.2.4 A new reaction scheme... 249
5.3.2.5 Comparison to existing theories... 251
5.3.3 Outlook... 253
5.3.4 Conclusion... 254
5.4 Anisotropy Measurements with DACs... 255
5.4.1 Results and Discussion... 257
5.4.1.1 Steady-state absorption spectra... 257
5.4.1.2 Single wavelength TA dynamics... 258
5.4.1.3 TA spectra for PMDA/methylbenzene DACs... 262
5.4.1.4 TA spectra for the PMDA/Py DAC ... 269
5.4.2 Discussion and Outlook ... 272
5.4.2.1 DAC geometry ... 272
5.4.2.2 Experimental considerations ... 275
5.4.3 Conclusion... 276
6 Results III. Towards Applications ...278
6.1 Introduction... 279
6.1.1 Natural and Artificial Photosynthesis ... 279
6.1.1.1 Plant photosynthesis ... 279
6.1.1.2 Mimicking photosynthesis ... 280
6.1.1.3 Self-assembling multichromophoric NDI systems ... 283
6.1.2 Supramolecular Organic Photovoltaics... 286
6.1.2.1 The bulk heterojunction concept ... 287
6.1.2.2 Photovoltaics with small organic molecules... 288
6.1.2.3 Zipper assembly on gold surfaces ... 291
6.2 The Photophysics of NDI/POP Systems... 294
6.2.1 Steady-State Results... 295
6.2.2 Time-Resolved Fluorescence Results ... 298
6.2.3 Transient Absorption Results... 300
6.2.3.1 The red NDI systems ... 301
6.2.3.2 The blue NDI systems... 307
6.2.3.3 TA anisotropy measurements... 312
6.2.4 Discussion... 319
6.2.4.1 Nature of the CSS ...319
6.2.4.2 CS dynamics ...320
6.2.4.3 CR dynamics ...322
6.2.4.4 Excitation energy hopping and exciton annihilation ...324
6.3 NDI/POP Systems in Organized Media ... 325
6.3.1 B8 in LUV Membrane ... 326
6.3.2 NDI Molecules on Gold Nanoparticles ... 328
6.3.2.1 Bare gold nanoparticles...329
6.3.2.2 NDI-functionalized gold nanoparticles ...330
6.3.2.3 Zipper assembly on gold nanoparticles ...336
6.4 NDI/OPE Systems in Solution ... 338
6.4.1 Steady-State Results ... 340
6.4.2 Time-Resolved Fluorescence Results ... 342
6.4.3 Transient Absorption Results... 344
6.4.3.1 400 nm excitation of R10...344
6.4.3.2 530 nm excitation of R10...346
6.4.3.3 400 nm excitation of B10...348
6.4.3.4 620 nm excitation of B10...349
6.4.3.5 TA anisotropy measurements ...351
6.4.4 Discussion... 354
6.4.4.1 Excitation energy transfer ...354
6.4.4.2 Charge separation pathways ...355
6.4.4.3 Charge recombination dynamics ...358
6.4.4.4 Comparison to systems with a POP scaffold ...360
6.5 Conclusion... 360
7 General Conclusions... 366
Appendix One: List of Publications ... 372
Appendix Two: Résumé de la Thèse ... 374
References ... 378
Chapter One
Introduction
1 Introduction
During the past four years, I investigated photoinduced electron transfer (ET). As the name suggests, this involves the transfer of an electron form a donor (D) to an acceptor (A), after one of them has been brought to an electronically excited state by the absorption of light. It can be considered as one of the simplest chemical reactions, as no bonds are broken or formed. Two questions may spring to mind. First, why would it be it interesting to study photoinduced ET during four years? Second, how comes that there are still things left to study concerning such a simple reaction?
The first question can be answered by the fact that photoinduced ET is a key step in photosynthesis, which allows converting solar light to chemical energy. Given the ever-growing global demand for energy, it is not surprising that research interest in understanding and mimicking photosynthesis is growing together with the interest in excited state ET. Beyond the applications of this reaction in solar energy conversion to produce fuels and electricity, it also plays an important role for example in the design of a variety of optoelectronic devices, in the mechanism of vision, in photo- polymerization and in photography.
To answer the second question, the rate of photoinduced ET must be invoked. It is indeed usually an ultrafast reaction occurring on a femtosecond or picosecond time scale. Considering that one femtosecond compares to one second as five minutes compare to the age of the Earth, it is by no means trivial to explore a reaction occurring with so short a time constant. It has indeed only become possible to directly follow excited state ET processes when appropriate ultrafast spectroscopic techniques were developed starting in the 1980s. As those involve laser pulses with femtosecond duration, their accessibility goes hand in hand with advances in laser technology. Although the relatively new experimental methods certainly brought insight to photoinduced ET, they also raised new questions and revealed discrepancies with already existing ET theories, which now need to be understood. Photoinduced ET turned out to be more complex than it might initially appear and so, yes, there is still much to be learned about this reaction.
