TURNING ON FLUORESCENCE IN SILICO: FROM RADICAL CATIONS TO 11-CIS LOCKED RHODOPSIN ANALOGUES
Elena N Laricheva
A Dissertation
Submitted to the Graduate College of Bowling Green State University in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
August 2012
Committee:
Dr. Massimo Olivucci, Advisor
Dr. Gabriela Bidart-Bouzat Graduate Faculty Representative
Dr. Marshall R Wilson
Dr. Alexander N Tarnovsky
© 2012
Elena N. Laricheva
All Rights Reserved
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ABSTRACT
Prof. Massimo Olivucci, Advisor
Over the last decade, a significant progress has been made in the design and development of novel fluorescent probes with the major focus on genetically encoded fluorescent proteins (FP). The conventional route to the FP design is based on tuning and improving the spectral properties of the green fluorescent protein (GFP) from the jellyfish Aequorea victoria and its homologs from other marine organisms. The major challenge of this work was to investigate computationally the possibility of turning a non-fluorescent protein into a fluorescent one. At the quantum-mechanical level, this means to find a way of increasing the excited state lifetime of a molecule by changing the shape of its barierless excited state potential energy surface to a barrier-controlled one. Here, we report the results of the ab initio CASPT2//CASSCF/6-31G*/AMBER hybrid quantum mechanics/molecular mechanics (QM/MM) study indicating that members of the rhodopsin family may be engineered to yield alternative source of FPs, despite the ultrafast photoisomerization reaction characterizing these systems.
Indeed, the replacement of the natural chromophore with an artificial (locked) one in the visual pigment rhodopsin leads to a three-order of magnitude increase in excited state lifetime: from ca. 100 fs to 85 ps. To explain the origin of such an increase, we constructed consistent models of the wild-type and artificial rhodopsins and investigated the shapes of their excited state potential energy surfaces in a comparative way. Our
f results show that observed fluorescence (λ max= 620 nm) is due to a locally excited
iv intermediate whose lifetime is controlled by a small energy barrier. The analysis of the decay path of such an intermediate provides information useful for engineering rhodopsin variants with augmented fluorescence efficiencies.
Preliminarily, to gain more insight into the phenomenon of the barrier-controlled fluorescence lifetime, we also investigated using ab initio multiconfigurational QM and
QM/MM protocols the photochemistry and photophysics of N,N,N’,N’-tetramethyl-p- phenylenediamine radical cation, known as Wurster’s Blue (WB). This relatively small and stable organic species, exhibiting a temperature-dependent fluorescence behavior, was used as a training system for mapping of the excited state potential energy surfaces featuring a barrier.
v
Моим дорогим родителям, Ирине и Николаю Ларичевым:
За все те дни, что я провела вдали от Вас
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ACKNOWLEDGMENTS
Many thanks go to:
Prof. Massimo Olivucci, my advisor—for his patience, guidance and unwavering support during every stage of my research work, but, more specifically, for constantly prodding me onward, encouraging me to move on, and helping me to complete the projects that once seemed to be unthinkably large. I owe you my deepest gratitude, Massimo!
Prof. Marshall Wilson, Prof. Alexander Tarnovsky, and Prof. Gabriela Bidart-Bouzat, my committee members—for the valuable time they spent reading and correcting my dissertation and for insightful questions they asked during its defense.
Prof. Eric Vauthey and Dr. Jakob Grilj, our collaborators from the University of Geneva,
Switzerland—for initiating a project on Wurster’s Blue and for generating bright ideas along the way that helped to bring this project to completion.
Samer Gozem, Dr. Federico Melaccio, Dr. Igor Schapiro, Dr. Mike Ryazantsev, Dr. Wan
Jian Ding, Dr. Mark Huntress, Silvia Rinaldi, Alessio Valentini—for being great colleagues, smart academics and very nice people. To all of you guys, it has been a pleasure working with you and learning from you!
Mom and Dad, my loving parents—for showing me every day that standing by and caring does not necessarily mean to be near. Without your unconditional love, encouragement, emotional support, and inexhaustible patience nothing would ever be accomplished. No more doctorates, I swear!
Armen, my dear man—for teaching me how to fight my own fears and stand up strong and still against all odds, for turning my life upside down, and for showing me that there is never a limit for curiosity and self-education.
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LIST OF PUBLICATIONS
1. Igor Schapiro, Federico Melaccio, Elena N. Laricheva, and Massimo Olivucci. Using
the computer to understand the chemistry of conical intersections, Photochem.
Photobiol. Sci., 2011, 10, 867-886.
2. Jakob Grilj, Elena N. Laricheva, Massimo Olivucci, and Eric Vauthey. Fluorescence
of radical ions in liquid solutions: Wurster’s Blue as a case study, Angew. Chem. Int.
Ed., 2011, 50, 4496-4498.
3. Elena N. Laricheva, Samer Gozem, Silvia Rinaldi, Federico Melaccio, Alessio
Valentini, and Massimo Olivucci. Origin of fluorescence in 11-cis locked bovine
rhodopsin (under revision).
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TABLE OF CONTENTS
Page
CHAPTER 1: INTRODUCTION ...... 1
1.1 Fluorescence Microscopy: a Bit of History ...... 1
1.2 Super-Resolution Microscopy: Breaking the Diffraction Limit ...... 2
1.3 Genetically-Encoded Fluorescent Proteins for Super-Resolution Microscopy ... 5
1.4 Current Strategies for Design of New Fluorescent Proteins ...... 10
1.5 Rhodopsins: General Overview ...... 12
1.6 Rhodopsins as Actuators in Optogenetics...... 18
1.7 Rhodopsins as Fluorescent Probes ...... 20
BIBLIOGRAPHY ...... 23
CHAPTER 2: METHODOLOGY ...... 33
2.1 Computational Photochemistry and Photobiology ...... 33
2.2 Potential Energy Surfaces and Their Topological Features ...... 34
2.3 Photochemical Reaction Path ...... 37
2.4 Conical Intersections ...... 40
2.5 Born-Oppenheimer Approximation ...... 44
2.6 From Hartree-Fock to Post-SCF methods...... 46
2.7 Complete-Active Space Self-Consistent Field (CASSCF) Method...... 50
2.8 Complete Active Space Second Order Perturbation Theory (CASPT2) Method 52
2.9 Hybrid Quantum Mechanics/Molecular Mechanics (QM/MM) Method ...... 53
BIBLIOGRAPHY ...... 57
CHAPTER 3: PHOTOCHEMISTRY OF WURSTER’S BLUE RADICAL CATION ...... 62 ix
Abstract ...... 62
3.1 Introduction ...... 63
3.2 Methodology ...... 69
3.3 Results and Discussion ...... 76
3.4 Conclusions ...... 90
BIBLIOGRAPHY ...... 92
CHAPTER 4: PHOTOCHEMISTRY OF 11-CIS LOCKED BOVINE RHODOPSIN ...... 97
Abstract ...... 97
4.1 Introduction ...... 97
4.2 Methodology ...... 103
4.3 Results and Discussion ...... 107
4.4 Conclusions ...... 117
BIBLIOGRAPHY ...... 118
CHAPTER 5: CONCLUSIONS AND FINAL REMARKS ...... 122 x
LIST OF FIGURES
1.1 Comparison of spatial and temporal resolutions of different bio-imaging
techniques ...... 3
1.2 Fluorescence of the jellyfish Aequorea Victoria ...... 6
1.3 Color palette of various fluorescent proteins ...... 7
1.4 Optical highlighters ...... 9
1.5 Structure of the GFP protein and its chromophore ...... 11
1.6 Structure of the type I and type II rhodopsins...... 13
1.7 Photocycle of the visual pigment ...... 15
1.8 Scaled-CASSCF/AMBER classical Rh → bathoRh (top, left) and bathoRh → Rh
S1 trajectories (top, right) ...... 16
1.9 Scaled-CASSCF/Amber semi-classical Rh → bathoRh (left) and bathoRh → Rh
(right) S1 trajectories ...... 17
1.10 Schematic illustration of the neural activation and neural inhibition by ChR2 and
NpHR ...... 19
2.1 Comparison between the Nature’s landscape and the PES of a chemical reaction ... 35
2.2 Shapes of the stationary points: minimum (A), saddle point (B), maximum (C) ...... 36
2.3 Schematic illustration of the most common light-induced photochemical and
photophysical events ...... 38
2.4 Three-dimensional (left) vs. two-dimensional (right) schematic representation of
the ultrafast barrierless photochemical reaction path (full lines) ...... 39 xi
2.5 Comparison of the Van der Lugt and Oosterhoff’s avoided crossing (left) to the
conical intersection model (right) mediating the photochemical conversion of
buta-1,3-diene into cyclobutane ...... 41
2.6 Pictorial representation of the intersection space between two PESs ...... 43
2.7 Major differences between the transition state (left) and conical intersection
(right) ...... 44
2.8 Illustration of the QM/MM partitioning ...... 54
3.1 Dominant resonance formula of WB ...... 64
3.2 Hypothetic radiationless deactivation channels for D1 state of WB...... 65
3.3 Schematic representation of the radiationless deactivation mediated by the CI ...... 66
3.4 Gas-phase linear interpolated path between the D1 min and D1/D0 CI of WB
computed with three root state-average CASSCF wavefunction ...... 72
3.5 Low-temperature stationary fluorescence of WB in EtOH:MeOH (1:1) ...... 76
3.6 Temperature-dependence of WB fluorescence ...... 77
3.7 Geometrical parameters of the main stationary points ...... 78
3.8 Transient absorption (TA) data ...... 82
3.9 Characterization of the conical intersection ...... 84
3.10 Pictorial representation of the two root state-average D0 and D1 CASSCF energy
profiles along a circular cross-section centered at the gas phase D1/D0 CI...... 85
3.11 Characterization of the CI branching plane ...... 86
3.12 Excited state relaxation path of WB ...... 88
3.13 Mechanistic picture of WB photochemistry...... 89
4.1 Structure of Rh and photoisomerization reaction of its chromophore ...... 99 xii
4.2 Excited state paths of Rh and Rh5 ...... 100
4.3 Artificial (11-cis locked) rhodopsin analogues ...... 101
4.4 Fluorescence spectrum of Rh5 excited with the green pulse ...... 102
4.5 Comparison between the CASSCF/6-31G*/AMBER (blue) and
CASPT2//CASSCF/6-31G*/AMBER (red) S1 energy profiles computed with
three-root state average CASSCF wavefunction ...... 106
4.6 Charge distribution and relevant geometrical parameters (dihedral angles are
given in parentheses) of the stationary points along the S1 path of Rh5...... 108
4.7 Charge distribution and relevant geometrical parameters (dihedral angles are
given in parentheses) of the stationary points along the S1 path in Rh ...... 109
4.8 Comparison between the S1 state paths of Rh and Rh5...... 110
4.9 S1 state path of Rh ...... 112
4.10 Analysis of the LE and CT states ...... 115
4.11 Mechanistic picture of the Rh5 photochemistry ...... 116 xiii
LIST OF TABLES
3.1 Solvent properties at 25°C ...... 69
3.2 Relative CASPT2//CASSCF/6-31G*, CASPT2/6-31G*, and CASPT2/6-31++G*
energies ΔE (the latter two are in parentheses where indicated) for all the D0 and
D1 structures computed in the gas-phase (where applicable) and in solution (all
CASPT2 values are shown for the fixed solvent shell only, CASPT2//CASSCF –
for relaxed solvent configuration), oscillator strength f and values of absorption
and fluorescence maxima (λmax) computed at both CASPT2//CASSCF/6-31G* and
CASPT2/6-31G* level of theory (in parentheses) ...... 79
3.3 Fluorescence properties of WB as a function of temperature: fluorescence lifetime
f measured by TCSPC (IRF = 0.8 ns), radiative rate constant r calculated from
the Strickler-Berg relationship, and relative fluorescence intensity rel ...... 81
3.4 Time constants obtained from the global analysis of the fluorescence dynamics of
WB at room temperature measured by fluorescence up-conversion ...... 81
4.1 Relative energies (ΔE), oscillator strength (f) and values of the absorption and
fluorescence maxima (λmax) computed at the CASPT2//CASSCF/6-31G* level for
both Rh5 and Rh ...... 107 1
CHAPTER 1: INTRODUCTION
1.1 Fluorescence Microscopy: a Bit of History
In the 17th century, when two Fellows of the Royal Society—Robert Hooke and Antoni van Leeuwenhoek—achieved first success in studying microorganisms using light microscopes, the era of great discoveries in cell biology began.1-3 By focusing light through a set of lenses, it has become possible to get the magnified images of tiny objects that human eye, with its resolution of ca. 100 µm, could not see. The cellular structure of the tissues, the circulation of blood corpuscles in capillaries, the flow of sap in plants, the fascinating life forms in a droplet of water—all these things and many more could now be observed using the light microscope.3
The progress in the field was further advanced in the mid-19th century when George
Gabriel Stokes coined the term “fluorescence” to describe red emission observed in mineral fluorspar excited with UV light.4 Later, Otto Heimstaedt and Heinrich Lehmann exploited the phenomenon of fluorescence to construct first fluorescence microscopes.5
Initially, those microscopes relied on autofluorescence of imaged objects and, therefore, had limited applications. However, in the next two decades, the idea of attaching exogenous fluorescent chemicals to a sample emerged and the technique of secondary fluorescence was introduced.6, 7 By the 1930s, the use of exogenous chemical tags, also called fluorochromes or fluorophores, became widespread to stain and study tissues, bacteria, and pathogens.8
Despite overall success, it was not until the 1940s that fluorescence microscopy has boomed after Coons and Kaplan started to label antibodies with fluorescent dyes to investigate the antibody-antigen interactions in living cells.8-10 The method reached the peak of its popularity in 1994, when Chalfie et al.11 successfully expressed the gene of now-famous green fluorescent protein (GFP) in the nematode Caenorhabditis elegans,12 initiating the start of revolution in the 2 field of bio-imaging using genetically encoded fluorescent proteins. This revolution continues up to date and is accomplished through continuous development of new microscopy techniques and design of novel fluorescent probes.
1.2 Super-Resolution Microscopy: Breaking the Diffraction Limit
Since its discovery, fluorescence microscopy has quickly become a favorite tool of cell biology for the visualization of cellular architecture and key events occurring inside cells, tissues, and whole organisms.13, 14 Compared to other imaging techniques, it has two major advantages: it is compatible with living cells and, at the same time, permits the observation of their dynamics.15 Indeed, alternative methods (Figure 1.1), such as magnetic resonance imaging,16-18 positron emission tomography19, 20 and optical coherence tomography,21-23 allow a real-time dynamic imaging but fail to resolve the objects smaller than ca. 100µm, 1mm and 10
µm, respectively.15
On the other hand, such a powerful approach as electron microscopy24-26 permits a near- molecular level spatial resolution, but cannot visualize the movement of investigated objects in real time.15 In this respect, fluorescence microscopy is the only technique that offers reasonable ranges for both temporal and spatial resolution, though the latter has long been limited by the fundamental laws of physics.13, 15
The limitation lies in a wave-like character of light that diffracts when passing through the lenses. As a result, two objects that are closer together than half the wavelength of light cannot be discerned by the microscope.27 Thus, conventional microscopy, according to Ernst
Abbe28 and Lord Rayleigh29, cannot resolve objects smaller than ca. 250 nm in the lateral and ca.
500 nm—in the axial directions,13, 30 producing blurry images similar to the unreadable letters on the last line of the eye chart.31 This is called Abbe diffraction limit.30, 32 3
Figure 1.1. Comparison of spatial and temporal resolutions of different bio-imaging techniques. Spatial resolution is given for the focal plane and the size scale is logarithmic. The temporal resolution is not applicable (NA) for electron microscopy (EM) and near-field scanning optical microscopy (NSOM) because they image fixed samples. Ground-state depletion (GSD) and saturated structured-illumination microscopy (SSIM) have not been shown on biological samples, therefore their temporal resolutions are not determined (ND). ER, endoplasmic reticulum; MRI, magnetic resonance imaging; OCT, optical coherence tomography; PALM, photoactivated localization microscopy; PET, positron-emission microscopy; STED, stimulated emission depletion; STORM, stochastic optical reconstruction microscopy; TIRF, total internal reflection fluorescence; US, ultrasound; WF, wide-field microscopy. [Adapted from ref.15]
However, most cellular components, such as intramembranous organelles (nucleus, endoplasmic reticulum (ER), Golgi apparatus, mitochondria, vesicles), have much smaller dimensions13 (Figure 1.1) and most biological events occur on the scale below the diffraction limit, in the size range of tens nm.31-33 Therefore, development of new fluorescence microscopy techniques capable of circumventing the diffraction barrier has long been a major scientific challenge.13, 27, 32, 34 4
Initial attempts in this direction led to the invention of the near-field methods, such as near-field scanning optical microscopy (NSOM),35, 36 that use special lenses with small apertures positioned very close to the object to prevent light from diffraction. However, a short range of the near-field region capable of imaging only the surface of a sample, as well as the difficulties in the fabrication of effective apertures, significantly limited the applications of the near-field microscopy.31, 35 As a result, the far-field methods, such as confocal37 and multiphoton38 microscopy based on the design of a classical microscope with the lenses positioned at the distance from a sample, quickly emerged. But, unlike conventional microscopy, these techniques use non-linear optical approaches to reduce the effective size of the focal spot, thereby improving spatial resolution.31, 35
Further improvement of the far-field methods resulted in a whole new class of super- resolution microscopy techniques (SRM) that can be divided into two major groups:
(i) deterministic34 or illumination-based13;
(ii) stochastic34 or probe-based13.