The objective of the current thesis was thus to continue the extensive efforts of Professor Eric Vauthey’s research group to shed more light on the precise mechanism of photoinduced ET occurring for organic molecules in liquid solution. As a tool for those investigations, steady-state and femtosecond-resolved spectroscopy was used. In particular, the influence of a number of parameters on the rate of ET was studied. Those include the driving force, the
1 Introduction
solvent and intramolecular rearrangements brought about by the redistribution of electron density during ET, and the electronic coupling. All those factors depend on the relative geometry within the D-A system during ET, thus on the distance and mutual orientation of the reaction partners. The latter plays a most important role in the electronic coupling, as this depends on the overlap of the electronic orbitals of D and A. The geometrical considerations of excited state ET were thus especially emphasized during this work. Furthermore, I had the opportunity to investigate a large variety of different D-A systems, spanning from relatively simple D-A pairs to complex architectures incorporating several D and A units. The more simple model systems, in which D and A were either covalently linked (intramolecular ET) or freely diffusing in solution (bimolecular ET), allowed fundamental studies on the ET mechanism. On the other hand, photoinduced ET in the more complex systems was investigated in view of potential applications.
The next chapter (Chapter Two) reviews the theoretical concepts underlying this thesis. It first describes electromagnetic radiation, its interaction with matter and basics of spectroscopy, before pursuing with the properties of electronically excited organic molecules and overviewing the existing electron transfer theories.
Chapter Three is the experimental part of this work. After a brief introduction on pulsed lasers and how to convert the frequency of ultrashort light pulses using nonlinear optical effects, the different experimental techniques used during this thesis (steady-state absorption and fluorescence, time-resolved fluorescence and transient absorption spectroscopy) are described. In each case, the principle, experimental setup and ways to analyze the obtained data are discussed. The information that can be acquired from each technique concerning photoinduced ET is particularly emphasized.
The results obtained during this thesis are then presented and discussed in Chapters Three, Four and Five. For all the undertaken research projects, an overview of related literature is given in an introduction, in order to underline the relevance of the investigations and to situate them within the current research status.
Chapter Four is about intramolecular photoinduced ET in D- A dyads. In this case, intrinsic ET without the complications arising from translational diffusion of the reactants becomes accessible. In the majority of investigated systems, D and A are either directly linked or have a short rigid spacer, so that the degrees of freedom in their distance and mutual orientation are constrained to very small intramolecular rearrangements. Two projects are presented. The first consists of perylene derivatives (A) linked to N,N-dimethylaniline (D), while the second concerns free base or zinc tetraphenylporphyrins (D) attached to the core of a naphthalene diimide derivative (A).
Although the separate electron donors and acceptors are almost prototypic in the study of photoinduced ET, the linked compounds presented here are entirely novel and the very precise elucidation of their excited state properties and dynamics provides new insight to the ET reaction.
Bimolecular photoinduced ET in solution is the topic of Chapter Five. D and A are now no longer covalently linked, but either entirely free to diffuse in solution, or held together by non-bonding interactions in a ground state complex. In both cases, the number of conformations with different distances, mutual orientations and electronic coupling of A and D is much more important than for the intramolecular situation. Out of the distribution of D-A geometries in the ground state, which change and interconvert by diffusion, only some will be able to undergo photoinduced ET. This leads to an initial selection of geometries in the ion pair reaction product, which then also change due to diffusion. A lot of debate surrounds the nature and structure of this ion pair as well as the driving force dependence for bimolecular excited state ET. We have chosen here to investigate simple organic D-A pairs (perylene/1,4-dicyanobenzene, 3-methylperylene/tetracyanoethylene as well as complexes of pyromellitic anhydride with methylbenzenes and pyrene) whose excited state ET has often already been studied in the past, but with a lower time resolution than the one available to us. Furthermore, we introduce a new experimental technique to the study of bimolecular photoinduced ET, which is transient absorption spectroscopy in the infrared range. This tool allows for the first time to directly spectroscopically distinguish different types of ion pairs and to follow their dynamics. Additional information on the mutual orientation of D and A within those ion pairs is then obtained by polarization- sensitive transient absorption measurements in both the visible and infrared range.
Chapter Six presents more complex systems involving several covalently linked D and A units, which are moreover capable of forming supramolecular architectures in organized media and which have potential applications in solar energy conversion. Those compounds consist of several core-substituted naphthalene diimide chromophores attached to a rigid backbone (p-octiphenyl or oligophenylethynyl) that sometimes also absorbs visible light. They were synthesized by the group of Professor Stefan Matile (University of Geneva), who also designed and realized artificial photosynthetic centers and photovoltaic cells based on those molecules. At the origin of their function is their very rich excited state dynamics, which involves both energy and electron transfer processes. It was characterized during this thesis in both solution and organized environments (in the lipid membrane of vesicles and on the
1 Introduction
conducting surface of gold nanoparticles). As the multichromophoric molecules are rather flexible, they can adopt a variety of conformations and geometries even in the intramolecular case. The intimate D-A structure changes again when going from solution to organized media, where several molecules form supramolecular assemblies. This affects the excited state dynamics and allows insight to the role played by geometry.
Finally, the general conclusions of this thesis are given in Chapter Seven. The results obtained during this work also led to a number of publications, which are listed in Appendix One.
Chapter Two
Light, Matter and Electron Transfer
2 Light, Matter and Electron Transfer 2.1 Electromagnetic Radiation
There is no doubt that life on Earth as it exists today would not exist without sunlight. It brings us daytime, heat and is the ultimate energy source for a planet that can be regarded as a closed system. Through photosynthesis, it provides us with food and fuels.
It is also responsible for climate and weather, as it drives winds, ocean currents and the water cycle. Nevertheless, the powerful energy from the Sun can also do us harm, by burning our skin and provoking dangerous mutations to DNA. Given the almost 150 million kilometers of empty space separating the Earth from the Sun, it is obvious that solar energy must reach us as some form of radiation. This radiation is commonly referred to as “light”. But what is this radiation? What is actually the nature of light?
2.1.1 The Nature of Light across History
Standing before the magnificence of light without any rational understanding of it, ancient civilizations often ascribed it to the Divine and decided to worship it. They slowly learned to tame light, first through the handling of fire, then by the development of more and more complex lamps, which allowed extending life to after sunset. Soon, ways to manipulate the rays of the sun were found, such as simple mirrors or burning glasses. The Ancient Greek started to study optics in a more systematical way and speculated about the nature of light.[1] Interestingly, there was already debate at the time on whether it consists of a stream of particles (Pythagoras) or rather of waves (Aristotle). This debate extended right into the 19th century and opposed many eminent “particle” advocates such as Sir Isaac Newton to eminent “wave” advocates such as Cristiaan Huygens or Leonhard Euler.
In the 19th century, experimental evidence seemed to clear up the picture and the wave theory was now greatly favored. In parallel to advances in optics, electricity and magnetism were also being studied. Michael Faraday was amongst the first to realize the link between light and electromagnetism. James Clerk Maxwell summarized the idea that light is an electromagnetic field in his famous equations. Many experimental observations could be explained with this new wave theory, but unfortunately not all. The introduction of quantum mechanics in the 20th century revolutionized the picture once again. Albert Einstein revealed that light consists of discrete particles called photons, which are quanta of radiant energy. However, this new corpuscular theory does not contradict the electromagnetic wave theory. On the contrary, a
2.1 Electromagnetic Radiation
duality between the two exists. Light will behave in some cases as a wave and in other cases as a stream of particles. Let us now look at the theory of light in some more detail.
2.1.2 Light Propagation in Vacuum
In the classical description, light consists of an electromagnetic field, which evolves in time and in space and whose source is an oscillating charge.[1-3] As the electric field (E) generates the magnetic field (B) and vice versa, they mutually regenerate each other, leading to the propagation of the radiation. The properties of such an electromagnetic field are given by the Maxwell equations, shown below for the case of vacuum propagation (eq. 2.1 to 2.4).
=0
⋅
∇ E (2.1)
=0
⋅
∇ B (2.2)
- t
∂
= ∂
×
∇ E B (2.3)
0 t
0 ∂
ε ∂ μ
=
×
∇ B E (2.4)
Here, ∇⋅ represents the divergence operator, ∇× is the curl operator (both are function of the spatial coordinates), t is the time, μ0 and ε0 are the permeability and permittivity of free space. Note that all vector quantities are written in bold. The equations stipulate amongst others that both E and B are perpendicular to the direction of radiation propagation, that they are mutually perpendicular and that they oscillate in phase. They can be rearranged into differential wave equations for E and B, relating their space and time variations (eq. 2.5 and 2.6, where∇2 is the Laplace operator).
t2 0
2 0 0
2 =
∂ ε ∂ μ
−
∇ E E (2.5)
t2 0
2 0 0
2 =
∂ ε ∂ μ
−
∇ B B (2.6)
An obvious solution is the harmonic wave, where E and B vary in space (r) and time (t) in a sinusoidal way. Eq. 2.7 shows this for the E, both in sinusoidal and exponential writing.
[
i( t)]
c.c.2 exp t) 1 (
sin t) ,
(r =A k⋅r−ω⋅ = E k⋅r−ω⋅ +
E 0 (2.7)
A is the amplitude of the wave, k is the wavevector, ω is the angular frequency and E0 is the complex amplitude (E0=A/i). The wavevector points in the direction of wave propagation and its amplitude is related to the wavelength (λ) as illustrated in eq. 2.8. On the other hand, ω gives the temporal dependence of the wave’s phase and is linked to its frequency (υ) and period (T), as shown in eq. 2.9.
λ
= π
=k 2
k (2.8)
Τ
= π πυ
=
ω 2 2 (2.9)
A plane wave, oscillating only in one direction, is called linearly polarized. For this case, the vector notation can be omitted and eq. 2.7 for the electric field becomes eq. 2.10 (the wave propagates along x).
t) x Asin(k t)
, x (
E = ⋅ −ω⋅ (2.10) A representation of an electromagnetic field, in which both E
and B are planar sinusoidal waves with linear polarization, is shown in Figure 2.1.