The secret of deterministic methods in achieving spatial resolution far beyond the diffraction limit is the use of spatially structured excitation35 enhanced by non-linear effects such as reversible saturable optical fluorescence transitions (RESOLFT).39 This group of methods includes stimulated emission depletion (STED),40 ground state depletion (GSD),41 saturated patterned excitation (SPEM),42 saturated structured illumination (SSIM),43 and dynamic saturation optical microscopy (DSOM).44
Another group, based on stochastic activation of fluorescence in a sparse subset of molecules using phoactivatable (PA), photoswitchable (PS) or photoconvertable (PC) fluorescent probes,30 is comprised of photoactivation localization microscopy (PALM),45 fluorescence 5 photoactivation localization (fPALM),46 PALM with independently running acquisition
(PALMIRA),47 stochastic optical reconstruction microscopy (STORM),48 direct STORM
(dSTORM),49 point accumulation for imaging in nanoscale topography (PAINT),50 single- molecule active control microscopy (SMACM),51 ground state depletion followed by individual molecule return (GSDIM),52 photoactuated unimolecular logical switching attained reconstruction microscopy (PULSAR),53 and blink microscopy (BM).54
Both deterministic and stochastic approaches helped to unveil the structural features of the cell organelles such as endoplasmic reticulum, mitochondria, lysosomes, endo- and exocytic vesicles.35, 55 They also resolved the organization of chromosomes and nuclear envelopes,56 imaged the cytoskeleton of mammalian cells,35 solved the structure of telomeres,57 and shed the light on the dynamic movement of the focal adhesion and bacteria polarity complexes.13, 58, 59
Overall, these achievements drastically changed our understanding of biological systems and unlocked many of life’s mysteries—thanks to more than an order of magnitude improvement of spatial resolution in the SRM methods (ca. 10-20 nm) compared to conventional light microscopy.13 The advent of genetically encoded fluorescent proteins (FP), serving as endogenous fluorescent tags, had a great impact on the rise and success of the SRM methods.27, 60
1.3 Genetically-Encoded Fluorescent Proteins for Super-Resolution Microscopy
On December 10, 2008 three scientists—Osamu Shimomura, Martin Chalfie, and Roger
Tsien—were awarded the Nobel Prize in Chemistry in recognition of the “discovery and development of the green fluorescent protein, GFP”,61 the molecule that in a short period of time revolutionized many areas of science and medicine.62-65 6
Figure 1.2 Fluorescence of the jellyfish Aequorea Victoria. Calcium-binding protein aequorin (bottom left) is chemiluminescent. GFP (bottom right) absorbs 509 nm blue light emitted by aequorin and fluoresces 470 nm green.
Investigating a faint liquid squeezed out of the bioluminescent organs of the umbrella- shaped jellyfish Aequorea victoria, Shimomura discovered that two proteins—aequorin and
GFP—work in a tandem to produce an intense green glow.66 His biochemical experiments revealed that the mechanism of the Aequorean bioluminescence is based on GFP that emits green
(λmax = 509 nm) after absorption of a blue light (λmax = 470 nm) from the chemiluminescent calcium-binding aequorin (Figure 1.2).67
Following Shimomura’s findings, Martin Chalfie and co-workers expressed GFP in bacterium Escherichia coli11 and in neurons of Caenorhabditis elegans12 using the gene first cloned and sequenced by Douglas Prasher68 who by a virtue of bad luck did not become a Nobel 7 laureate, despite his tremendous contribution to the field and envision of the GFP role as a genetic tag.69
Figure 1.3. Color palette of various fluorescent proteins. From BFP and EGFP (A) to mFruits (B). [Adapted from ref.73]
In turn, Roger Tsien and co-workers70 engineered a whole palette of the fluorescent proteins (Figure 1.3): from blue fluorescent protein (EBFP)71 to the enhanced version of GFP
(EGFP)72 and variously colored mFruits.73 The latter are based on the monomeric mRFP1 variant of the red fluorescent protein (DsRed)74 discovered by Lukyanov and Labas in corals.
“Chemistry Nobel Glows Fluorescent Green”,75 “Glowing Jellyfish Earns Nobel
Prize”,76 “Glowing Proteins – a Guiding Star for Biochemistry”77—with those headlines the 8
2008 Nobel Award was highlighted in the news. While in 1990 the literature search for the keyword “green fluorescent protein” revealed only 1 paper, by 2008 this number has reached
4210.67 Moreover, by the time Nobel Prize was announced, several books about GFP have been written, and it has already found its way in numerous biological and medicinal applications.78-80
Nowadays, scientific interest in the genetically engineered variants of the GFP from
Aequorea victoria and its homologues from other marine organisms, commonly referred to as fluorescent proteins (FPs), is continuously growing, especially due to their applications as fluorescent tags for the SRM imaging of living cells.15, 64, 65, 81-83 Unlike other fluorophores, such as fluorescent organic dyes and quantum dots,13, 15, 34 FPs have a unique ability to be genetically encoded and expressed together with the target protein using transgenic approaches. This enables one to create fluorescent labels directly inside the cell without the use of invasive exogenous tags that are often toxic and require special fixation and permeabilization procedures to be attached to the target.13, 34, 83
Certainly, organic dyes and quantum dots used for the SRM imaging have a number of advantages over the FPs based probes. Those include small size, increased brightness, and high photostability.34 However, they cannot be “built in” inside a cell and, therefore, have limited applications for studying biological machineries of living cells.83
Developed over the last decades, a whole family of natural and genetically engineered
FPs exists, with emission colors spanning an entire visible light spectrum—from deep blue to deep red.64, 84 Some famous and widely used representatives of this family include bright blue
(EBFP2),85 bright cyan (Cerulean),86 stable green (Emerald),70 and bright yellow (Venus)87
Aequorean FPs; red FP from the anemone Discosoma striata (DsRed or mRFP)74 and its bright red variants tdTomato and mCherry;73 and FPs derived from the corals: bright teal (mTFP),88 9 orange (Kusabira Orange) and red (mKate).89 However, for applications in the SRM imaging a special class of FPs called optical highlighters has been developed.13, 84 This class of proteins is usually divided into three groups (Figure 1.4): (i) photoactivatable FPs (PA-FP), (ii) photoconvertable FPs (PC-FP), and (iii) photoswitchable FPs (PS-FP).13, 84
Figure 1.4. Optical highlighters. Photoactivation (A), photoconversion (B), and photoswitching (C) mechanisms. [Adapted from ref.84]
Photoactivatable proteins, such as PA-GFP,90 PA-mCherry191 and Phamret,92 normally have week fluorescence but can be switched on with the light of a specific wavelength. Examples of the photoconvertable FPs, capable of changing the color of emission upon excitation, include mEos2,93 mKikGR,94 and Dendra2.95 Among photoswitchable FPs that can be turned on and off 10 with different excitation wavelengths the most widely used are Dronpa,96 KFP1,97 and rsCherry.98 In addition, a unique IrisFP99, exhibiting both photoconversion and photoswitching behavior, is known.
1.4 Current Strategies for Design of New Fluorescent Proteins
Even though an astounding number of FPs has already been developed, none of them possess all characteristics of an “ideal” fluorescent probe. These characteristics include exceptional brightness defined by high molar extinction coefficient and high quantum yield, superior optical contrast, stability at low pH and high temperatures, monomeric quaternary structure, and effectiveness in fusion with other proteins.65, 100 For example, genetically improved blue Aequorean variants—Azurite, SBFP2 and EBFP2—have much higher brightness and photostability compared to their precursor EBFP but exhibit dimeric character.84 A monomeric teal-colored mTFP1 is an excellent alternative to the cyan mECFP and mCerulean because of the higher quantum yield, but a more narrow width of its emission spectrum requires a special filter set for optimal imaging.100 The far-red mPlum has excellent photostability but exhibits very limited brightness.84
Therefore, most current attention is paid to the design of novel FPs with as many characteristics of an “ideal” probe as possible. In this respect, a particular focus is made on the protein variants emitting in the orange-to-far-red and near-infrared regions of the light spectrum.83
The key to successful design is a unique structure of the jellyfish and coral FPs that consists of the tightly packed and extremely rigid β-barrel motif formed by 11 β-sheets surrounding the α-helix located in the center (Figure 1.5A).83, 101, 102 11
Figure 1.5. Structure of the GFP protein and its chromophore. A. Three-dimensional β-barrel structure of GFP formed by 11-stranded β-sheets and one central α-helix. B. Formation of the GFP chromophore from Ser65-Tyr66-Gly67 tripeptide during autocyclization reaction and its maturation in the presence of oxygen.
In GFP, a few essential amino acids—Ser65, Tyr66 and Gly67—are located in the heart of α-helix and, during the intramolecular cyclization catalyzed by inward-facing backbones of
Arg96 and Glu222, form the chromophore 4-(p-hydroxybenzylidene) imidazolidin-5-one (HBI)
(Figure 1.5B). The mechanism of the chromophore formation is similar in all known FPs, regardless of the source. In addition, oxygen is always required for the chromophore to maturate.102
The spectroscopic properties of the FP chromophore highly depend on the unique arrangement of the amino acids surrounding it. Therefore, replacement of certain residues can induce dramatic changes in the emission spectra of FPs, as well as in their photostability, pH, temperature resistance, and other characteristics.103 12
As a consequence, the most widely used strategy for the construction of novel FPs is based on tuning and improving the photophysical properties of already known FPs through the site-specific mutagenesis targeting all but evolutionary conserved residues located in the immediate vicinity of the chromophore.83, 84 Other strategies include (i) combination of a targeted structure-based library approach with quantitative screening for improved characteristics,104, 105 (ii) random mutagenesis,106 (ii) iterative somatic hyper mutation (SHM),107 and (iv) search for new fluorescent homologues in marine or coelenterate organisms.82
A completely different approach, neglected by the scientists, is to find a new source of
FPs with no homology to GFP.108 Pursuing the FP design in this direction is challenging, but it can help to overcome a number of problems that GFP-based proteins often pose. These problems include insufficient speed of the chromophore maturation controlled by the presence of oxygen in the system, the cytoplasmic nature of the proteins, and their tendency to oligomerize.15, 82 In this work, we emphasize the role of the light-sensitive transmembrane rhodopsin proteins as alternative sources of FPs.
1.5 Rhodopsins: General Overview
Among all known families of biological photoreceptors, rhodopsins are characterized in most details.109 These photoactive proteins are generally divided into two major sub-groups: microbial (type I) and vertebrate-like (type II) rhodopsins.110 The evolutionary relationships between these sub-groups are still a subject of hot debate, though a lot of evidence point to the fact that they originated in a convergent evolution rather than from a single progenitor/ancestor.111 Low percentage of sequence similarity, differences in the protein binding pockets and performed functions, and presence in the evolutionary distant species are among the facts supporting the idea of a convergent evolution.112 On the other hand, both type I and II 13 families have similar protein structures. They are comprised of seven transmembrane α-helices
(7TM) and share a chromophore with six conjugated double bonds (Figure 1.6).110, 111
Figure 1.6. Structure of the type I and type II rhodopsins. A. Seven transmembrane α-helixal proteins. B. Schematic illustration of the photoisomerization reaction.
This chromophore, called retinal protonated Schiff base (PSB), results from the condensation of the retinal (vitamin A aldehyde) with the terminal amino group of the lysine residue located on the seventh α-helix. In addition, the key photochemical event that defines the functions of the type I and II rhodopsins is the same—light-induced cis/trans isomerization.
However, in microbial rhodopsins all-trans retinal protonated Schiff base (PSBT) isomerizes into
13-cis form (PSB13) (Figure 1.6A), while in the vertebrate-like proteins 11-cis (PSB11) to all- trans (PSBT) isomerization takes place (Figure 1.6B). In both cases, the positive charge of the 14
PSB is stabilized by the counterion—negatively charged carboxylate (e.g. Glu113 for bovine
Rh).113, 114
Microbial rhodopsins have been first found in archea, and later on—in both bacterial and eukaryotic organisms.110 The most well-known representatives include bacteriorhodopsin115 functioning as a light-driven proton pump, light-dependent anion importer halorhodopsin116 involved in osmotic homeostasis of bacteria,117 sensory rhodopsins I and II 118 responsible for phototaxis, channelrhodopsins119-122 fluxing ions across the membrane, and Anabaena sensory rhodopsins.123, 124 In addition, archaerhodopsins,117, 125, 126 sharing a significant sequence similarity with bacteriorhodopsin, are known and function as proton pumps.
Type II family includes visual rhodopsins found in animal retinas.110, 114 Unlike type I, they are highly specific G-protein coupled photoreceptors with the major functions of vision and signal transduction.114, 127, 128
a 114 The process of vision starts when rhodopsin (Rh) captures a photon (λ max = 498 nm) inducing the ultrafast isomerization of PSB11 to PSBT.129 This step, called a primary event in vision, is one of the fastest and most efficient photochemical reactions in nature (Figure 1.7). As
a shown on Figure 1.7, the formation of the first red-shifted (λ max = 570 nm) ground state transient called photorhodopsin (photo) happens in less than 200 fs and the quantum yield of the process is
67% compared to a maximum of 24% for the photoisomerization of PSB11 in solution.114, 130 15
Figure 1.7. Photocycle of the visual pigment. The formation of the first transient photorhodopsin happens in less than 200 fs.
Within the next 2-3 ps of vibrational relaxation, a metastable intermediate
a 131 bathorhodopsin (bathoRh) is formed (λ max = 543 nm). As experiments at low temperatures
(77K) show, the irradiation of Rh with 580 nm light generates a photostationary state that can be characterized by the 61:1 Rh/bathoRh ratio. This indicates that bathoRh can be photochemically converted to Rh.132, 133 The observed Rh/bathoRh photochromism is supported by the close values of the molar extinction coefficients132, 133, as well as by the quantum yields (0.67 and 0.49 for Rh and bathoRh, respectively).132 However, at room temperature bathoRh decays through a series of intermediates to metharhodopsin-II which triggers the phototransduction cascade.114, 134
The photocycle of Rh has been extensively studied, with the major portion of both experimental114, 129, 135 and theoretical136-142 efforts devoted to the primary photochemical reaction. 16
In this context, excited state dynamics of both Rh and bathoRh has been thoroughly investigated and the mechanism of the low temperature (77K) photochromic equilibrium between them has been revealed.142 A comparison between the Rh→bathoRh and bathoRh→Rh classical trajectories is given on Figure 1.8.140, 143
Figure 1.8. Scaled-CASSCF/AMBER classical Rh → bathoRh (top, left) and bathoRh → Rh S1 trajectories (top, right). Bottom: Rh → bathoRh S1 classical trajectories computed with different initial conditions. [Adapted from ref.143]
17
As shown, experimentally observed ca. 100 fs135 lifetime of Rh has been computationally reproduced: within 120 fs Rh reaches the intersection space that is only partially explored due to the adiabatic nature of the classical trajectories. On the other hand, bathoRh reaches the same intersection space but from a different direction and on a shorter time scale (ca. 70 fs), consistently with the distorted nature of its all-trans chromophore.
The classical trajectories are consistent with the mechanistic picture provided by the more realistic semi-classical (i.e. non-adiabatic) trajectories (Figure 1.9).140, 143 The latter reveal that both the decay region and the region of the vibrationally hot photoproducts is reached on a sub- picosecond timescale. However, while the excited state parts of the Rh→bathoRh and bathoRh→Rh semi-classical trajectories are substantially the same, the decay regions are somewhat different. The Rh trajectory remains close to the CI after its decay, whereas in bathoRh the intersection space is immediately abandoned and the relaxation on the ground state begins instantaneously.
Figure 1.9. Scaled-CASSCF/Amber semi-classical Rh → bathoRh (left) and bathoRh → Rh (right) S1 trajectories. The scaling of the CASSCF is used to simulate the effect of the CASPT2 energy correction. The more accurate CASPT2 energy profile along the scaled-CASSCF trajectory is also provided (dotted lines). [Adapted from ref.143]
18
1.6 Rhodopsins as Actuators in Optogenetics
Similar to visual rhodopsins, microbial have also been studied in great details.110 The reason why type I rhodopsins have kept the attention of the scientific community since 1970s is the superior ability of many proteins belonging to this family to transport specific ions across the membrane upon light excitation.144, 145 This process is driven by the photoinduced PSBT to
PSB13 isomerization followed by the fast conformational changes in the protein that assist ion transport.110
In this context, bacteriorhodopsin (bR) from Halobacterium salinarium plays central role.115, 146 Known as a light-driven proton pump, it transports protons out of the cell during the photocycle, thus, creating a light-dependent voltage across the cell membrane. This behavior has been widely utilized to create bR-based photoelectrical detection devices such as artificial retinas.147 The ability of bR to translocate protons has also helped to design special membranes for the desalinization of sea water.148, 149 In addition, several optical devices for holographic recording and information storage media have been developed based on the photochromic properties of bR.150
The other famous members of the type I family are Natronomonas pharaonis halorhodopsin (NpHR)116 and channelrhodopsins I and II from the green algae Chlamydomonas
(ChR1 and ChR2).119, 120, 122 In the recently emerged and constantly growing field of optogenetics, these genetically encoded light-gated ion channels are widely used as actuators to control the activity of specific neurons in the brain with high spatio-temporal resolution.151, 152 Delivered into neurons using transgenesis, transfection, electroporation, or viral transduction, halorhodopsins and channelrhodopsins work as antagonists.152, 153 For example, ChR2 stimulates firing of 19 neurons using blue light (λ = 500 nm) while NpHR shuts off the neural activity in response to yellow light (λ = 570 nm) (Figure 1.10).153
Figure 1.10. Schematic illustration of the neural activation and neural inhibition by ChR2122 and NpHR.116 Light-induced isomerization of PSBT to PSB13 (A) induces the conformational change in the opsin that causes the flux of ions across the cell membrane (B).
By means of optogenetics tools, scientists have been able to precisely determine how different types of neurons function in the processes such as somatosensation, learning, awakening, vision, breathing, and movement.152, 154 The relationships between the brain activity and anxiety, fear, depression, addiction, autism and Parkinsonism have also been uncovered.152
Novel optogenetics tools, more powerful, more light-sensitive, with novel spectral characteristics, are constantly emerging. The same strategies that revolutionized the development 20 of FPs are successfully used to expand the toolbox of optogenetics.152 They include site-specific mutagenesis and chimeragenesis of the existing opsins, as well as directed evolution and high- throughput screening.152, 155 The alternative strategy is to search the microbial genomes for the new light-regulated proteins with desirable properties. For example, using this approach channelrhodopsin homolog from Volvox (VChR1)156 and archaerhodopsins117 have been discovered.
In fact, visual rhodopsins can also be used in optogenetics research.153 Original experiments have shown that endogenous rhodopsins can regulate activity of the native ion channels by participating in a G-protein coupled biochemical cascade.157 However, this approach required exogenous expression of the multiple genes encoding several proteins of the pathway.153,
157 Instead, the use of exogenous rhodopsin has been much more successful. 158 Through the coupling to endogenous signaling proteins, rat visual rhodopsin controls neural activity and modulates synaptic transmission by activating the G-protein-gated inward potassium and voltage-gated calcium channels. Similar results have been obtained with exogenous expression of the melanopsin from retinal ganglion cells.159 However, the light response of neurons using visual rhodopsins is slow; therefore, they are less attractive compared to microbial ones for the optogenetics purposes.153
1.7 Rhodopsins as Fluorescent Probes
In spite of the fact that most design strategies discussed above are focused on the development of new actuators that use light to control cells, one should not underestimate the importance of the tools that exploit light to monitor them.151, 160, 161 The sharer of the 2008 Nobel
Prize in Chemistry, Roger Tsien, who tremendously contributed to the “design and development of GFP and GFP-like fluorescent proteins”70-72, 162 (see Chapter 1.4), first had an idea to couple 21 the gene encoding the light-controlled actuator ChR2 with the gene of the fluorescent protein.151
Even though his initial attempts in this direction failed, the idea of fusing the protein that uses light to control cells (e.g. light-driven neural activator ChR2 or neural silencer NpHR) with the light-emitting protein that reports on them have been quickly absorbed by the scientific community.160, 161
As a result, nowadays more and more “rhodopsin-fluorescent protein” hybrids are being created. Capable of reporting on the voltage, ion or biochemical activity inside the cell, these hybrid biosensors are immensely important.163, 164 However, the use of sophisticated genetic engineering tools to create them makes the overall design process time- and resources- consuming.
But what if one protein could perform both functions—those of the actuator and reporter—all in “one box”, simultaneously? What if one could engineer a microbial rhodopsin to become intrinsically fluorescent, without the need to attach the exogenous fluorophores or endogenous fusion with FPs?
In fact, Kralj and co-workers have recently reported on the genetically encoded voltage- sensitive fluorescent indicators—proteorhodopsin optical proton sensor (PROPS)164 and archaerhodopsin 3 (Arch)108—capable of recording and reporting the action potentials from many neurons simultaneously. As a way to create new reporters, the authors have suggested to further explore the family of microbial rhodopsins for the ability to fluoresce and label biological membranes.108, 164 Intuitively, the systematic mutagenesis and directed evolution of PROPS and
Arch, as well as the high-throughput screening of microbial genomes for their homologs, is the most logical way to generate new rhodopsin-based reporters. 22
Instead, the major challenge of this work was to investigate in silico the possibility of turning a non-fluorescent rhodopsin into a fluorescent one. At the quantum-mechanical level, this means to find a way of increasing the excited state lifetime of the molecule by changing the shape of its barrierless excited state potential energy surface to a barrier-controlled one. Using a well-studied114, 127, 129, 135-140, 142 bovine Rh as a model system, we have shown that members of the rhodopsin family may be engineered to yield alternative source of FPs, despite the ultrafast photoisomerization reaction135, 142, 165, 166 characterizing these systems (see Chapter 4).
Preliminarily, to gain more insight into the phenomenon of the barrier-controlled fluorescence lifetime, we have also investigated using ab initio multiconfigurational methods the photophysics of the N,N,N’,N’-tetramethyl-p-phenylenediamine radical cation, known as
Wurster’s Blue (WB) (see Chapter 3).167, 168 This relatively small and stable organic species, exhibiting a temperature-dependent fluorescence behavior, has been used as a training system for mapping of the excited state potential energy surfaces featuring a barrier. For our purposes, WB had two advantages: (i) it allowed the use of state-of-the-art quantum chemical methods providing a quantitative description of both geometrical and electronic structure of the species and (ii) it could be carefully investigated using time-resolved spectroscopic methods.
23
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33
CHAPTER 2: METHODOLOGY
2.1 Computational Photochemistry and Photobiology
Photochemistry was born in the beginning of the 20th century, when two Italian chemists—Giacomo Ciamcian and Emanuele Paterno—started to investigate the interaction of sunlight with organic substances.1, 2 At that time, the need for a microscopic-level understanding of what happens to a molecule after it absorbs a photon has emerged.3
In the 1950s, when computers and algorithms capable of solving complicated mathematical equations came into use, scientific community has realized that quantum mechanics can be nicely applied to study such complex systems as molecules, especially as they chemically react.4 In 1970, the release of the GAUSSIAN quantum chemistry package5 has provided chemists with the first computational tools necessary to solve many chemical problems.6 Ever since, these tools have been constantly improved and more accurate quantum chemistry algorithms have been continuously developed.4
Initially, computational studies have been mainly focused on the thermal reactions happening in the ground state.7 In 1953–1956, the first photochemical calculations have been performed by Parr and Pariser to predict the electronic structure and spectra of such molecules as benzene,8 N-heterocyclic analogues,9 azulenes,10 and polyacenes11 using semi-empirical method based on the zero-differential overlap approximation (ZDO).12
However, a few decades have passed before the robust ab initio multiconfigurational quantum chemistry methods, capable of mapping the potential energy surfaces of both ground and excited states, have appeared.13-19 Using these methods,15 the computation of the entire photochemical reaction paths connecting photoexcited reactants to the ground state products has become a reality. Nowadays, ab initio multiconfigurational methods are considered the 34 ubiquitous tools for studying such processes as photosynthesis, phototropism, photochromism, vision, fluorescence, phosphorescence and many more, giving rise to the field of computational photochemistry and photobiology.4
The aim of this chapter is to introduce these methods in the context of the computational investigation of the photochemical reactions. The most common procedures for mapping ground and excited state potential energy surfaces of the molecules will be described and the underlying quantum chemistry concepts will be explained.
2.2 Potential Energy Surfaces and Their Topological Features
Being a direct consequence of the Born-Oppenheimer approximation20 that allows the molecular wavefunction to be split into its electronic and nuclear components (see Chapter 2.5),
Potential Energy Surface (PES) is a mathematical function RE )( that describes the electronic energy of a given molecular system for all of its possible nuclear arrangements.
It is a key concept in computational chemistry that helps to visualize how during the chemical reaction a molecular structure evolves over the surface provided by the electrons by changing the relative position of the nuclei. Even though in many cases (e.g. near the surface crossings) the Born-Oppenheimer approximation breaks down and nuclear and electronic motion become coupled,3 the language of the PESs continues to be a convenient way to describe the motion of the nuclei.
The topological features of the PESs are similar to those of the Nature’s landscape with mountains, valleys and hollows (Figure 2.1A). Similar to the roads going from one valley to another through the passes with a least possible height difference with respect to the valley, chemical reactions will take place along the minimum energy path (MEP)21, 22 connecting reactants and products (Figure 2.1B). 35
Figure 2.1. Comparison between the Nature’s landscape and the PES of a chemical reaction. A. Photograph of the green hills. B. Schematic representation of one-dimensional (left) and two- dimensional MEPs connecting reactant A and product B.
Due to the fact that PES is a (3N-6) dimensional hypersurface (where N is the number of atoms in a molecule), the calculation of the entire PES is complicated. Therefore, it is usually approximated by computing MEP along the most significant internal coordinate, also called reaction coordinate. The latter can be represented by either a single mode (e.g. bond stretching, torsion along a dihedral angle), or defined by two concerted (e.g. bond stretching and angle bending) or subsequent (e.g. bond stretching followed by torsion) molecular deformations. 36
The most important stationary points on PES include local minima corresponding to the equilibrium molecular structures associated with reactants, intermediates, or products and saddle points—non-stable species representing transitions states (TS).23, 24
Both types of stationary points share the same common feature: the first derivatives of energy with respect to the (3N-6) nuclear coordinates are equal to zero, i.e. the length of the gradient vector formed by these derivatives must have a zero length. However, the nature of the stationary points can be explicitly determined by looking at the eigenvalues of the second derivatives Hessian matrix. The stationary points with all positive Hessian eigenvalues are called local minima (Figure 2.2A), whereas a presence of at least one negative direction of curvature, called imaginary frequency, indicates a saddle point (Figure 2.2B). It is also worth noting that a local maximum on PES is defined by the Hessian with all negative eigenvalues (Figure 2.2C).
Figure 2.2. Shapes of the stationary points: minimum (A), saddle point (B), maximum (C).
In a quadratic approximation, a minimum can be visualized by the common vertex of the
(3N-6) parabolas each having a positive second derivative, while the saddle points, instead, are characterized by some of the parabolas with negative derivative. Depending on the number of such parabolas, one can distinguish the saddle points of the first, second, third, etc. order. The transition state of the reaction (TS) is normally referred to as the first order saddle point. The 37 internal coordinate corresponding to the negative direction of curvature of the TS is called a transition vector.
Localization of the stationary points on the ground state PES and calculation of the MEP connecting them allows a description of the thermal processes. To investigate the photochemical reaction paths, both ground and excited state PESs must be considered.
2.3 Photochemical Reaction Path
After a molecule absorbs light, several scenarios25 are possible, including those depicted in Figure 2.3. Notice that in each case the representation of the corresponding photochemical process includes the description of both ground and excited state PESs.
In the first example (Figure 2.3A), after a molecule is promoted to vibrationally excited state, the intramolecular vibrational relaxation (IRV), that can often be accompanied by the vibrational energy transfer (VET) to the solvent or surrounding molecules, takes place within
10-14–10-11 s. Alternatively, a nuclear reorganization can cause a formation of new excited state species via a Photoadiabatic Reaction (PAR) (Figure 2.3B). In both above-described cases, once the excited state minimum is reached, the molecule then relaxes radiatively to the ground state either by fluorescence (if radiative emission involves the states of the same multiplicity) or by phosphorescence (when the states multiplicities are different). The time scales of the processes are 10-9–10-6 s and 10-3–10-2 s for the fluorescence and phosphorescence, respectively. Another way for a molecule to dissipate its energy is to decay non-radiatively from the higher to the lower energy state through either singlet-triplet crossings (Figure 2.3C) or via so-called conical intersection (CI) controlling the transition between the PESs of the same spin multiplicity
(Figure 2.3D). 38
Figure 2.3. Schematic illustration of the most common light-induced photochemical and photophysical events. [Adapted from ref.25]
In order to figure out according to which scheme the photochemical reaction proceeds, one has to investigate thoroughly the topology of the PESs relevant to the photochemical reaction of interest.
A schematic representation of the photochemical reaction path typical for an ultrafast process, such as PSB11 to PSBT photoisomerization of Rh, is given in Figure 2.4. Here, the excited state MEP connects Franck-Condon (FC) point with two different ground state MEPs through the CI. While one of the ground state MEPs is aborted photochemical reaction driving the system back to the initial reactant A, another one describes the relaxation of the molecule in a normal photochemical reaction leading to the formation of the ground state photoproduct B. 39
Figure 2.4. Three-dimensional (left) vs. two-dimensional (right) schematic representation of the ultrafast barrierless photochemical reaction path (full lines). The decay is controlled by a conical intersection (CI). A thermal path (thinner full line) is controlled by the transition state (TS). Schematic reactive and non-reactive photochemical trajectories that can be computed using semi-classical molecular dynamics are also reported (dotted line). [Adapted from ref.3]
The most well-known way to compute both excited and ground state MEPs is the calculation of Intrinsic Reaction Coordinate (IRC)26 defined as the steepest-descent path in mass- weighted Cartesian coordinates starting from the corresponding initial structure (FC or CI) and following the gradient. The IRC calculations on the ground state PES are always assisted by defining the initial relaxation direction (IRD)—vector connecting the CI to either products or reactants. To calculate the IRD, the gradient difference and derivative coupling vectors XX 21 ),( defining the branching plane of the CI must be computed, according to the procedure described in ref.27 40
2.4 Conical Intersections1
As it was already mentioned above, unlike thermal reactions, governed exclusively by the topology of the ground state PES, photochemical reactions require investigation of the excited state as well.4 In particular, to compute a photochemical path4, 28-30 one needs to connect the reactants residing on the excited state to the products accumulating on the ground state.
To do so, it is vital to establish the “critical structures” where the decay probability from the excited to the ground state is the largest.4 These “critical structures” are called photochemical funnels31, 32 and, in case when two states have the same spin multiplicity, correspond to the CIs.
Used primarily to explain the radiationless transitions, CIs provide structurally and electronically well-defined connection between different electronic states: for example, by describing the reaction stereochemistry and hemolytic/heterolytic bond breaking in the reacting species.4
Original ideas on the crossings of the PESs belong to von Neumann and Wigner,33 followed by the contributions from Teller34 and Herzberg and Longuet-Higgins35 who proposed that (i) the non-crossing rule valid for diatomic molecules fails in polyatomic systems where the states of the same symmetry are allowed to cross; (ii) the crossings between the states are conical.
Later, van der Lught and Oosterhoff36 and Devaquet et al.37 introduced the idea of the avoided crossing controlling the photochemical conversion of buta-1,3-diene into cyclobutane
(Figure 2.5, left). The excited state decay time, corresponding to the avoided crossing energy gap
(ca. 30 kcal mol-1), was estimated to be in the order of nanoseconds, similar to the typical fluorescence lifetimes. Nowadays, we know that the photochemical conversion of buta-1,3-diene is mediated by the CI rather than the avoided crossing (Figure 2.5, right).
1 This section is based on the article: Schapiro, I.; Melaccio, F.; Laricheva, E. N.; Olivucci, M. Using the computer to understand the chemistry of conical intersections. Photochem. Photobiol. Sci., 2011, 10, 867–886.
41
Figure 2.5. Comparison of the Van der Lugt and Oosterhoff’s36 avoided crossing (left) to the conical intersection model (right) mediating the photochemical conversion of buta-1,3-diene into cyclobutane. Adapted from ref.3
At the time when van der Lught and Oosterhoff presented their observations, the radiationless decay through the avoided crossing could easily be explained by the theory of the radiationless transitions dominated by the Fermi’s golden rule38, 39. According to this rule, the probability of the non-radiative transition λif can be defined as
2 2 EV )( (2.1) if f if f where i and f are initial and final vibrational eigenstates between which the transition happens,
Vif is a matrix element representing the electronic coupling between these states, and f E)( is the density of the final states.
However, this theory failed to explain the ultrafast photochemical events occurring in less than a few picoseconds and associated with a weak or no fluorescence, thus, suggesting that the energy gap between excited and ground states is smaller than a few kcal mol-1.3 42
The search for the funnels that could explain the selectivity of the photochemical reactions led Zimmerman,40 Michl41 and Salem42 to independently suggest that, for a broad class of organic reactions, the real “cone-shaped” CIs exist. In the later years, Yarkony43-45 and
Rudenberg46 located the CI geometries for a number of small molecules. However, the idea of the CIs was not widely accepted until the development and implementation of ab initio multiconfigurational quantum chemistry methods and algorithms capable of locating the minimum energy points on the seam of the crossing between the two states.3, 4
When the methodology became available, many groups started to investigate the mechanisms of various photochemical reactions. In 1990-2000, Bernardi, Robb, Olivucci and co- workers studied 25 different compounds involved in 16 different types of photochemical reactions.47 Other CIs were reported by Ruedenberg,48, 49 Martínez,50, 51 Domcke,52-54 Koppel and
Cederbaum,55 Yarkony45, 56 for different molecules.
Generally speaking, any CI is the element of the (3N-8) dimensional intersection space formed by the infinite collection of the CIs and orthogonal to the XX 21 ),( branching plane 43, 47 defined by the derivative coupling X 1 and gradient difference X 2 vectors. As shown on
Figure 2.6 (left), the situation can be visualized by the seam of the crossing points resulting from the intersection of two PESs. These PESs are plotted along the coordinate plane defined by one of the branching plane vectors and one of (3N-8) molecular modes belonging to the intersection space.