Figure 2.1 Electromagnetic field consisting of sinusoidal planar waves
The speed of light (c) in vacuum is equal to its phase velocity (νφ, speed at which a constant phase point propagates). This constant can be expressed as a function of wavelength and frequency (eq.
2.11).
k ) T
(
c=νφ= μ0ε0 -1/2 =λ⋅υ= λ =ω (2.11) As light carries energy (which is equally distributed between
its electric and magnetic component), it is useful to know how much and how fast this energy is transmitted. Light intensity is referred to as irradiance (I), giving the average energy per unit area per unit
2.1 Electromagnetic Radiation
time. For a plane wave in vacuum, I is proportional to the squared amplitude of the electric field wave (eq. 2.12).
0 2
2
I= cε E0 (2.12)
In the quantum mechanical picture, electromagnetic energy is quantized.[1] Light can therefore be absorbed and emitted only as discrete quanta, called photons (stable, massless and chargeless elementary particles). The photon energy (E) is related to the frequency via Plank’s constant (h), as shown in eq. 2.13. In this frame of mind, it is interesting to express the intensity of (monochromatic) light as mean photon flux (qp), i.e. average number of photons per unit of time (eq. 2.14). P is the optical power. We will see that the quantum mechanical picture becomes important when the interaction between electromagnetic radiation and matter is considered.
υ
=h
E (2.13)
= υ h
qp P (2.14)
2.1.3 The Electromagnetic Spectrum
Until now, we have only mentioned light as a form of electromagnetic radiation. However, visible light is only a small part of the electromagnetic spectrum, which extends from highly energetic gamma rays to low energy radio waves. This is shown as a function of wavelength and frequency in Figure 2.2.
Figure 2.2 The electromagnetic spectrum
2.1.4 Electromagnetic Propagation in a Dielectric Medium A classical description of the propagation of electromagnetic radiation in matter is presented here.[2, 3] For the moment, the
discussion is limited to non-absorbing dielectric materials (with bound charges) and to relatively low light intensities. In this case, the frequency of the electromagnetic radiation is not affected by the medium, but the velocity and wavelength are reduced. The interaction between electromagnetic radiation and matter is mainly due to the electric field component, which causes oscillations of the material’s electric charges. As oscillating charges are a source of electromagnetic radiation, they will in their turn affect the incident radiation.
The light-induced dipole moments of the oscillating charges create a macroscopic polarization (P), which oscillates with the same frequency as the incoming radiation. P is proportional to the electric field E of the radiation, and is related to it through the electric susceptibility (χ~), as shown in eq. 2.15. χ~ is a complex quantity (denoted with a tilde) and is extremely important in determining the optical properties of the material (absorption, emission, refraction, reflection, diffusion etc.).
(t)
~ε (t) 0E
P =χ (2.15)
The effect that P has on the electric field of the light can also be expressed in terms of χ~. By manipulating Maxwell’s equations for a dielectric medium, the following differential wave equation for E is found (in analogy to the vacuum case):
t 0
~) (1 22
0 0
2 =
∂ χ ∂ + ε μ
−
∇ E E (2.16)
The phase velocity (~νφ) of the electromagnetic radiation in the medium is deduced (eq. 2.17). It is a complex quantity with no real physical meaning. It allows defining the complex refractive index (n~), which can be decomposed into the real refractive index (n) and the imaginary attenuation index (K), as shown in eq. 2.18.
[
0 0(1 ~)]
-1/2~ = ε μ +χ
νφ (2.17)
iK n
~) (material) (1
~
(vacuum)
n~ = +χ-1/2= + ν
= ν
φ
φ (2.18)
K affects the amplitude of the electric field and is thus concerned with absorption phenomena. It will be discussed in section 2.1.5. In the non-absorbing case, K is zero, so that ~χ and n~ become real quantities. It is now the refractive index (n) that defines
2.1 Electromagnetic Radiation
the optical properties of the material and the way it affects light. The effects of n on the real phase velocity (νφ) and λ are given in eq. 2.19 and 2.20. The refractive index of a material is strongly dependent on the frequency of the light. For visible light, if the latter is far from the absorption frequency of the material, n increases with frequency (normal dispersion).
n
=c
νφ (2.19)
n (vacuum)
=λ
λ (2.20)
2.1.5 Absorption of Electromagnetic Radiation
In the classical description, the dielectric material is treated as an ensemble of linear oscillators with a natural frequency ω0.[2, 3]
When the angular frequency (ω) of the electromagnetic radiation approaches ω0, there is resonance and therefore energy exchange between the radiation and the material. If the intensity of the electromagnetic field is decreased, the observed phenomenon is absorption. On the other hand, if the intensity of the radiation increases, there is stimulated emission (which will be described in section 2.3.3). The attenuation index K (eq. 2.18) accounts for the absorption properties of the material. It can be shown that K has a Lorentzian dependence on ω and peaks at ω = ω0.