While decay to the lower PES may occur from any point of the intersection space, it is feasible to assume that this happens through the minimum energy conical intersection (MECI) which is the most chemically significant crossing point belonging to the intersection seam.3
43
Figure 2.6. Pictorial representation of the intersection space between two PESs. Left: The CIMEP and MECI refer to the crossing points located using the MEP calculations and conical intersection optimization. The CITraj refers to the intersection point located using trajectory computations. Right: Shapes of the photochemical reaction paths and crossing regions leading to peaked (top) and sloped (bottom) CIs. [Adapted from ref.3]
According to the relative orientation of the PESs in the vicinity of the crossing point, one can distinguish two major types of CIs: peaked and sloped (Figure 2.6, right). In the peaked CI, two intersecting curves have gradients of the opposite sign so that the apex of the cone is the lowest energy point on the excited PES and the highest energy one—on the ground state. Instead, if the gradients of the two curves have the same sign, the resulting CI is tipped (sloped). When one of the curves has near-zero gradient, this is case of the intermediate CI not shown on Figure
2.6.
To summarize, the major differences between the CI mediating light-induced process and the TS controlling thermal reaction are depicted on Figure 2.7. 44
Figure 2.7. Major differences between the transition state (left) and conical intersection (right). [Adapted from ref. 3]
As illustrated, the TS is a stationary point on a single PES, while the CI is a singularity on both upper and lower states so that the first derivative of the potential energy in the region of the
CI is not a smooth function of its nuclear coordinates. Second, the reactivity of the TS is defined by the transition vector, while for a proper description of the CI two molecular modes X 1 and 43 X 2 are needed.
2.5 Born-Oppenheimer Approximation
The time-independent Schrödinger equation is a key equation in non-relativistic quantum chemistry
ˆ RrRERrRrH ),()(),(),( (2.2)
Here, Rr ),( represents a molecular wavefunction that depends on both electronic r and nuclear R coordinates. ˆ RrH ),( is a Hamiltonian that can be rewritten in terms of the nuclear and electronic contributions 45
ˆ ˆ ˆ ˆ ˆ ˆ ),( n )( e )( nn )( en ),( ee rVRrVRVrTRTRrH )( (2.3)
ˆ ˆ In Equation 2.2, n RT )( and e rT )( are nuclear and electronic kinetic energy operators,
ˆ ˆ ˆ nn RV )( and ee rV )( are nuclear-nuclear and electron-electron repulsion terms, and en RrV ),( is electron-nuclear attraction term.
To separate the nuclear and electronic parts, the Born-Oppenheimer approximation20 is introduced. This approximation is based on the idea that the nuclei are nearly fixed with respect
ˆ to the electron motion because the former are much heavier than the latter. Thus, n RT )( and
ˆ nn RV )( in the Equation 2.2 can be neglected and the “clamped-nuclei” Schrödinger equation can be introduced
ˆ (2.4) el el elel RrRERrRrH ),()(),(),(
Therefore, in order to describe the quantum chemical system, one has to solve the electronic part of the Schrödinger equation and find the electronic energy el RE )( . In the
Equation 2.3, the electronic wavefunction el Rr ),( explicitly depends on the electronic coordinates and only parametrically on the nuclear coordinates so that is the r R el RE )( potential energy surface created by the electrons and experienced by the nuclei. For the fixed nuclei, the nuclear-nuclear repulsion term Vnn has to be added to the electronic energy in order to find the total energy of the system
tot el nn RVREE )()( (2.5) 46
2.6 From Hartree-Fock to Post-SCF methods
Hartree-Fock (HF)62, 63 is a fundamental method of the electronic structure theory for solving the electronic part of the time-independent Schrödinger equation in the framework of the
Born-Oppenheimer approximation (see Section 2.5)
According to HF, the wavefunction of the N-electron system can be described by the
Slater determinant built using orthogonal antisymmetric one-electron wavefunctions.64
χ (x χ) (x1211 χ) N(x1 ) 1 χ (x χ) (x χ) (x ) 2221 N 2 (2.6) Ψ(x ,x21 , ,xN ) N! χ1(xN χ) 2(xN χ) (xNN )
In Equation 2.6, x)( represents a spin orbital of the electron which is a product of a
2/1 spatial orbital r)( and a spin function (either or ). Here, N )!( is a normalization factor.
In a short-hand notation with an implicit normalization factor, the Equation 2.6 can be written as follows
xx 2211 xNN )()()( 21 a b N (2.7)
If we have an orbital set k consisting of the N occupied spin orbitals with the indices a, b, c, etc. and (2K-N) unoccupied (virtual) orbitals with the indices r, s, t, etc., than the situation can be illustrated using Slater determinant according to Scheme 2.1. This determinant represents a ground state configuration; therefore, the HF method is only suitable for the description of the ground state properties. 47
Scheme 2.1. Slater determinant in the Hartree-Fock method (possible degeneracies are neglected).
For characterization of the excited states other configurations corresponding to the promotion of the electrons from the occupied to the virtual orbitals must be added to Slater determinant which serves as a reference wavefunction 0 .
For example, a single excitation promoting the electron from the occupied orbital a to
r the virtual orbital r can be described by the wavefunction a . In a similar fashion, a double
rs excited determinant ab illustrates the situation when two electrons are excited from the occupied orbitals and to the virtual orbitals and (Scheme 2.2). a b r s
Using the short-hand notation, single and double excited determinants are as follows
r a 21 r b N (2.8)
rs ab 21 sr N (2.9)
48
Scheme 2.2. Single (left) and doubly (right) excited determinants (possible degeneracies are neglected)
For all possible configurations, from the single and double to the higher excited determinants, the exact wavefunction of the system is given by Equation 2.10.
r r rs rs rsm rsm 00 cc a a cab ab cabc abc (2.10) ra , srba , msrcba
The expansion of any N-electron wavefunction by including all possible excitations is called Full Configuration Interaction (FCI).65 The lowest eigenvalue obtained using this method represents the exact non-relativistic ground state energy of the system. This energy E differs from the Hartree-Fock energy E0 by a certain value called correlation energy Ecorr
corr EEE 0 (2.11)
In fact, the major limitation of the HF method is its failure to describe the significant portion of the correlation energy. In particular, the use of the antisymmetric one-electron wavefunctions to construct the Slater determinant enables to take into account the motion of the electrons with the same spin (Fermi correlation), but cannot properly characterize the interaction of the electrons with the opposite spin functions (Coulomb interaction). 49
The so-called Post-SCF methods help to recover the portion of the correlation energy missed by the HF. In this respect, the FCI performed in a complete one-electron basis set is capable of obtaining the exact non-relativistic energy E with all electron correlation effects taken into account. However, the excessive cost of the FCI computations has led to the development of more approximate methods.
Indeed, the ground states of some systems can be well described by a single configuration with a Hartree-Fock reference wavefunction. The examples include Møller-Plesset perturbation theory (MP2, MP3, MP4), singles and doubles configuration interaction (CISD), and coupled cluster (CC) methods.65
However, in many cases a single configuration does not provide a qualitatively good representation of the system. For example, this is true for the photochemical reactions involving excited states, as well as for the thermal processes that require the investigation of the PES regions in the vicinity of the TS.
To overcome the problem, the Multiconfigurational Self-Consistent Field (MCSCF)39, 66,
67 method has been developed. The MCSCF wavefunction corresponds to a truncated FCI with both the coefficients CI and the orthonormal orbitals variationally optimized
MCSCF C II (2.12) I
For any closed-shell system, the MCSCF method is equivalent to the HF with the wavefunction defined by the ground state configuration only. In this work, we have extensively used the MCSCF variant called the Complete-Active Space Self-Consistent Field (CASSCF)16, 68 method which is briefly described in the next section. 50
2.7 Complete-Active Space Self-Consistent Field (CASSCF) Method
Generally speaking, the CASSCF16, 68 is a combination of the HF and FCI methods with the CASSCF wavefunction being a linear combination of all possible configurations arising from the distribution of the active electrons of a given system among its active orbitals. Both active electrons and active orbitals constitute the so-called complete active space (CAS), and the choice of the CAS fully depends on the problem under investigation. For example, for a correct description of the excited state of the chromophore containing a π-system, the orbitals involved in the photoexcitation must be included in the CAS. Likewise, for the investigation of the chemical reaction the orbitals participating in the bond-breaking and bond-making processes must be included.
An example of the CASSCF wavefunction constructed for the ethylene molecule is given in Scheme 2.3.
Scheme 2.3. The CASSCF wavefunction of ethylene. The active space of ethylene consists of 2 π electrons on 2 π orbitals. 51
The active space of ethylene encloses two active π electrons distributed among two π and
π* orbital. As a result, the molecular wavefunction consists of four different Slater determinants representing all possible excitations within a given active space.
The first determinant depicted on Scheme 2.3 corresponds to the electronic configuration of the closed shell system with the doubly-occupied π orbital and the variational coefficient c1.
All the other configurations describe the promotion of the electrons to the higher energy orbital.
While the wavefunction of the ground state minimum is dominated by the closed shell configuration, along the reaction path governed by the Z/E isomerization other configurations contribute. According to Scheme 2.3, the inactive and secondary (virtual) orbitals are also defined in the CASSCF. The inactive orbitals remain occupied in all CASSCF configurations, while the virtual ones stay empty. During the variational process, both inactive orbitals and active orbitals are optimized, but the former are rather treated as in the HF method. At the same time, the virtual orbitals remain
Often, during the computation of the excited states the phenomenon called root flipping occurs. It is associated with the interchange of the roots during the CASSCF optimization procedure. To prevent this from happening, a modification of the CASSCF method called State-
Average CASSCF (SA-CASSCF) is normally used.4
Overall, the CASSCF methodology, widely used for mapping of both ground and excited
PESs, has proven its validity to give accurate description of the chemical reactivity (e.g. the treatment of the situations involving partially broken bonds and the development of the biradical character), but fails to reproduce the correct energy gaps (e.g. absorption and fluorescence maxima) and activation barriers. This is due to the fact that, while being able to treat the long 52 range static correlation effects, it cannot adequately describe the short-range instantaneous interelectronic repulsion called dynamic electron correlation effect.
The latter effect can be accounted by the multireference configuration interaction
(MRCI)65, 69 or multireference second order perturbation theory (MRPT2).70 In this thesis, the
Complete Active Space Perturbation Theory of the second order has been widely applied to correct the energies obtained using CASSCF wavefunction.
2.8 Complete Active Space Second Order Perturbation Theory (CASPT2) Method
In general, all perturbative methods are based on the idea of finding an accurate solution to the complex problem by taking a known solution of a simple Hamiltonian Hˆ 0 as a reference and by adding to it an additional part Hˆ ' that weakly perturbs the system. The following set of the equations with the arbitrary real parameter λ proportional to the value of perturbation can be written in this case
Hˆ E )()()()( (2.13)
ˆ )( )0( HHH ˆˆ ' (2.14)
)( )1()0( 2 )2( (2.15)
)( EE )1()0( 2 )2( (2.16)
While the expansion of Equation 2.16 is exact in the limit of the infinite terms, it is sufficient to truncate it at the second order to ensure an accurate solution. If the zeroth-order reference function is that of the HF, then the perturbation method is called Second Order Møller-
Plesset Perturbation Theory (MP2)71, extensively used to treat the dynamic electron correlation of the ground states. 53
If the CASSCF wavefunction is used as a reference, the method is the Complete Active
Space Second Order Perturbation theory (CASPT2)72, 73. The CASPT2 can be visualized as a full generalized application of the Rayleigh-Schrödinger perturbation theory for the case of the multirefence wavefunctions.74 By introducing a single-point CASPT2 energy correction on the
CASSCF-optimized geometries, one can get a good agreement between the computed and experimental properties of the system.3
While ab initio multiconfigurational CASPT2//CASSCF methodology provides accurate results for the sizable organic molecules in the gas phase, it is not suitable for a full quantum mechanical (QM) description of the large systems due to its excessive computational cost.
Instead, such systems can be treated using hybrid quantum mechanics/molecular mechanics
(QM/MM) protocol.
2.9 Hybrid Quantum Mechanics/Molecular Mechanics (QM/MM) Method
The history of the hybrid methods dates back to 1976 when Warshel and Levitt75 performed first semi-empirical QM/MM calculations on the lysozyme. But it was not until 1990s when the QM/MM methodology received wide acceptance.76 Nowadays, it is a ubiquitous tool for the description of the complex biomolecules76-81 (e.g. chromophores embedded in a protein environment) and explicit solvent studies82-84 (e.g. chromophores in a solvent bulk) as it combines the accuracy of the quantum mechanical (QM) methods with the low computational cost of the molecular mechanics (MM) treatment.3 The QM/MM has also been successfully applied to study the inorganic/organometallic85-87 and solid-state systems.88-90
In a typical QM/MM setup, the system is partitioned into two regions that play different roles: the chemically important region (e.g. active site of the enzyme or chromophore in solution) 54 requires a high level QM treatment, while the surroundings (e.g. box of the solvent molecules or the protein hosting the QM part) are modeled using MM force field (Figure 2.8).
Figure 2.8. Illustration of the QM/MM partitioning. A. Chromophore (solute) in a solvent bulk. B. Chromophore (active site) embedded in a protein.
According to the way of computing the total energy, all QM/MM methods are classified into:3, 76, 81
(i) subtractive methods that require the calculation of the entire system at the MM level (
MM QM E full ), the pure QM calculation of the inner QM region ( Esmall ), and the MM
MM calculation of the QM part ( Esmall ), so that the total energy is given by
QM /MM MM QM MM Etot full small EEE small (2.17)
(ii) additive methods that include in the calculation of the total energy an explicit
QM/MM coupling term added to the energies of the MM and QM regions
QM /MM MM QM QM /MM Etot full small EEE coupl (2.18)
The coupling term consists of the contributions from the bonded, van der Waals, and
electrostatic interactions between the QM and MM atoms 55
QM /MM QM /MM QM /MM QM /MM Ecoupl bond vdW EEE el (2.19)
Different schemes are used to treat the electrostatic interactions between the QM and
MM regions.76 In the mechanical embedding scheme, these interactions are accounted for at the
MM level by deriving the MM-like charges for the QM atoms resulting in the poor description of the QM polarization by the MM environment. This shortcoming can be overcome using the electrostatic embedding scheme that includes the MM point charges in the QM Hamiltonian to polarize the QM wavefunction. However, for this type of embedding the MM part is not polarized by the QM atoms. In the Electro-Static Potential Fitted operator (ESPF) method, the
QM wavefunction is polarized by the MM potential while the electrostatic energy is calculated by deriving the MM-multipoles for the QM atoms.
When the QM and MM parts polarize each other until their charge distributions are self- consistent, the scheme is called the polarized embedding. A mutual polarization can be achieved by using polarizable force fields for the MM part and the iterative algorithm with electrostatic embedding for the whole system.
The bonding term from the Equation 2.18 describes the covalent bond at the boundary between the QM and MM regions. According to the Link-Atom (LA) scheme, the frontier
(usually hydrogen) is introduced to saturate the pending valence of the QM fragment. Other schemes use localized orbitals at the QM/MM boundary. In some systems (e.g. solutions) there is no need for a special QM/MM frontier and the boundary is chosen as the surface between the solute and solvent molecules that does not cut any covalent bonds.
Throughout this work, we used the QM/MM scheme with the electrostatic embedding and no covalent bonding for the Wurster’s Blue radical cation in methanol solution (see Chapter 56
3), whereas the link-atom scheme was applied to treat the QM/MM boundary of rhodopsin proteins (see Chapter 4).
57
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62
CHAPTER 3: PHOTOCHEMISTRY OF WURSTER’S BLUE RADICAL CATION2
Abstract
The fluorescence lifetime of N,N,N',N'-tetramethyl-p-phenylenediamine radical cation, a well-known Wurster's Blue, decreases from 260 ps at 82 K to 200 fs at room temperature.
Quantum chemical calculations point to the presence of a small barrier between the excited state minimum and the conical intersection of the excited and ground state potential energy surfaces.
This intersection is reached within 200 fs upon a small torsion of a single C–N bond. The whole process is associated with the charge transfer from the nitrogen centers to the phenyl ring and back (Scheme 3.1).
Scheme 3.1. Photocycle of Wurster’s Blue. D0 min and D1 min are ground and excited state equilibrium structures; D1/D0 CI is a conical intersection between ground and first excited states; IVR stands for intramolecular vibrational relaxation and VC—for vibrational cooling.
2 This chapter is based on the article: Grilj, J.; Laricheva, E.N.; Olivucci, M.; Vauthey, E. Fluorescence of Radical Ions in Liquid Solution: Wurster’s Blue as a Case Study. Angew. Chem., Int. Ed. 2011, 50, 4496–4498. 63
3.1 Introduction
Recently, organic mixed-valence (MV) compounds of the [M-B-M]+ type, consisting of two identical charge-bearing units M connected by the molecular bridge B, have received considerable attention.1-6 In particular, due to the possibility of intramolecular electron transfer between the M units, arylamine and p-phenylenediamine based MV compounds have been investigated as model hole-transporting materials for the fabrication of high-performance switching devices and organic light-emitting diodes (OLEDs).1, 5 In this context, the photochemical and photophysical properties of a blue-colored and remarkably stable N,N,N’,N’- tetramethyl-p-phenylenediamine radical cation, commonly known as Wurster’s Blue (WB), have been the subject of intensive experimental and theoretical studies.3, 5 The displacement of the electron density associated with the first charge-resonance electronic transition makes WB an ideal model system for the investigation of the photoinduced intramolecular charge transfer.
WB has played a key role in understanding of the electron transfer phenomenon in organic compounds.3, 7, 8 Also, being the first organic radical cation prepared by the one-electron photooxidation of the corresponding p-phenylenediamine (TMPD)9 and studied by means of the
ESR spectroscopy,10, 11 it has become important for the development of the radical cation chemistry.12 Due to its colored appearance and the ease of preparation via oxidation or irradiation of a suitable precursor, the production of WB has been exploited in composite electrochromic systems1, 13 and for the development of the photochromic systems based on
TMPD-doped polymer matrices.14
WB provides an example of the Robin-Day class III MV systems,7 wherein the mixed valence is completely delocalized. Indeed, according to the crystallographic data15 and Raman
16 measurements, it features a planar semiquinoid ground state (D0) equilibrium structure. 64
According to the Raman data, the N-ring stretching frequencies are intermediate between those of single and double bonds, pointing towards strong conjugation of the free N-atom lone pairs with the benzene π-system (Figure 3.1).
Figure 3.1. Dominant resonance formula of WB. The resonance yields hybrid characterized by the short quinoid C=N bonds.
This is also in agreement with the fact that, in homologous compounds, a bathochromic shift is observed as a function of the degree of N-alkyl substitution.7 Based on the resonance
16 Raman enhancement factors, Poizat et al. have concluded that a visible D0←D1 transition leads to a structure change reinforcing the interactions of the N-alkyl groups with the π-system. An intense blue color arises from the well-structured absorption band with a maximum at 610 nm
17-19 corresponding to a single D1←D0 electronic transition. The latter fact, as well as the absence of the lower-lying excited states, has been confirmed by the quantum chemical calculations.3
In spite of its intense absorption, WB, like most open-shell species,20 does not fluoresce at room temperature. To the best of our knowledge, only one fluorescence spectrum has been reported so far, at liquid nitrogen temperature.17 The lack of fluorescence in the open-shell systems makes the detection of their electronically excited states extremely difficult so that their properties remain mostly unknown. Previous investigations of the excited-state dynamics in a few radical ions have shown that the lack of fluorescence can be explained by two factors:21-23 (i) relatively small oscillator strength of the D1←D0 electronic transition and (ii) presence of a very efficient non-radiative deactivation pathway favored by a small energy gap between the D1 and 65
D0 states, and/or by the two consecutive D2/D1 and D1/D0 conical intersections (CIs). Such a pathway results in the recovery of the D0 population on a picosecond or sub-picosecond time scale.
Below, we show the results of the steady-state spectral measurements pointing to the dominant factor ii. Accordingly, the main target of the present work was to establish the molecular mechanism allowing WB to efficiently dispose its D1 electronic energy. Even though different internal conversion mechanisms have been documented for neutral and charged molecules, the mechanism of the non-radiative decay in the [M-B-M]+ open-shell MV compounds has never been established. Thus, in order to increase our ability to control the spectral properties and lifetime of the [M-B-M]+ excited state, we have to describe the molecular mode controlling its radiationless deactivation. First, we would like to establish whether such a mode is localized on a single M or B unit. Second, we need to determine its exact nature.
Figure 3.2. Hypothetic radiationless deactivation channels for D1 state of WB. Left, benzene-like CI featuring a -(CH)3- moiety. Right, trimethine cyanine-like CI featuring a charge transfer from the Me2N-Ph moiety to the remaining Me2N- unit. 66
For instance, as illustrated in Figure 3.2, the decay may require an out-of-plane deformation of the phenyl bridge (similar to the deactivation of benzene24); feature a twisting
(isomerization) motion of the dimethylamino unit (similar to the deactivation of the trimethine cyanines25 or protonated Schiff bases26, 27; or involve a less demanding geometrical deformation.
During the last two decades, it has become increasingly apparent that efficient non- radiative excited state deactivation through the CI, leading either to the internal conversion or photochemical transformation, are common mechanistic features.28, 29
Figure 3.3. Schematic representation of the radiationless deactivation mediated by the CI. A. Barrierless (ultrafast) radiationless deactivation. B. Deactivation via a barrier-controlled peaked CI. C. Deactivation via a CI lying higher in energy than the excited state equilibrium structure.
In particular, this is true for the ultrafast processes when deactivation occurs on a sub- picosecond timescale. In these cases, the presence of the CI between ground and excited state potential energy surfaces (PES) constitutes a key mechanistic element for fully efficient return of the molecule to the ground state and for a primary photoproduct formation.29 A barrierless 67 excited state path, connecting vertical excitation region to the CI (Figure 3.3, curve A) yields a sub-picosecond excited state lifetime and a negligible fluorescence quantum yield.
The deactivation through the CI channel also operates in those cases where the opening of the radiationless decay path depends on the temperature or, in other words, available excited state vibrational excess energy.
Among other fluorophores,30 this behavior has been reported for closed-shell hydrocarbons such as benzene,24 octatetraene,31-33 indacene,34 pentalene,35 fulvene,36 azulene,37 annulene,38 for hetherocycles like chromene,39 for closed-shell cations like cyanine dies25 and even for biological chromophores such as cytosine40 and p-hydroxybenzylideneimidazolidinone
(HBI) anion.41 Temperature-dependent radiationless deactivation, determined by the CI, has been also found to control the quenching of azoalkane fluorescence with chlorinated hydrocarbon, water, and aldehyde quenchers.42
Two different mechanisms have been found to control the access to the CI channel. The first one (Figure 3.3, curve B) requires the presence of the transition state (TS) located between the fluorescent state (FS) and the CI. If the internal vibrational energy at the FS is not enough to overcome the energy barrier at the TS, the system will fluoresce. When the amount of the vibrational energy is increased (e.g. by raising the temperature), the barrier can be easily overcome and internal conversion, driven by the CI, dominates. As in the barrierless case, the decay may lead to reconstitution of the original reactant R or, partially, to the formation of an unstable intermediate I (e.g. a radical pair) that can be reverted to the original reactant thermally.
A third documented mechanism is shown by curve C on Figure 3.3. Here, the FS is directly connected to the CI lying above it. Again, a suitable amount of vibrational excess energy at the
FS allows the system to access the CI and decay to the ground state. 68
To the best of our knowledge, previous computational studies of WB have been mostly focused on the description of the D0 PES; whereas the topological features of its D1 state have never been documented. The only theoretical result, reported in the literature, is that of Risko et
3 al., who have been able to locate the D1 minimum of WB at time-dependent density functional
(TDDFT(B3LYP)/6-31G*) level of theory. On the other hand, the presence of the CIs on the
PESs of the radical cations has been first detected and investigated by Bally and co-workers, using matrix isolation techniques as well as suitable quantum chemical calculations.43, 44
Recently, Bearpark and co-workers have shown that the ultrafast thermal deactivation of the excited states in WB-like photostable open-shell species, namely naphthalene45 and pyrene,46 happens via two consecutive sloped D1/D2 and D1/D0 CIs.
In general, investigation of the excited state dynamics in reactive intermediates, such as radical cations, is impaired by the difficulty to perform the ultrafast spectroscopy on chemically unstable species. As mentioned above, this results in the limited knowledge of their photophysics and excited state reactivity. Being stable as a salt in the solid state and in many solvents, WB represents a unique opportunity for the extensive transient absorption (TA) and temperature- dependent fluorescence studies by means of time-correlated single photon counting (TCSPC) and fluorescence up-conversion techniques. Furthermore, its limited molecular size and extension of the π-system allow mapping of the relevant excited state PESs using state-of-the-art ab initio multiconfigurational quantum chemistry.
Below, we present a combined experimental and computational study of the excited state dynamics and radiationless deactivation mechanism of WB. According to our results, experimentally observed temperature-dependent fluorescence of WB with the lifetime decreasing from 260 ps at 82 K to 200 fs at room temperature, is controlled by the small (≤3 kcal/mol) 69
barrier between the D1 minimum and the D1/D0 CI. In the presence of a limited amount of vibrational excess energy the intersection is reached within 200 fs upon a small torsion of a single C–N bond. The whole process is associated with a charge transfer from the nitrogen centers to the phenyl ring and back.
3.2 Methodology
Samples
WB was synthesized as described in the literature,18 and was re-crystallized four times from methanol. All solvents were from Fluka, except deuterated water (Armar Chemicals) and the room temperature ionic liquid (RTIL), 1–ethyl–3–methylimidazolium ethylsulfate (ECOENG
212, Solvent Innovation).
Table 3.1. Solvent properties at 25°C. Parameters in the table are index of refraction nD, dielectric constant ε, and viscosity η).
solvent abbrev nD ε η /cP ionic liquida RTIL 1.481 27.9 120.40 methanol MeOH 1.760 32.66 0.59 ethanol EtOH 1.359 24.6 1.19
water H2O 1.776 78.3 1.00
heavy water D2O 1.776 78.3 1.00 propanol PrOH 1.384 20.5 2.19 acetonitrile MeCN 1.800 35.94 0.36 propionitrile EtCN 1.364 29.32 0.43 benzonitrile PhCN 2.328 25.2 1.34
chloroform CHCl3 2.082 4.79 0.57
methylene chloride CH2Cl2 2.020 8.93 0.41
70
All solvent were of the highest commercially available purity and were used as received.
Table 3.1 summarizes some of their properties as well as the text abbreviations. For fluorescence measurements, the sample concentration was adjusted to have an absorbance of at most 0.1 at the band maximum on 1 cm, whereas for transient absorption the absorbance was around 0.4 on
1 mm. The poly(methyl methacrylate) (PMMA) was purchased from Kremer Pigmente and the film was prepared from a dichloromethane solution.
Apparatus
Steady state absorption and fluorescence spectra were measured on Cary 50 and Cary
Eclipse spectrograph (Varian), respectively. Fluorescence spectra were corrected for the spectrometer’s wavelength-dependent sensitivity and transformed according to literature47 for a proper evaluation of the mirror-image relationship. The low temperature measurements were carried out with an Oxford OptistatDN cryostat.
The time-correlated single photon counting (TCSPC) unit was the same as described in ref.48 except that the excitation source was LED (Picoquant PLS600) generating 600 nm pulses.
The fluorescence was detected at 90 degrees with the analyzer polarized at magic angle. The instrument response function (IRF) of the setup had a full width at half maximum (FWHM) of
0.8 ns. The obtained kinetics was analyzed by iterative convolution of a mono-exponential trial function with the IRF in a least square fit algorithm (MATLAB, The MathWorks).
The transient absorption (TA) setup was described in details elsewhere.49, 50 Briefly, the pump pulse was tuned to 610 nm using a non-collinear optical parametric amplifier and the probe pulse was spectrally broadened to give a white light continuum which was spectrally dispersed and registered on a CCD. The IRF of the TA setup is around 0.2 ps. The dynamics obtained when following the time evolution of the TA signal at certain wavelengths were 71 reproduced by both a scheme of consecutive reactions following exponential kinetic laws and by triple-exponential fit functions in a global fit routine with linked lifetimes (Igor, Wavemetrics).
By using a pump pulse at 610 nm we ensure to excite only WB and neither the neutral nor the dication compound that are always present at low concentration due to disproportionation.
The fluorescence up-conversion setup was essentially the same as described in ref.51, except for the laser source (MaiTai, Spectra-Physics). The sample was excited at 500 nm and the fluorescence was up-converted with the polarization of the gate pulse at magic angle with respect to the pump pulse. The IRF of the setup had a FWHM of 0.2 ps.
Gas-phase calculations
The geometry optimization of the gas-phase D0 min at the CASPT2/6-31++G* level was performed using MOLCAS 7.552 developer version with unambiguously defined complete active space (CAS), including nine electrons and eight orbitals. The orbital set comprises two nitrogen atom lone-pairs of the dimethylamino groups and six π/π* orbitals of the benzene ring. For consistency, the gas phase geometry optimization at the CASPT2 level was also attempted for the D1 state. However, all attempts to localize such a minimum failed (see part b).
The vertical excitation energies were computed to simulate the absorption maximum. The
CAS state interaction protocol (RASSI) available in MOLCAS 7.5 was used to compute the transition dipole moments (µ) and the oscillator strengths (f) for the D1←D0 and D2←D0 transitions on the basis of the perturbation-modified CASSCF53, 54 reference wavefunction. In
contrast to previous works, the computed gas-phase vertical excitation energy (λabs = 600 nm) is in good agreement with the experimental observable, while at the QM/MM55 level (see part b) the structure and excitation energy of the solvated WB yields a slightly different λabs of 590 nm
(Table 3.2). 72
Due to unrealistic computational cost of the CASPT2/6-31++G* calculations, the gas- phase D1 PES along the coordinate connecting the Franck-Condon point (FC) and located conical intersection D1/D0 CI (see part c) was mapped using ab initio CASPT2//CASSCF/6-
31G* protocol.29, 56-58
Figure 3.4. Gas-phase linear interpolated path between the D1 min and D1/D0 CI of WB computed with three root state-average CASSCF wavefunction. The D2/D1 intersection hyperline lies above approximated D1 MEP.
To do that, an approximate D1 equilibrium structure was located at the CASSCF/6-31G*
59 level of theory via geometry optimization. At this level a planar D1 min structure can be located while, as mentioned above, it is not found at the CASPT2. Due to the flatness of the CASSCF/6-
31G* PES, the D1 transition state (D1 TS), connecting the D1 min and the D1/D0 CI, could not be analytically optimized. To overcome this problem, we computed a relaxed PES scan keeping benzene ring bond lengths and the dihedral angle of the rotating C–N bond fixed and using the 73 values resulting from a linear interpolation between the defined initial and final structures. The resulting path was assumed to provide a qualitatively good representation of the minimum energy path (MEP)60, 61 for WB (Figure 3.4).
By inspection of such a path, one can see the evolvement of a small (1.5 kcal/mol, in agreement with the experimental data) barrier, responsible for the ultrafast relaxation of the excited species. At the same time, the position of the D2/D1 hyperline, lying above the linear interpolated path, confirms the idea of the D2 state to be unpopulated and not involved in the ultrafast relaxation process. This hyperline corresponds to the D2/D1 CI structures featuring allyl- like character with both C-N bonds twisted.
To account for the effect of missing dynamic electron correlation, the energy profile was then reevaluated at the complete active space second-order perturbation theory method
56 (CASPT2). Single-point CASPT2 calculations with a three root (D0, D1 and D2) state-average
(weights 0.33, 0.33, 0.33) CASSCF reference wavefunction were performed at the path geometries using MOLCAS 7.5.
Calculations in explicit solvent
The effect of the solvent was modeled by placing the system in a rectangular box of methanol molecules positioned within 10Å from any given atom of WB using the xleap module of the AMBER62 package. This module gives an initial solvent configuration adapted to the
63 solute point charges, calculated as restricted electrostatic potential (RESP) charges for the D0
64 and D1 states using MK option in GAUSSIAN03 program. In order to determine an average solvent configuration, the model was than minimized at the molecular mechanics (MM) level for
1000 steps using the steepest descent method and was equilibrated for 5 ns using molecular dynamics (MD) program NAMD65 while keeping the chromophore rigidly fixed. Both the MM 74 energy minimization and MD simulations were carried out using periodic boundary conditions to simulate the solvent bulk. In all cases, the charges of the methanol molecules were described by the standard AMBER62 force field. The coordinates from a few last frames of the MD simulations were used to build the final QM/MM model (using electrostatic embedding66) representing: (1) a solute embedded in a solvent box with a relaxed solvent shell defined by the methanol molecules within 5 Å from any given atom of the solute (keeping the remaining solvent molecules, more distant from the solute, frozen) and (2) a solute embedded in a solvent box with fixed methanol molecules (mimicking the effect of infinite viscosity). In these QM/MM models, the MM and QM segments interact as follows:66 (i) QM electrons and the full set of MM point charges interact via one-electron operator; (ii) stretching, bending and torsional potentials, involving at least one MM atom, are described by the MM potential; (iii) QM and MM atom pairs, separated by more than two bonds, interact via either standard or reparametrized van der
Waals potential. Similarly to the gas-phase calculations, the effect of including dynamic electron correlation energy was taken into account by performing CASPT2/6-31G*/AMBER geometry optimization of the D0 and D1 min in the solvent box. However, due to the excessive computational cost of the numerical gradients calculations, only fixed solvent shell calculations
(when only QM part is optimized) were performed.
Computed D1 and D0 minima in solution closely resemble those in the gas-phase.
However, due to the asymmetry of the solvent cavity derived from a snapshot of an equilibrated
MM-based MD simulations, the solvated WB structure is slightly asymmetric (at the D0 and the
D1 min), with small twisting angles at both C-N bonds.
As already mentioned above, any attempt to optimize a planar gas-phase D1 min at the
CASPT2/6-31++G* level failed, pointing towards significant solvent stabilization of the D1 75 charge distribution. At this level, the gas-phase geometry optimization without symmetry constrains leads, via a barrierless path, to a twisted CI on the D1 PES. The fact that a stable planar minimum exists at the CASPT2 level only in solution suggests that a D1 energy barrier controls the relaxation towards the intersection.
The D1 path computations were performed with the same protocol used for the gas-phase.