When monochromatic light passes through a material of thickness l, its incident intensity (I0) is reduced to I due to the absorption. The Bouguer-Lambert-Beer law relates this to K (eq.
2.21, where α is the absorption coefficient).[3] In chemistry, especially when working in solution with concentration c, it is useful to talk about the absorbance (A) of the sample, which is defined in eq. 2.22.
The factor ε is the molar extinction coefficient. An absorption spectrum is obtained by plotting A or ε as a function of λ or υ. It usually shows a band centered around ω0.
l) (- exp I c Kl) 2 ( exp I
I= 0 − ω = 0 α (2.21)
I lc log I - A
0
ε
=
= (2.22)
From a quantum mechanical point of view, matter exists in discrete stationary states described by a wavefunction (ψ) with an associated quantized energy E. The time-independent Schrödinger
equation theoretically allows finding the wavefunction for any system by applying the Hamiltonian operator Hˆ (eq. 2.23).[4]
ψ
= ψ E
Hˆ (2.23)
Let us consider an isolated system in vacuum. The absorption of a photon leads to a transition between two quantum states (|a〉 and |b〉), given that the photon energy corresponds to the energy difference of the two states (eq. 2.24).
a
b E
E −
= υ
h (2.24)
Due to the transition from |a〉 to |b〉, the probability of finding the system in the upper state (Pb) increases.[3, 4] The rate at which this probability changes due to absorption is called the transition rate (wabs). It determines the intensity of the absorption and is related to the intensity of the incoming light at frequency ω through the Einstein coefficient for absorption B (eq. 2.25).
) ( I t B
wabs = Pb = ⋅ 0 ω d
d (2.25)
A semiclassical approach allows a better understanding of the absorption intensity.[2, 3] Here, matter is treated quantum mechanically, while the electromagnetic radiation is introduced as a purely classical time-dependent perturbation (oscillating electric field). The perturbation will transfer the system from the stationary state |a〉 to the stationary state |b〉 through a series of superposition states. Those are solutions of the time-dependent Schrödinger equation and can be expressed as a linear combination of the wavefunctions of states |a〉 and |b〉. Even if the system has no permanent dipole moment when it is in a stationary state, it might have an oscillating transition dipole moment (μab) if it is in a superposition state. This is defined in eq. 2.26, where μˆ is the electric dipole moment operator and ψa and ψb are the wavefunctions of the stationary states.
a bμˆψ ψ
ab =
μ (2.26)
It is the interaction between μab and the electric field vector which leads to absorption if i) μab oscillates at the same frequency as E (this is equivalent to eq. 2.24), ii) the polarization of E has a non- zero component parallel to μab (see anisotropy discussion in section 3.4.3) and iii) μab ≠ 0. The last condition is intrinsic to the states of the system and implies selection rules which decide whether a
2.1 Electromagnetic Radiation
transition is allowed or forbidden. We will discuss the selection rules for electronic transitions in section 2.2.2. The magnitude of μab will determine the absorption intensity and is related to B and ε (eq.
2.27a and 2.28a). Here, f is the oscillator strength. It varies between 0 and 1 and gives the probability that a transition takes place. The mass and charge of the electron are given by me and e, respectively, while NA is Avogadro’s constant. The central frequency of the absorption band is υ0, while the integral over the absorption spectrum (ε as a function of wavenumber υ in cm-1) is given by
∫
ε(υ)dυ.0h
2
ε B 6ab
μ
= (2.27a)
2 2 0 e 2 2
A 0 e
3he m d 8
) ( 10 e ln Ν
c
f=3m ε
∫
ευ υ= π υ μab (2.28a)2.1.6 Spectroscopy
Spectroscopy studies the interaction between matter and electromagnetic radiation. It measures the exchange of energy between the two by looking at the absorption, emission or scattering of photons. We have seen that the electromagnetic spectrum extends over a large range of frequencies. All parts of it can interact with matter, leading to different types of transitions and different types of spectroscopy. In the following, we will concentrate on matter consisting of discrete molecules, which are of course made up of nuclei and electrons. As electrons are much lighter and move much faster than the nuclei, the wavefunction can be separated into an electronic and a nuclear part (Born-Oppenheimer approximation, eq.
2.29).[3] The nuclear motion can be vibrational or rotational, leading to a further factorization of the total wavefunction into electronic, vibrational and rotational wavefunctions (eq. 2.30).
e n⋅ψ ψ
=
ψ (2.29)
e rot ib
v ⋅ψ ⋅ψ
ψ
=
ψ (2.30)
As shown in Figure 2.3, the energy separation between the rotational states is smaller than that of the vibrational states which is smaller than that of the electronic states. It is therefore electromagnetic radiation in the microwave region (λ = 100 μm to 1 cm) that will provoke rotational transitions, while infrared (IR) radiation (3 μm to 100 μm) leads to vibrational transitions. Finally,
ultraviolet and visible light (UV-vis, 100 nm to 1 μm) gives rise to electronic transitions. This thesis is mainly based on the latter, so it is discussed in more detail in section 2.2.