Accordingly, the CASSCF/6-31G*/AMBER geometry optimizations for the D1 state were carried out using MOLCAS 7.5 and TINKER68 programs. The reaction coordinate was approximated via a relaxed scan driven exclusively by the dihedral angle of the rotating C-N bond while the remaining coordinates were all optimized. In order to get a correct reaction energy profile, single point CASPT2//CASSCF/6-31G*/AMBER calculations along the scan geometries were then performed.
Localization and characterization of the conical intersection
The gas-phase D1/D0 and D2/D1 CIs were optimized at the two root state-average
CASSCF level using the algorithm69 implemented in GAUSSIAN03. The resulting geometry of the D1/D0 CI was taken as a guess structure for the CI search in solution at the QM/MM level in
MOLCAS 7.5. The MOplot70 software was used to characterize the CASSCF branching plane of the D1/D0 intersection and describe the D1 and D0 relaxation pathways (Figure 3.7)
Such characterization of the gas-phase CI is considered to be a good approximation of the branching plane in solution. To improve the computed energies of the optimized CI points, the dynamic electron correlation was accounted for using single point CASPT2 correction. 76
3.3 Results and Discussion
Ground and excited state equilibrium structures
No steady-state WB fluorescence was detected at room temperature, neither in liquid solutions nor in a solid polymer film. However, when the temperature is lowered below 120 K, the emission band, that is a mirror image of the absorption and fluorescence excitation spectra, becomes apparent (Figure 3.5).
Figure 3.5. Low-temperature stationary fluorescence of WB in EtOH:MeOH (1:1).
Both fluorescence emission and excitation spectra in the visible range were found independent on the excitation/emission wavelengths. At the lowest temperature investigated (77
K), the fluorescence quantum yield was estimated as 0.01. The temperature dependence of the fluorescence intensity, illustrated on Figure 3.6, is identical in EtOH, EtOH:MeOH (1:1), and in
PMMA film. Within the same temperature range, the absorption spectrum remains essentially unchanged perfectly resembling the one at room temperature. The only exception is a slight red shift, attributed to the change of the refractive index that takes place when going from the room 77 temperature to the matrix freezing point. Further temperature decrease does not lead to any significant shift. At room temperature, the maximum of the visible absorption band is 612 nm, whereas in the low temperature matrix it is equal 630 nm. On the other hand, the low- temperature fluorescence maximum is found at 640 nm. This corresponds to a very small Stokes shift, namely 200 cm−1, and indicates 0–0 transition energy of 2.0 eV.
Figure 3.6. Temperature dependence of WB fluorescence A. Temperature-dependence of the WB (TMPD+·) fluorescence intensity in EtOH:MeOH (1:1). B. Temperature-dependence of the relative fluorescence quantum yield (Φr =1 at 85K). C. Time profile of the fluorescence intensity at 710 nm measured in D2O at room temperature. 78
The gas-phase equilibrium geometry (D0 min), optimized at the state-of-the-art
CASPT2/6-31++G* level, shows a quinoid structure (Figure 3.7) with the charge and unpaired electron localized on the two CN bonds, in agreement with experimental data and previous calculations.
Figure 3.7. Geometrical parameters of the main stationary points. Top: CASPT2/6-31++G* ground and first excited state minima (D0 min and D1 min, respectively). Bottom: CASPT2//CASSCF/6-31G* D1/D0 CI and D1 transition state (D1 TS) calculated for the gas phase (in italic) and solution phases.
In contrast to previous works, the computed gas-phase vertical absorption maximum
(abs=600 nm) agrees well with experiment observable (see Table 3.2). In fact, our calculations emphasize the importance of including dynamic electron correlation energy for a correct description of WB’s photochemistry. As you can see from Table 3.2, the ground state 79 calculations with the less correlated CASPT2/6-31G* and CASPT2//CASSCF/6-31G* methods yield rather blue-shifted absorption maxima.
Table 3.2. Relative CASPT2//CASSCF/6-31G*, CASPT2/6-31G*, and CASPT2/6-31++G* energies ΔE (the latter two are in parentheses where indicated) for all the D0 and D1 structures computed in the gas-phase (where applicable) and in solution (all CASPT2 values are shown for the fixed solvent shell only, CASPT2//CASSCF – for relaxed solvent configuration), oscillator strength f and values of absorption and fluorescence maxima (λmax) computed at both CASPT2//CASSCF/6-31G* and CASPT2/6-31G* level of theory (in parentheses). aRelative energies and values of absorption and fluorescence maxima computed at the CASPT2/6-31++G* level of theory in order to account for extra electron correlation energy. bExperimental values of absorption and fluorescence maxima at T<140 K in EtOH: MeOH = 1:1
λmax / nm ΔE/ kcal mol-1 f (comp.) λmax / nm structure state (exp.) gas-phase solution gas-phase solution gas-phase solution
a a D0 0 (0, 0 ) 0 (0 ) a a 544 545 b D1 52.6 (49.1, 47.7 ) 52.7 (51.5, 48.5 ) 0.259 0.253 612, 630 D0 min a a a a (582, 600 ) (555, 590 ) D2 65.6 (64.6, 63.5 ) 64.0 (63.4, 65.0 ) forbidden forbidden
a D0 (0, 0 ) a a b D1 min D1 — (46.2, 45.9 ) 0.290 0.330 — (619, 623 ) 640 a D2 (65.3, 64.7 ) forbidden forbidden
D0 3.0
D1 TS D1 — 43.8 — 0.336 — —
D2 54.8 forbidden
D0 28.3 27.8
D1/D0 CI D1 31.4 32.2 — — —
D2 77.4 74.0
Consistently with the gas-phase results, the geometry of the D0 min in solution is quinoid
(Figure 3.7). Instead, the D1 equilibrium structure (D1 min) computed in the same solvent box
(using fixed solvent shell) has -* character with the charge and the unpaired electron delocalized on the phenyl ring. In agreement with a small value of the Stokes shift, D1 min 80
structure closely resembles that of the D0 min, the only difference being 0.03 Å symmetrical elongations of the C–N bonds (Figure 3.7). However, all attempts to localize the gas phase D1 min at the CASPT2 level failed, pointing towards significant stabilization of the D1 charge distribution by the solvent.
Both vertical absorption (abs= 590 nm), and emission (fl=623 nm) energies computed for WB in solution agree well with experiment (Table 3.2). To our knowledge, this is the first model of the organic MV compound with quantitatively reproduced experimental max for both absorption and emission.
As mentioned above, at the D1 min the positive charge is localized on the benzene ring.
On the other hand, at the D0 equilibrium structure the charge is delocalized over the entire π- system formed by the benzene ring and two conjugated nitrogen atom lone-pairs. This charge re- distribution, derived from the Mulliken population analysis of the partial atomic charges, is consistent with the geometrical changes corresponding to the relaxation from the FC point towards benzene-like planar D1 min.
Time-resolved spectroscopy
The fluorescence lifetime was found to be strongly temperature dependent. It amounts to
650 ps at 82 K (Table 3.3), whereas femtosecond resolution was required to detect fluorescence at room temperature (Table 3.4).
Using the Strickler-Berg relationship,71 a radiative lifetime is calculated to be 34 ns.
Combining this value with the measured fluorescence lifetime gives a fluorescence quantum yield of 0.02, in good agreement with that estimated experimentally. The quantum yield varies from ~0.02 at 82 K to <10-5 at room temperature.
81
Table 3.3. Fluorescence properties of WB as a function of temperature: fluorescence lifetime f measured by TCSPC (IRF = 0.8 ns), radiative rate constant r calculated from the Strickler-Berg relationship, and relative fluorescence intensity rel.
T (K) f (ns) r (ns) rel 140 34.0 0.16 130 ≤0.4 110 ≤0.4 34.5 0.21 105 34.3 0.28 100 33.8 0.37 97.5 33.9 0.45 95 0.53 33.9 0.56 92.5 33.8 0.70 90 0.59 33.8 0.82 87.5 33.6 0.9 85 0.65 33.6 1 77.2 0.66
Table 3.4. Time constants obtained from the global analysis of the fluorescence dynamics of WB at room temperature measured by fluorescence up-conversion.
solvent 1 (ps) 2 (ps) acetonitrile 0.06 0.21
H2O 0.11 0.24
D2O 0.10 0.23
Transient absorption measurements upon D1D0 excitation of WB in 12 solvents of different polarity and viscosity have been carried out to get a complete picture of the deactivation pathway of the excited-state population (Figure 3.8). These spectra reveal the optically generated
D1 state population, identified by the stimulated emission band above 700 nm, to decay directly 82
to the D0 ground-state with a 200-300 fs time constant in all solvents investigated, in agreement with the fluorescence lifetime (Table 3.5).
Figure 3.8. Transient absorption (TA) data. TA spectra were recorded at different time delays after 610 nm excitation of WB in water at room temperature (GS: ground-state depletion; HOT: hot ground state absorption; SE: stimulated emission).
Table 3.5. Time constants obtained from the global analysis of the TA dynamics of WB in different solvents upon excitation at 610 nm using a triple-exponential function. a1-ethyl-3- methylimidazolium ethylsulfate; bsample degradation by 60% during TA measurement; c530 nm excitation.
Solvent 1 (ps) 2 (ps) 3 (ps) RTILa 0.22 0.38 3.5 methanol 0.15 0.31 3.8 ethanol 0.26 0.38 5.0
H2O 0.19 0.28 3.1
D2O 0.29 0.38 5.0 1-propanolb 0.31 0.38 4.3 acetonitrile 0.22 0.31 6.7 acetonitrilec 0.25 0.38 7.4 proprionitrile 0.22 0.37 7.2 benzonitrile 0.25 0.37 6.6
CHCl3 0.23 0.32 7.0
CH2Cl2 0.18 0.41 8.3
83
This process is so fast that the D0 ground state appears first vibrationally hot. This can be seen in the transient spectra by the positive band above 620 nm, i.e. on the low energy side of the absorption band of the thermally equilibrated D0 state. The decay of the hot band is accompanied by a shift to the lower wavelengths. The dynamics of this process can be satisfactorily reproduced by a bi-exponential function. The short, almost solvent independent, ~300 fs time constant, is most probably due to intramolecular vibrational relaxation, whereas the longer one, ranging from 3 to 7 ps depending on the solvent (Table 3.5), can be ascribed to vibrational cooling. After this process, the negative transient band between 500 and 650 nm, due to the depletion of the ground-state population, has totally vanished.
This ultrafast D1-D0 internal conversion cannot simply be explained in terms of the energy gap law, as the 2 eV D1-D0 gap of WB is similar to the S1-S0 gap of many closed-shell molecules with nanosecond fluorescence lifetimes. This, together with the non-Arrhenius temperature dependence of the fluorescence intensity, points to the involvement of a CI in the ultrafast relaxation of WB excited-state. To identify the relevant modes associated with this process, a search for the CI connecting the D1 and D0 states was performed.
Fluorescence lifetime and D1/D0 CI
The temperature dependence of the observed fluorescence lifetime points to the existence of the energy barrier separating D1 min, assigned to the fluorescent state, from the region where efficient radiationless decay takes place (curves B or C on Figure 3.3). Indeed, the structural parameters of the low-lying D1/D0 CI, successfully located 10-15 kcal/mol below the D1 min, are given in Figure 3.9A. 84
The structure of the CASPT2//CASSCF/6-31G*/AMBER D1/D0 CI in solution correlates well with the gas phase one, the only difference being the degree of rotation around single C–N bond.
Figure 3.9. Characterization of the conical intersection. A. Geometrical parameters of the low- lying D1/D0 CI computed at the CASPT2//CASSCF/6-31G*/AMBER level of theory in solution. B. Branching plane vectors of the gas-phase CASPT2//CASSCF/6-31G* D1/D0 CI: X1–gradient difference, X2–derivative coupling vectors. C. Two roots state-average D0 and D1 CASSCF/6- 31G* energy profiles along the circular cross-section centered at the D1/D0 CI. The trust radius is 0.001Ǻ. The minimum on the D0 curve corresponds to the reactive “exit” channel pointing towards the D0 min. The minima on the D1 curve are two identical “entry” channels.
The gas phase CI features 90 degrees twisted C–N bond, whereas in solution the degeneracy of the D0 and D1 states can be reached already at 70 degrees. Therefore, the
CASPT2//CASSCF/6-31G* branching plane of the gas-phase D1/D0 CI (Figure 3.9C and Figure
3.10) is considered to be a good approximation of the branching plane in solution. 85
Figure 3.10. Pictorial representation of the two root state-average D0 and D1 CASSCF energy profiles along a circular cross-section centered at the gas phase D1/D0 CI. The minima on the D1 profile correspond to the two mirror-image “entry” channels. The single minimum on the D0 curve corresponds to the “exit” channel ultimately leading to reconstitution of D0 min. The branching plane vectors X1 (gradient difference) and X2 (derivative coupling) are schematically reported on the bottom and given in Figure 3.9B.
Gradient difference (X1) and derivative coupling (X2) vectors, constituting the branching plane of the D1/D0 CI, are the only two out of (3N-6) independent modes/coordinates capable of lifting the degeneracy between the D0 and D1 states and orthogonal to the remaining (3N-8) dimensional intersection space. These vectors are illustrated on Figures 3.9B and Figure 3.10.
The X1 vector points towards a quinoid structure of the phenyl ring, while vector X2 describes a coordinate connecting the D1 min and D0/D1 CI (see part d). 86
An interpretation of the X1 and X2 modes in terms of the electronic structure is provided in the branching plane diagram on Figure 3.11A.
Figure 3.11. Characterization of the CI branching plane. A. Change in electronic structure at the branching plane of the D1/D0 CI described with the resonance formula illustrating the charge location, radical center distribution and geometrical change consistently with the results of our electronic structure calculations. B. Orbital occupancies along the circular cross-section at the D1/D0 CI.
As shown on Figure 3.11A, each mode, corresponding to the branching plane vectors of
Figure 3.9B, is represented by the change in geometrical and electronic structure of the D1/D0 CI conical intersection leading to degeneracy lifting. The change in electronic structure is described with pairs of resonance formula illustrating the charge location, radical center distribution and geometrical change consistently with the results of our electronic structure calculations. The information in this diagram is supported by the scan along a circular cross-section of the 87 branching plane centered at the intersection point (Figure 3.9C). The change in the electronic wavefunction along the circular cross-section is monitored by plotting the occupancies of the molecular orbitals π4 and π5 extracted from the diagonal elements of the first order density matrix of the D1/D0 CI (Figure 3.11B).
Inspection of the D1 and D0 energy profiles along a circular cross-section of the branching plane centered at the CI, clearly reveals the existence of single entry and exit channels (Figure
3.9C and Figure 3.10) developing in the opposite directions along the X1 mode. The D1 channel has a “double well” character, indicating that trajectory from the D1 TS enters CI region along coordinates described by strongly coupled stretching and torsion modes. In contrast, the D0 channel corresponds to the relaxation along a wide channel reaching an unstable twisted structure with the unpaired electron and charge delocalized on the phenyl ring and in-plane
NMe2 group (Figure 3.10). Analysis of the wave-function along the two channels (Figure 3.11B) shows that, upon decay, the electronic structure changes by moving a single electron from a doubly occupied π-orbital of the phenyl ring into the singly occupied n-orbital of the twisted
NMe2 group. Ultimately, the lower lying initial planar D0 min geometry structure is reconstituted through skeletal and C-N bond torsion.
Mechanism of the D1 state decay
Given the high computational cost of the numerical CASPT2 gradients, the D1 energy profile of gas-phase WB was scanned along a selected coordinate (see legend of Figure 3.12) using the CASPT2//CASSCF/6-31G* protocol.
The same coordinate was scanned in methanol solution using a quantum mechanics/molecular mechanics (QM/MM) protocol (CASPT2//CASSCF/6-31G*/AMBER). 88
Figure 3.12. Excited state relaxation path of WB. Linearly interpolated D1 state paths connecting the D1 min and D1/D0 CI in the gas phase and in methanol (both relaxed and fixed solvent shells are presented. The calculations were performed in the gas phase with constrained benzene ring bond lengths and dihedral angles for twisting about the C–N bond, and in solution with fixed dihedral angles only.
To account for the fact that the solvent can only partially rearrange within the sub- picosecond timescale of the reaction, we performed the QM/MM calculations for two limiting cases: with a relaxed and fixed (at the D0 configuration) solvent shells.
As shown in Figure 3.12, the D1/D0 CI, located 10-15 kcal/mol below D1 min, can in all cases be reached by twisting one of the C-N bonds. The path to this CI from D1 min features a barrier of ≤3 kcal/mol at ~200 twist angle. Initially, it is dominated by the bond stretch altering the quinoid geometry with the unpaired electron and the positive charge on the C-N groups into a 89 structure with both the electron and the hole delocalized on the phenyl ring. A coupled increase in the bond stretch and C-N twisting induces a further change: the unpaired electron and the radical center localize on the twisting dimethylamino-group (NMe2). Upon decay and relaxation to D0, progressive planarization reconstitutes the original quinoid situation where both C-N bonds hold the unpaired electron and the positive charge.
Both ultrafast spectroscopic data and computational results give a consistent picture of
WB dynamics (Figure 3.13).
Figure 3.13. Mechanistic picture of WB photochemistry. Schematic representation of the D1 PES in methanol along two coordinates responsible for the ultrafast radiationless deactivation of WB (stretching and C-N torsion). Two paths from the D1 min drive the system to the corresponding D1/D0 CI through the mirror-image transition structures (D1 TS). D1 TS was not located as a first-order saddle point due to the extreme flatness of the CASSCF D1 PES, but was rather approximated as a maximum of the corresponding energy profile. The maximum is obtained from the linear interpolation between the D1 min and the D1/D0 CI. 90
Upon optical population of the D1 state at room temperature, geometrical deformation of the benzene ring and C-N bonds and torsion around a single C-N bond bring WB in ~200 fs to
0 the D0 state via D1/D0 CI. To reach CI only ~60-70 twist one NMe2 group is required, and calculations show that the solvent cavity is large enough accommodate such twist without significant friction. The thermally equilibrated ground-state population is then restored within a few picoseconds upon intra- and intermolecular vibrational relaxation. The whole process is associated with an electron transfer from nitrogen centers to the phenyl ring and back. As temperature is lowered, the ≤3 kcal/mol barrier, located on the way to the CI, comes into play and the lifetime of the D1 state becomes long enough for fluorescence to be a significant deactivation pathway.
3.3. Conclusions
As we already mentioned, in recent years the idea of non-avoided crossings (CIs), postulated first more than seventy years ago, has been used to describe the opening of radiationless deactivation channels in a variety of photoexcited organic molecules, resulting in their ultrafast decay to the ground state.
Following this idea, we have been able to provide computational evidence for the CI- mediated mechanism explaining the experimentally observed non-Arrhenius temperature- dependent fluorescent behavior of WB. Using a combination of femtosecond spectroscopy and ab initio multiconfigurational quantum chemistry, we have shown that the ultrafast decay of WB within 200 fs at room temperature is controlled by the D1/D0 CI, located 10-15 kcal/mol below the fluorescent D1 min. The accessibility of the CI is determined by ≤3 kcal/mol energy barrier that can be easily overcome in a presence of a limited amount of vibrational excess energy. 91
Thus, the hypotheses proposed until now to explain the absence of fluorescence in open- shell radical ions, namely a small D1-D0 gap and the involvement of the D2 state, do not hold for
WB. Although a gas phase D2/D1 CI is accessible upon deformation of the phenyl ring, it lies
13.5 kcal/mol above the D1 min and is unlikely to be reached on the ultrafast timescale (Figure
3.4). Instead, the deactivation of the D1 state population is associated with an initial charge transfer from the NMe2 groups to the benzene ring. This is followed by a localization of the electron and hole on the twisting NMe2 group via further bond stretching and C-N bond torsion.
Upon decay at the D1/D0 CI, the charge goes back to the phenyl ring and during the D0 relaxation moves first to the in-plane (conjugated) NMe2 group and, after planarization of the twisted NMe2 group, to the original D0 min symmetric distribution. Further studies with other radical ions are required to see if the behavior found for WB is more general.
92
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97
CHAPTER 4: PHOTOCHEMISTRY OF 11-CIS LOCKED BOVINE RHODOPSIN3
Abstract
The excited state lifetime of bovine rhodopsin (Rh) increases from ca. 100 fs to 85 ps when the C11=C12 bond of its chromophore is locked by a cyclopentene moiety (Rh5). To explain such an increase, we employ ab initio multiconfigurational quantum chemistry to construct computer models of Rh and Rh5 and to investigate the shape of their excited state potential energy surfaces in a comparative way. Our results show that observed Rh5 fluorescence
f (λ max = 620 nm) is due to a previously unreported locally excited intermediate whose lifetime is controlled by a small energy barrier. The analysis of the properties and decay path of such an intermediate provides information useful for engineering rhodopsin variants with augmented fluorescence efficiencies.
4.1. Introduction
Understanding of biological systems depends on our ability to visualize, track and quantify signaling molecules and events in living cells with high spatial and temporal resolution.1-44 For this purpose, fluorescent imaging has long been one of the most powerful and convenient tools.35 Over the last decade, a significant progress has been made in the design of new fluorescent probes1, 3, 6-10 and development of fluorescent imaging techniques6, 11, 12 with the aim to revolutionize biological and physiological research.
Optical detection of cellular states has first been accomplished with organic dyes and quantum dots3 and, more recently, with fluorescent proteins (FPs).6, 7, 9, 10 However, the dyes added exogenously can often be incompatible with living systems. The same is true for quantum
3 This chapter is based on the article: Laricheva, E.N.; Gozem, S.; Rinaldi, S.; Melaccio, F.; Valentini, A. Origin of fluorescence in 11-cis locked bovine rhodopsin. J. Chem. Theory Comput. (under revision) 98 dots. On contrary, genetically encoded FPs are more suitable. They have been shown to respond to a wider variety of events, provide higher sensitivity, greater versatility and lower photodynamic toxicity when expressed inside a cell.6-8
Currently, the majority of FPs are based on the genetically engineered variants of green fluorescent protein (GFP) from the jellyfish Aequorea victoria and its homologs from other marine organisms.9, 10 However, in order to further expand the existing FPs toolbox, it would be advantageous to have light-emitting proteins with no homology to GFP, especially because the latter has a few drawbacks such as insufficient speed of chromophore maturation controlled by the presence of oxygen in the system, ease of photobleaching and low signal-to-noise ratio.3, 8
In this contribution, we report the results of the computational study indicating that members of the rhodopsin family may be engineered to yield alternative FPs, despite the ultrafast photoisomerization characterizing these systems.
Recently, Kralj and co-workers have discovered two microbial rhodopsin-based voltage- sensitive fluorescent proteins: proteorhodopsin optical proton sensor (PROPS)1314 and archaerhodopsin 3 (Arch).14 The authors have suggested further exploring the family of microbial rhodopsins for the ability to fluoresce. Novel rhodopsin-based FPs would become a great addition to the category of optogenetics tools called reporters.15 Accordingly, a systematic mutagenesis and directed evolution of PROPS and Arch, as well as the high-throughput screening of microbial genomes for their homologs, represents one possible way to generate new reporters. Another strategy is to turn a known non-fluorescent rhodopsin into a fluorescent one by finding a way to increase the excited state lifetime of its chromophore so that fluorescence becomes competitive with the ultrafast photoisomerization and non-radiative deactivation. 99
To design this type of systems, the use of quantum chemical models is crucial. One first needs to unveil the structural basis for the optical properties of non-fluorescent rhodopsin by computing the electronic structure of the opsin-embedded chromophore, understand its interactions with the apoprotein in both ground and excited states, and gain insights into the mechanism of the photoisomerization reaction. In this context, the well-studied16-20 bovine rhodopsin (Rh) represents a good "laboratory" system.
As illustrated on Figure 4.1A, in Rh, a member of the G-protein coupled photoreceptors family (GPCR), the chromophore 11-cis retinal, embedded in the apoprotein opsin, is covalently bound to a lysine residue (Lys296) forming a protonated Schiff base (PSB11).19, 21 The positive charge of PSB11 is stabilized by the presence of counterion—negatively charged carboxylate
(Glu113).19, 22
A B
Figure 4.1. Structure of Rh and photoisomerization reaction of its chromophore. A. Structure of Rh (top) and PSB11 chromophore (bottom). W1 and W2 are water molecules trapped inside the retinal binding pocket. [Adapted from ref.23]. B. Schematic representation of the PSB11 to PSBT photoisomerization in Rh. 100
Upon absorption of light, PSB11 isomerizes to all-trans form (PSBT) at extremely high speed (ca. 200 fs) going through a conical intersection (CI) to a primary photoproduct photorhodopsin, which then decays to bathorhodopsin.24, 25 Such an ultrafast relaxation, illustrating a primary step of a protein photocycle and a primary event of vision, is the evidence of a barrierless excited state path (path 1, Figure 4.2A) and, consequently, negligible
-5 26 fluorescence quantum yield (an average value Φf = 1.2 * 10 ) and short excited state lifetime
19, 20 (τfl = ca.100 fs). However, in principle, one can significantly increase τfl by imposing the S1 barrier (TS) on the way from the fluorescent state (FS) to the CI (path 2, Figure 4.2A).
Figure 4.2. Excited state paths of Rh and Rh5. A. Schematic representation of the barierless (1) and barrier-controlled (2) S1 path (a – absorption, b – emission). B. Chemical structures of the retinal in Rh and Rh5. The curly arrows indicate the corresponding reactive double bonds.
One extreme way to do so is to restrain the isomerization of the C11=C12 bond by locking it with a cyclic moiety (Figure 4.2B). Indeed, significant changes in the excited state lifetime have been observed for a series of rhodopsins with PSB11 chromophore substituted with 101 synthesized retinal analogues in which the reactive C11=C12 bond was locked by the cyclic moieties (Figure 4.3).27-31
Figure 4.3. Artificial (11-cis locked) rhodopsin analogues. Schematic representation of the ground (S0) and excited (S1) potential energy surfaces along the 11-cis bond torsional coordinate of a free (Rh) and locked rhodopsin chromophores (Rh5, Rh7 and R8). Values in parentheses indicate the difference absorption maxima of the original pigments and the corresponding intermediates. Dotted structures for Rh8 and Rh7 show the formation of transoid double bonds in the ring. [Adapted from ref.19] 102
The biggest increase of the lifetime (τfl = 85 ps), along with a fluorescence signal with
λmax = 620 nm (Figure 4.4) and no photoproduct formation (Figure 4.3), has been observed by
Kandori and co-workers19, 27 for Rh with C11=C12 bond incorporated in a five-membered ring
(Rh5). This is due to the inhibition of photoisomerization along this bond. Notice, that similar increase in the lifetime (τfl = 15 ps) has been detected in bacteriorhodopsin with C13=C14 bond of PSBT fixed by the cyclopentene (bR5).31
Figure 4.4. Fluorescence spectrum of Rh5 excited with the green pulse. [Adapted from ref.27]
In this respect, one could think of a possible way to further increase the lifetime and S1 barrier by enlarging the size of the lock, thus, creating additional steric hindrance for the rotation.
However, in the previous studies27-29 no direct dependence between the lifetime and the size of the ring has been revealed. For example, fixing C11=C12 bond with seven-membered ring (Rh7) allows some flexibility for the rotation, and intermediate photorhodopsin is formed during rapid excited state relaxation (Figure 4.3).27, 32 In case of eight-membered lock (Rh8), the photoisomerization rate is even 90 fs faster with respect to the ca.100 fs of wild-type Rh, and the formation of both photo- and bathorhodopsin is observed (Figure 4.3).29 Thus, locking C11=C12 103 bond by the cyclopentene ring is the most optimal way to prevent PSB11 to PSBT photoisomerization in Rh, avoiding the formation of the photoproducts and increasing the excited state lifetime by almost a three orders of magnitude.
The results of the a ndori’s have been used to confirm that cis/trans isomerization is a primary event in vision. However there have been no attempts to look at such a result as a demonstration that rhodopsins can be turned into fluorescent proteins. We have constructed the
CASPT2//CASSCF/6-31G*/AMBER hybrid quantum mechanics/molecular mechanics
(QM/MM) models of both Rh and Rh5 to study the origin of the observed fluorescent lifetime increase in a comparative way.
4.2. Methodology
Details of the computational QM/MM protocol
According to our CASPT2//CASSCF/6-31G*/AMBER QM/MM protocol,33 based on the electrostatic embedding34, 35 and link atom scheme,36 the geometry optimizations of the chromophore backbone, treated as the quantum mechanics (QM) part, were carried out using ab initio complete active space self-consistent field method (CASSCF),37, 38 while the electrostatic and steric effects of the protein cavity were described at the molecular mechanics (MM) level using AMBER39 force field. The QM/MM model of Rh was built based on the crystallographic structure of bovine rhodopsin (PDB ID: 1U19).40 The ionization states of the amino acid residues in the opsin cavity were assigned using PROPKA 2.0.41, 42 Where it is necessary, the missing hydrogen atoms were added to the residues and retinal, followed by their minimization at the
MM level using TINKER 4.2 program.43 In agreement with the results from PROPKA2.0, the most important internal amino acids, such as Asp83, Glu181, and Glu122, were kept neutral. The retinal counterion, Glu113, was left deprotonated. 104
The following atoms were then selected for the QM/MM geometry optimization using
MOLCAS44 developer version 7.5 coupled with TINKER 4.2 program:
a) QM part: all retinal atoms and first five atoms of the Lys296 side chain connected to it
(nitrogen, ε-carbon and three hydrogen atoms, see ref.33 for atom labels);
b) MM part: the remaining nine atoms of the Lys296 side chain;
c) ACTIVE atoms: every atom of the side chain or water molecule with at least one atom
being 4Å away from the QM selection.
To calculate the charges on the QM atoms in the final QM/MM model, the single point
HF/3-21G/AMBER calculations with electrostatic potential fitting (ESPF)45 were performed, followed by the MM minimization of the MM atoms using the computed charges. On the next step, the system was MOLCAS/TINKER optimized at the HF/3-21G/AMBER level with
ACTIVE atoms relaxed.
This was followed by a gradual increase of the level of theory until the ground (S0) state equilibrium geometry of Rh (FCRh) was obtained at the three-root state average (SA3)
CASSCF/6-31G*/AMBER level where complete active included the full π-system of the PSB11 consisting of 12 electrons in 12 orbitals. The QM/MM model of Rh5 was constructed based on the HF/3-21G/AMBER optimized geometry of Rh. The structure of the retinal chromophore was manually modified by incorporating the C11=C12 bond in a cyclopentene ring, followed by the reoptimization of the final structure until SA3 CASSCF/6-31G*/AMBER geometry of its S0 state
46 was obtained (FCRh5). All geometry optimizations were performed with microiterations in such a way that the MM atoms were always minimized by TINKER 4.2 between each QM/MM optimization step. 105
Starting from the FCRh5, an unconstrained geometry optimization on the excited (S1) state in Rh5 was performed. The LERh5 energy minimum, featuring a lengthening of the bonds in the middle part of the retinal and partially preserved BLA pattern of the S0 state, was located.
Another equilibrium structure, corresponding to the CTRh5, was found starting from a geometry biased towards bond length inversion. Though the well-studied S1 state path in Rh is known to be barierless, we could locate the “regions” corresponding to the LERh and CTRh using constrained geometry optimization starting from the guess structures resembling LERh5 and CTRh5 and using loose convergence criteria. It is also worth noting that due to the unrealistic computational cost, the frequency calculations could not be performed to unambiguously determine the nature of all the stationary points found in this study.
Computed absorption/fluorescence maxima and oscillator strengths
Throughout the study, the SA3 CASPT2 energy reevaluation at the single point level was performed on the equilibrium geometries of Rh5 and Rh to estimate the corresponding
a f absorption (λ max) and fluorescence (λ max) maxima. The CAS state interaction protocol (RASSI), available in MOLCAS developer version 7.5, was used to compute the oscillator strengths (f) for the S1←S0 and S2←S0 transitions on the basis of the perturbation-modified CASSCF reference wavefunction.47
Computed S1 paths of Rh5 and Rh
In order to investigate the shape of the S1 state PES in Rh5, the following steps were performed. First, the CASSCF/6-31G*/AMBER relaxed scan between LERh5 and CTRh5 was computed using the values resulting from the linear interpolation between two structures. During the scan, the C8–C9–C10–C11 dihedral angle of the retinal was constrained while the rest of the chromophore was relaxed. Second, starting from the maximum of the resulting CASSCF/6- 106
31G*/AMBER energy curve, the TSRh5 was located using restricted-step rational-function optimization algorithm48 implemented in MOLCAS developer version 7.5.
This TSRh5 differs from the LERh5 structure in the amount of BLA, representing a geometry intermediate between the LERh5 and CTRh5 minima in terms of bond lengths parameters. The torsions around former double and single bonds in TSRh5 remained substantially unchanged with respect to the LERh5. It is also worth noting that upon the SA3 CASPT2 correction, which accounts for the missing dynamic electron correlation energy, the positions of both the LERh5 and TSRh5 points were shifted as illustrated on Figure 4.5. The energy barrier at the CASPT2//CASSCF/6-31G* level was estimated to be ca. 2.0 kcal∙mol-1.
Figure 4.5. Comparison between the CASSCF/6-31G*/AMBER (blue) and CASPT2//CASSCF/6-31G*/AMBER (red) S1 energy profiles computed with three-root state average CASSCF wavefunction.
To complete the S1 state path, the relaxed scan was continued starting from the CTRh5 structure by gradually twisting the C8–C9–C10–C11 dihedral angle with a 10° step until 90°- twisted conical intersection (CIRh5) was reached. Following the same procedure, the S1 state path of Rh was computed. In contrast to Rh5, this path is steeper with no barrier separating the 107
regions of the LERh and CTRh, and the CTRh from the CIRh. Here, the conical intersection (CIRh) features 80°-twisted C11=C12 bond, consistently with previous studies.
In order to confirm the intramolecular origin of the TSRh5, we also recomputed the S1 path of Rh5 at the single point CASPT2//CASSCF/6-31G* /AMBER level in the gas phase.
4.3. Results and Discussion
First, the quality of the CASPT2//CASSCF/6-31G*/AMBER QM/MM protocol was
a assessed by modeling the λ max values of Rh and Rh5.
Table 4.1. Relative energies (ΔE), oscillator strength (f) and values of the absorption and fluorescence maxima (λmax) computed at the CASPT2//CASSCF/6-31G* level for both Rh5 and Rh. The reference CASSCF values for the ΔE are given in parentheses. a, b indicate that the a f corresponding λmax values are the absorption (λ max) and fluorescence (λ max) maxima, respectively.