Figure 2.3 Energy states of a typical molecule
2.2 Electronic Absorption Spectroscopy
In an atom, the electrons are confined to atomic orbitals (AO).
Those combine to molecular orbitals (MO) in molecules. The way that electrons arrange in the orbitals is called electronic configuration. It is determined by a series of quantum mechanical rules, which state that the orbitals are filled in order of increasing energy, that one orbital can contain a maximum of two electrons and that those two electrons must be of opposite spin.[5] Formally, electronic states are linear combinations of electronic configurations (configuration mixing) and transitions take place between those states.
Figure 2.3 shows the potential energy diagram of two electronic states for a typical molecule. Here, the energy of the state is represented as a function of nuclear coordinates, giving rise to a Morse potential. For a molecule in solution, it can also be drawn as a function of solvent coordinates (solvation). It is clear from the diagram that every electronic state has associated vibrational and rotational states related to the nuclear wavefunction. Each potential curve also has a minimum, indicating an equilibrium position in which the molecule presents a certain geometry. In general, only the lowest electronic state (ground state) is populated in a relaxed molecule, because the energy spacing between the states is too large to have thermal population of the higher states (excited states).[5]
2.2 Electronic Absorption Spectroscopy
2.2.1 Organic Closed-Shell Molecules
For simplicity, a picture in which a light-induced electronic transition is simply the transfer of an electron from one orbital to another will be adopted (no configuration mixing). The discussion is also limited to closed-shell organic molecules. Here, the ground state (S0) has singlet multiplicity and two electrons fill the highest occupied molecular orbital (HOMO). Figure 2.4 shows some electronic configurations of a typical organic molecule. The horizontal lines correspond to orbitals and the arrows to electrons (spin up or down).
Figure 2.4 Examples of electronic configurations in a closed- shell organic molecule
Upon light absorption, the first possible transition is the promotion of one of the two HOMO electrons into the lowest unoccupied molecular orbital (LUMO). Depending on the relative spin of the two electrons, this gives rise to the first singlet excited state (S1) or the first triplet excited state (T1). Upon excitation with more energetic light, higher states, such as S2, can be populated.
2.2.2 Selection Rules
As seen before, the intensity of a typical electronic absorption spectrum is determined by the interaction of the molecule’s transition dipole moment with the electric field of the light. Selection rules will decide how allowed or forbidden a transition is (magnitude of the transition dipole moment, oscillator strength).[4, 6] They originate in the conservation of total angular momentum. Maybe the most important one is that the multiplicity of spin cannot change during a transition. Thus, transitions going from a singlet to a triplet state or vice versa are in principle forbidden.
Some selection rules are governed by the symmetry of the molecule.
For example, the Laporte rule for centro-symmetric molecules states that the parity of the involved wavefunctions must change during an electronic transition (only g↔u transitions are allowed). Selection rules are hardly ever strictly followed, meaning that forbidden transitions appear as weak features in absorption spectra. Factors that allow breaking the rules include spin-orbit coupling, vibronic coupling and collisions between molecules. Another aspect that will influence the intensity of an electronic transition is the spatial overlap of the involved orbitals. If there is no overlap, the transition cannot take place, even if it is allowed by the selection rules.
A vibrational or, to a much smaller extent, rotational structure is often observed in electronic absorption spectra.[6] In a vibronic transition, the molecule is promoted from the electronic ground state to a higher vibrational level of the electronic excited state, as shown in Figure 2.5b.
Figure 2.5 (a) Horizontally coincident and (b) horizontally shifted potential curves of an electronic ground and excited state. Vibrational levels with their probability functions are also shown, together with vertical absorption and emission transitions[6]
Here, the potential curves of the ground and excited electronic state are drawn as a function of nuclear position. Some vibrational levels and their probability functions are also shown.
According to the Franck-Condon principle, a transition must be vertical in this kind of diagram, as the nuclei have no time to move during an electronic transition. The rate of a typical electronic absorption transition (kabs) is 1015-1016 s-1 (less than the femtosecond (fs) time scale).[4] In Figure 2.5a, the potential curves have the same
2.2 Electronic Absorption Spectroscopy
horizontal position, meaning that the equilibrium geometry of the ground and excited state is the same. Here, the absorption is purely electronic (0-0 transition). In Figure 2.5b, the potential curves are horizontally shifted and of different shape and size, so that a vertical transition leads to a higher vibrational level (6-0 vibronic transition).
The intensity of vibronic bands depends on symmetry- induced selection rules and on the overlap between the initial and final vibrational (nuclear) wavefunction.[3, 5, 6] The latter is called Franck-Condon (FC) factor and gives the probability of finding a common nuclear geometry in the initial and final states. The transition dipole moment for a vibronic transition is calculated as shown in eq. 2.31. It depends on both the electronic (ψe) and nuclear (ψn) wavefunctions of states |a〉 and |b〉. The dependence on FC implies that vertical transitions leading to a maximum probability point in the vibrational level will be most intense (Figure 2.5).
a e, b e, a
e, b e, a n, b n,
a n, a e, b n, b e,
ˆ FC ˆ
ˆ
ψ μ ψ
= ψ μ ψ ψ ψ
≈
ψ
⋅ ψ μ ψ
⋅ ψ
ab=
μ (2.31)
A way to summarize the effect of all the above considerations on the intensity of an absorption band is to factorize the oscillator strength.[5] This is possible within the Born-Oppenheimer approximation. In eq. 2.32, fs is the spin overlap factor (it indicates whether the transition is spin-allowed and includes spin-orbit coupling), fp represents the spatial overlap of the orbitals involved in the transition, fy indicates whether the electronic transition is symmetry-allowed (conservation of the electron’s angular momentum) and fv is the Franck-Condon factor.
v y p
s f f f
f
f= ⋅ ⋅ ⋅ (2.32)
2.2.3 Molecules in the Condensed Phase
All measurements presented in this thesis took place in condensed phase and at room temperature. The samples were in general solids or liquids dissolved in liquid solutions. Instead of having a single isolated system, this gives an ensemble of N systems in a solvent bath. The macroscopic absorption is in this case the sum of the absorptions from all the individual systems. We have already seen in eq. 2.28a how the macroscopic molar extinction coefficient ε is related to the microscopic transition dipole moment μab, but the relation was given for light propagation in vacuum. In the condensed phase, light will propagate through the medium (solvent) with refractive index n. Beyond this, it will encounter a different local electric field in the solvent and in the light-absorbing molecule, if
they have different polarizabilities. The latter is accounted for by the local field correction factor fLF, which can be approximated as a function of n for example by the Lorentz expression or cavity-field expression.[2] To include the effect of the medium, eq. 2.27a and 2.28a become eq. 2.27b and 2.28b. Here, ε(υ) is the absorption spectrum expressed as a function of frequency (υ in s-1).
2 2 2 2
n 3 B 2
h
ab
μ
fLF
= π (2.27b)
d ) n ( 10 e ln Ν
c m 10 3he
m
f 8 2 2
A e 2 3
2 0 e
2 υ = π
∫
ευ υ= π
fLF ab
μ (2.28b)
The ensemble of N molecules is usually a canonical ensemble, as the population will be distributed at a given temperature in the available stationary energy levels according to the Boltzmann distribution. From a quantum mechanical point of view, this is best described by a density matrix.[7] The diagonal terms represent the population of the energy levels, while the non-diagonal terms represent the relative phase between the states. They are non- zero only in presence of an external coherent perturbation, such as the electromagnetic field generated by a laser (section 3.1).
Maybe the most important effect of being in condensed phase is the one on the spectral width.[3] According to the Heisenberg uncertainty principle, the width of an absorption band increases if the lifetime of the transition dipole moment decreases. It is the oscillatory interference between the stationary states that leads to the interaction with light and to the transition dipole moment. This decays due to population decay and pure dephasing according to the phenomenological Bloch equations. In condensed phase, the electronic dephasing is extremely fast (tens of fs), as it depends on fluctuations of the local electric field generated by the environment.
In fact, the solvent constantly fluctuates around the solute molecules, leading to a fluctuation of the transition frequency around an average value. The complex dynamic interactions with the environment thus lead to broad absorption bands of non-Lorentzian shape.
Interactions with the environment also have an effect on the electronic energy levels of the dissolved molecules and therefore on its absorption spectrum (position, width, shape). Non-specific electrostatic interactions with the solvent depend on the dipole moment and average polarizability of both solvent and solute.[5] The solvent is usually treated as a dielectric continuum whose macroscopic dipole moment is represented by the dielectric constant
2.2 Electronic Absorption Spectroscopy
εs, and whose macroscopic polarizability is characterized by the refractive index n. The four possible non-specific interactions are dipole-dipole interactions (polar solute in polar solvent), dipole- induced dipole interactions (polar solute in non-polar solvent), the solvent Stark effect (a polar solvent induces a small fluctuating dipole in a non-polar solute) and dispersion interactions (non-polar solvent and solute). In parentheses, the situation in which the interaction is most important is shown. The interactions are however not limited to those situations and several of them can occur for the same solute-solvent pair.
Specific interactions (e.g. hydrogen bonding) between the molecule and the solvent imply the formation of a loose complex between the two and require a certain geometry. Interactions (dipole- dipole, π-stacking, hydrogen-bonding etc.) can also exist between the solute molecules and will have a definite effect on the absorption spectrum. A typical example is the coupling of two light-absorbing molecules (chromophores), which is called excitonic coupling.[8] Here, the two molecules are so close that the excitation is delocalized between them. This leads to exciton splitting of the excited energy level and gives thus rise to new energy levels with new absorption and emission properties.
2.3 Excited State Relaxation
Once a molecule has absorbed light and is in the excited state, it will lose the excess energy by either relaxing back to the ground state or by undergoing a photochemical reaction. In this section, we will focus on basic photophysical processes occurring from the excited state. Photochemical reactions and quenching of the excited state by the interaction with other molecules will be considered in section 2.4.
A Jablonski diagram shows the energy states of a molecule and the transitions linking them.[5] It will help us here to understand the fate of an excited state, after its population by an electronic or vibronic transition due to light absorption. The Jablonski diagram for a typical organic molecule is shown in Figure 2.6. The vertical scale represents energy, while the horizontal scale indicates the spin multiplicity. The first electronic states of the molecule are drawn as bold horizontal lines. For simplicity, vibrational levels are only included for S0 and S1 as thin horizontal lines.
In most organic molecules, the energy gap between the electronic states decreases with increasing energy, as shown here.
The triplet state is always less energetic than the corresponding
singlet state (Hund’s rule).[5] This is related to the spatial overlap of the orbitals and electrostatic repulsion between the electrons. In the Jablonski diagram, transitions between the states are illustrated as solid arrows if they are radiative (i.e. if they involve absorption or emission of light). On the other hand, they are shown as dashed arrows if they are non-radiative (dissipation of energy as heat).
Radiative transitions include absorption, fluorescence and phosphorescence. Non-radiative transitions include vibrational relaxation (between vibrational levels), internal conversion (between electronic states of same multiplicity) and intersystem crossing (between electronic states of different multiplicity). Those processes will now be discussed in more detail.
S0 S1 S2 S3 E
T1 T2 T3
Abs Abs IC + VR
VR
VR Fluo
IC+ VR ISC+ VR
Ph ISC+ VR
Abs = Absorption Fluo= Fluorescence IC = Internal Conversion VR = Vibrational Relaxation ISC = Intersystem Crossing Ph = Phosphorescence S0
S1 S2 S3 E
T1 T2 T3
Abs Abs IC + VR
VR
VR Fluo
IC+ VR ISC+ VR
Ph ISC+ VR
Abs = Absorption Fluo= Fluorescence IC = Internal Conversion VR = Vibrational Relaxation ISC = Intersystem Crossing Ph = Phosphorescence
Figure 2.6 Jablonski diagram for a typical organic molecule
2.3.1 Vibrational, Geometry and Solvent Relaxation
We have seen in section 2.2.2 that a vibronic transition populates excited vibrational levels. A typical absorption process of this kind is shown in the Jablonski diagram (Figure 2.6, second upward arrow from the left), where an excited vibrational level of the S1 state is populated. The excess vibrational energy is lost as heat to the environment in a process called vibrational relaxation (VR), which leads to an equilibrium Boltzmann distribution over the vibrational states. At room temperature, this usually implies that only the vibrational ground state (ν = 0) is populated. In condensed phase, VR is an ultrafast and highly efficient process. The rate constant (kvr) is around 1012 s-1 (picosecond (ps) time scale). The
2.3 Excited State Relaxation
process is described as an entangled two-step mechanism.[9] First (in tens of fs), intramolecular vibrational energy redistribution (IVR) leads to a distribution of the excess vibrational energy amongst the vibrational modes of the system (after excitation, only the Franck- Condon active modes are populated). The molecule is still vibrationally excited, thus much “hotter” than the environment. In a second (not necessarily consecutive) step, the excess energy is lost as heat to the environment due to molecular collisions. This occurs on the ps time scale and is referred to as vibrational cooling (VC). On an ultrafast time scale, VR can be spectroscopically followed and shows as a typical narrowing in the absorption or emission spectrum of the excited state.
The ground and excited state do not necessarily have the same equilibrium nuclear geometry. As shown in Figure 2.5b, the potential energy curves are in this case shifted on the horizontal scale. Due to the Franck-Condon principle (vertical transition), the excited state will be populated in a non-equilibrium geometry, which relaxes on the tens to hundreds of ps time scale (if there is no faster competing process).[5] The geometrical changes between the two states are due to a different distribution of electrons in the molecular orbitals. One obvious effect is the increase of bond length in the excited state, if an electron is promoted into an antibonding orbital during the transition. Other examples of major geometrical changes upon photoexcitation include the bending of formaldehyde and the planarization of biphenyl in the excited state.
The difference in electron distribution in the ground and excited state does not only influence the bond length and geometry, but also the permanent dipole moment and the polarizability of the molecule. As discussed in section 2.2.3, the interactions with the solvent depend on those parameters. Thus, a change of the molecule’s properties will lead to a different solvation (solvent arrangement around the molecule) in the excited state. However, still according to the Franck-Condon principle, the solvent has no time to rearrange during the electronic transition and the excited state is populated with a non-equilibrium solvation. Solvent relaxation (mediated by time-dependent solvent fluctuations) then occurs on a typical time scale of tens to hundreds of ps.[8] Solvent relaxation can again be followed by ultrafast spectroscopy. It is accompanied by a typical red-shift of the excited state emission, which is probed by time-dependent Stokes shift measurements. Photon-echo techniques are also used to monitor solvent response.
Maroncelli and co-workers investigated solvent relaxation of a polar molecule (coumarin 343) in a variety of common polar solvents and ionic liquids.[10-12] For most solvents, the solvation dynamics