-1 ∆E, kcal mol f λmax (calc.)/ nm λmax (exp.)/ nm Structure State x= Rh5 x = Rh x = Rh5 x = Rh x = Rh5 x = Rh x = Rh5 x = Rh
S0 0.0 (0.0) 0.0 (0.0)
FCX S1 54.3 (78.7) 56.6 (84.5) 0.872 0.916 527a 505a 498a 495a S2 76.4 (93.5) 79.4 (97.8) 0.374 0.458
S0 0.9 (9.1) 1.2 (8.2)
LEX S1 45.3 (70.2) 48.5 (75.6) 1.040 1.464 — — 644f 620f S2 59.1 (78.4) 65.4 (83.3) 0.233 0.536
S0 7.1 (18.5)
TSX S1 46.9 (66.8) — 1.156 — — — — —
S2 62.9 (85.2) 0.136
S0 14.8 (28.7) 20.5 (34.4)
CTX S1 44.0 (65.0) 39.6 (62.0) 0.738 0.639 — — — 979 S2 67.0 (91.2) 78.5 (99.2) 0.220 0.136
S0 42.0 (59.7) 35.6 (46.1)
CIX S1 47.5 (66.1) 36.6 (61.6) — — — — — —
S2 81.0 (104.5) 89.6 (105.3)
108
Our results show that the ground state (S0) equilibrium geometries of Rh and Rh5 (FCRh
a and FCRh5) yield close computed λ max values (505 nm and 526 nm, respectively), in line with very closed observed values (498 nm24, 49 and 495 nm,27 respectively) and consistently within a
-1 a 3.0 kcal∙mol excitation energy error (Table 4.1). As the close λ max of Rh and Rh5 suggest, the
FCRh5 and FCRh geometries should be similar. Our calculations confirm this: both chromophores have twisted structures with a negative (counter-clockwise) helicity and similar geometrical parameters (Figure 4.6 for Rh5 and Figure 4.7 for Rh). However, due to the presence of the cyclopentene ring, the Rh5 backbone is more bent. In fact, the C6–N distances in Rh5 and Rh are
10.2Å and 11.3Å, respectively.
Figure 4.6. Charge distribution and relevant geometrical parameters (dihedral angles are given in parentheses) of the stationary points along the S1 path of Rh5. 109
Figure 4.7. Charge distribution and relevant geometrical parameters (dihedral angles are given in parentheses) of the stationary points along the S1 path in Rh.
As a result of the S1 geometry optimization in Rh5, the existence of two energy minima,
-1 LERh5 and CTRh5, separated by a small energy barrier (ca. 2.0 kcal∙mol ), was established (Figure
4.8A). Figure 4.6 shows that these structures differ by the charge distribution, amount of bond length alternation (BLA), and degree of torsion around the C9=C10 bond. The CTRh5 has a charge-transfer character and features strong BLA pattern similar to a loose non-fluorescent S1
50 intermediate previously reported by Andruniow et al. for Rh. The LERh5, located just 1.0
-1 kcal∙mol above CTRh5 (Figure 4.8A and Table 4.1), is characterized by a BLA pattern closer to the S0 state and featuring equally stretched bonds in the middle part of the chromophore backbone. We refer to LERh5 as locally excited state. 110
Figure 4.8. Comparison between the S1 state paths of Rh and Rh5. A. S2 (green), S1 (red) and S0 (blue) energies along a three-root state average (with equal weights) CASPT2//CASSCF/6- 31G*/AMBER S1 scan of Rh5 (solid lines) from the FCRh5 to the CIRh5 along the reaction coordinate dominated by the bond stretching in the region from the FCRh5 to the TSRh5 (see the insert on top) and later by torsion of the C9=C10 bond (indicated in degrees out-of-plane). For comparison, the dotted lines represent the S1 relaxed scan in Rh where the torsional deformation involves C11=C12 bond. The d1-d2 reaction coordinate shown on the insert represents the difference between the average sum of all the formal single bonds (d1) and all formal double bonds (d2). B. Change in oscillator strength (blue) and amount of the positive charge (red) on the framed fragment (i.e. the one starting at =C9-C8= and containing the β-ionone ring) along the S1 path in Rh5 (solid lines) and Rh (dotted lines). 111
To the best of our knowledge, this is a novel (previously not reported) rhodopsin intermediate located closer to the FC point in terms of geometry and electronic structure. On the other hand, in the literature, the simultaneous presence of an "LE state" and a "CT state" is widely used to describe the phenomenon of dual fluorescence in many fluorophores, with the LE state being responsible for emission at short wavelengths before the charge separation and formation of the CT state (often twisted) occurs.51-53
f Experimentally observed fluorescence in Rh5 (λ max = 620 nm) originates from the LERh5
f state. Indeed, as Table 4.1 shows, the λ max computed for LERh5 (644 nm) correlates well with the experimental observable (620 nm), while for CTRh5 the value is too red-shifted (979 nm). The oscillator strength computed for LERh5 (f = 1.0) is also higher than for the CTRh5 (f = 0.7).
54 Recently, Valsson and Filippi have investigated the structural relaxation in the S1 state of different gas-phase models of the retinal chromophores using the CASSCF, CASPT2, quantum Monte Carlo (QMC), and coupled cluster (CC) methods. In contrast with CASSCF, the
CASPT2, QMC and CC results reveal the existence of the S1 minimum similar to the LERh5
(located at the CASSCF/AMBER level). This suggests that such an intermediate is stabilized by the modeled protein environment and that, in such an environment, requires less dynamic electron correlation to exist.
Similar results have been recently reported by Muños-Losa et al.55 who simulated a five double-bond retinal chromophore model in methanol solution. For this model, the authors have been able to locate at the CASSCF/MM level two different S1 energy minima: one displaying similar bond lengths and small BLA value, and another one—ionic with a pronounced BLA pattern. These findings have been used to reinterpret the fluorescence spectrum of the all-trans retinal chromophore in methanol reported by Zgrablic et al.56 in terms of dual fluorescence with 112
the high-frequency part of the fluorescence band assigned to a "covalent" S1 minimum, and the low-frequency one to a charge-transfer S1 minimum. This situation is similar to the one reported here for Rh5.
Figure 4.9. S1 state path of Rh. A. Relaxed S2 (green), S1 (red) and S0 (blue) three-root state average CASPT2//CASSCF/6-31G*/AMBER S1 scan of Rh (solid lines) from the FCRh to the CIRh along the reaction coordinate dominated by the torsion of the C11=C12 bond (indicated in degrees out-of-plane). For comparison, the dotted lines represent the S1 relaxed scan in Rh5 where the torsional deformation involves C9=C10 bond (see main text). B. Change in oscillator strength (blue) and amount of the positive charge (red) on the β-ionone ring along the S1 path in Rh. 113
According to our results, LE (LERh) and CT (CTRh) regions also exist in Rh (Figure 4.9A
-1 and 4.7), but they are unstable. In contrast to Rh5, the CTRh region is located 9.0 kcal mol below the LERh region with no barrier separating the two structures (Figures 4.9A and Table 4.1).
As we will discuss below, these differences can be explained on the basis of the resonance stabilization of the translocated positive charge along the chromophore backbone.
To improve our understanding of the mechanisms driving the S1 decay in Rh5 and Rh, we also located the structures of the low-lying S1/S0 CI for each case (CIRh5 and CIRh, respectively).
The CIRh was extensively studied in the past, and its computed structure (Figure 4.6), featuring
80° twist of the C11=C12 bond, correlates well with the previous studies. In contrast, in Rh5 the isomerization around C11=C12 bond is restricted due to the presence of a cyclopentene ring and, therefore, CIRh5 features a fully twisted neighboring C9=C10 bond (Figure 4.5).
This is consistent with the notion that the reported S1 isomerization coordinate of Rh has a bicycle-pedale16 nature where the reactive C11=C12 twisting is accompanied by a partial twisting of the adjacent C9=C10 bond. It is, thus, apparent that if one blocks the rotation of the
C11=C12 bond, the C9=C10 undergoes the photoisomerization more likely than the C13=C14.
Indeed, Jang et al.57 observed the isomerization of the C9=C10 rather than C13=C14 bond in a rhodopsin analogue with the retinal chromophore locked by a cyclohexene ring.
As Figures 4.9A shows, in Rh the evolution of the S1 population from the FCRh to the
CIRh is driven by a substantially barierless reaction path consistently with previous results. Thus
LERh corresponds to a flat region from where the chromophore quickly relaxes to CIRh passing through a CTRh structure located along a steeper S1 path region. This is consistent with the sub- picosecond excited state lifetime (ca.100 fs) seen for Rh. 114
In contrast, the S1 energy profile of Rh5 is shallow (Figure 4.8A). While in Rh the CTRh
-1 -1 is located 9 kcal mol below the LERh, in Rh5 the CTRh5 is only 1.1 kcal mol more stable than the LERh5. The transition state (TSRh5) separating the LERh5 and CTRh5 regions is responsible for the substantial increase in the fluorescent lifetime observed experimentally (85 ps) which is assigned to the LERh5 structure. As reported on Figures 4.9B and 4.9B, the charge-transfer character of the S1 wavefunction, revealed by the 0.4-0.5 au increase in the charge residing on the β-ionone fragment of the chromophore, is maintained along the S1 path in both Rh5 and Rh.
The general trend in the change of oscillator strength (f) along the S1 path in these two models is also similar: starting from the FC point the f increases, reaches a maximum, and then constantly decreases when approaching the intersection region. However, in Rh5 the initial increase of the f is larger with a maximum of the curve corresponding to the fluorescent LERh5 structure.
As the shape of the barrier-controlled S1 path in Rh5 suggests (Figure 4.8A), a preferential stabilization of LERh5 with respect to CTRh5 should yield a further increase of τfl. The analysis of the differential charge distribution (Figure 4.10A) indicates that a promising strategy for LERh5 stabilization could be to increase the negative electrostatic potential projected by the amino acid residues on the middle part of the chromophore. In fact, a bigger fraction of the positive charge is localized on the =C10–C11=C12– fragment in LERh5 compared to CTRh5.
Our calculations suggest that the S1 barrier corresponding to the TSRh5 is mainly due to electronic effects and can be explained by resonance stabilization and the Hammond postulate. In fact, upon twisting of the C11=C12 bond in Rh, the positive charge, initially located on the –
N=C15 moiety, is gradually translocated along the chromophore backbone towards the β-ionone ring. This process ultimately leads to a full positive charge delocalized on the –C7=C8–
C9=C10–C11= pentadienyl fragment (Figure 4.10B, top). 115
Figure 4.10. Analysis of the LE and CT states. A. Differential (LERh5–CTRh5) charge distribution (top ) and changes in the amounts of positive charge on the C1-C9 (blue), C10-C12 (red) and C13-N (green) fragments along the S1 path of Rh5. B. Representation of the charge delocalization on the pentadienyl fragment in Rh and allyl — in Rh5.
In contrast, in Rh5, where the C9=C10 bond twists, the charge is delocalized on the shorter -C7=C8–C9= allyl fragment (Figure 4.10, bottom). This produces a less stable resonance hybrid of the (product) charge-transfer state in the locked model relative to the unlocked one. In this situation, the Hammond postulate would predict an energy barrier separating the LERh5 and
-1 CTRh5 structures, in agreement with our calculations (ca. 2 kcal∙mol ).
To confirm the intramolecular origin of the barrier, we recomputed the energy profile along the S1 path of Rh5 in the absence of the protein (Figure 4.11A) and demonstrated that the flat S1 energy surface of the locked system is mainly a consequence of its reaction coordinate
(i.e. of the structural changes imposed by the protein cavity). This indicates that one could increase the LERh5 lifetime by increasing the Rh5 barrier for the S1 isomerization of the C9=C10 116 bond via steric and electrostatic interactions. In particular, the proximity of the nearby T118 and
Y268 residues to the chromophore C9-methyl group suggests that they could play a role in increasing the barrier.
Figure 4.11. Mechanistic picture of the Rh5 photochemistry. A. Comparison between the CASPT2//CASSCF/6-31G*/AMBER S1 (red) and S0 (blue) energy profiles of 11-cis locked retinal in the protein (solid lines) and in the gas phase (dotted lines) computed with three-root state average CASSCF wavefunction. Note, that for the gas-phase the scan was rigid (single point calculations) while for the protein it was relaxed. B. Schematic representation of the fluorescence generation in Rh5. The formulas indicate the electronic structures characterizing the ground state and two different fluorescent states located on the spectroscopic state of the protein. 117
4.4. Conclusions
In conclusion, our QM/MM models support the mechanism displayed in Figure 4.11B.
The observed Rh5 fluorescence (620 nm) is assigned to a locally excited intermediate featuring an untwisted backbone with a BLA pattern still not completely inverted with respect to the S0.
The same calculations predict the existence of a second red-shifted fluorescent intermediate with a full charge-transfer character at ca. 980 nm, which, at the best of our knowledge, has not been spectroscopically investigated. These results provide the basis for engineering rhodopsin-based fluorescent proteins with a chemical modification of the chromophore and, possibly, suitable mutations. In perspective, we plan to construct and study a series of the QM/MM mutant models with amino acid substitutions that stabilize the positive charge in the middle part of the retinal and increase the steric hindrance for the rotation around the C9=C10 bond. The combination of these effects could be advantageous. If the tests are positive, Rh5 may be considered as a promising system for engineering novel fluorescent pigments with no homology to GFP.
118
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CHAPTER 5: CONCLUSIONS AND FINAL REMARKS
As highlighted in Chapter 1, our ability to precisely visualize, track and quantify signaling molecules and events in living cells depends on the availability of the super-resolution imaging techniques and constant development of new optical probes/reporters that are versatile, photostable, non-toxic, and respond to a wide variety of biological processes. In this respect, the major focus is on genetically encoded fluorescent proteins (FPs.) Compared to other fluorophores, such as organic dyes and quantum dots, FPs have a unique ability to be “built in” directly inside the cell by co-expression with the protein of interest. This helps to avoid the use of toxic exogenous tags that often require special fixation and permeabilization procedures to be attached to the target.
Design of new FPs is mostly accomplished by tuning and improving the spectral properties of already known blue to yellow variants of GFP from jellyfish Aequorea victoria or its homologs from other marine organisms. The most popular strategies used for this purpose are site-specific or random mutagenesis targeting all but evolutionary conserved residues located in the immediate vicinity of the protein chromophore. Other design techniques include iterative somatic hyper mutation, directed evolution, and high-throughput screening of marine and coelenterate genomes for new fluorescent proteins.
On the other hand, the same strategies have been widely applied in optogenetics to generate a special set of tools called actuators that are based on a completely different protein family with no homology to GFP—namely, rhodopsin photoreceptors. Light-induced ultrafast cis/trans isomerization, typical for rhodopsins, induces the conformational change in the microbial channel- or halorhodopsin actuators to permit the flux of specific ions in or out of the cell, thus, enabling to control the brain activity by switching the neurons on and off. In order to 123 report on the observed neural behavior, actuators are usually fused with the above-mentioned
FPs.
However, Kralj and co-workers have recently shown two examples of microbial rhodopsins—proteorhodopsin optical sensor (PROPS) and archaerhodopsin 3 (Arch)—that can function as actuators and reporters simultaneously. Those proteins act as neural silencers and, at the same time, can instantaneously report on the change in the membrane potential due to their endogenous fluorescence. Accordingly, the authors have suggested improving the spectral characteristics of PROPS and Arch 3 as well as searching the microbial genomes for their homologs as the most logical way to generate new reporters.
An alternative strategy could be to turn a known non-fluorescent rhodopsin into a fluorescent one by finding a way to increase its excited state lifetime so that fluorescence becomes competitive with the ultrafast non-radiative deactivation. From the computational point of view, this can be accomplished by imposing the barrier on otherwise barrierless excited state potential energy surface of non-fluorescent rhodopsin. For this purpose, the use of multiconfigurational quantum chemical models is crucial as one first needs to unveil the structural basis for the optical properties of wild-type rhodopsin by computing the electronic structure of the opsin-embedded chromophore, understand its interactions with the apoprotein in both ground and excited states, and gain insights into the mechanism of the photoisomerization reaction. In this respect, this thesis is a contribution addressing the following (i)–(iii) issues documented in Chapters 3 and 4.
(i) Preliminary, to understand the phenomenon of the barrier-controlled fluorescence lifetime, we have investigated the photophysics of N,N,N’,N’-tetramethyl-p-phenylenediamine radical cation, known as Wurster’s Blue (WB), using ab initio multiconfigurational methods both 124 in the gas phase and in explicit solvent. In collaboration with the group of Prof. Eric Vauthey from the University of Geneva, we have explored the photophysical and photochemical properties of WB by means of ultrafast spectroscopy and quantum chemistry. Experimentally, the fluorescence lifetime of WB has been observed to decrease from 260 ps at 82 K to 200 fs at room temperature. Our calculations have revealed the presence of a small barrier (< 3kcal mol-1) between the excited-state minimum (D1 min) and the conical intersection of the excited and ground state potential energy surfaces (D1/D0 CI) that is responsible for the observed temperature dependence of fluorescence. According to our results, the barrier associated with a transition state (D1 TS) can be ultimately reached from the D1 min upon just 10 degrees torsion of a single
C-N bond and it controls the accessibility of the D1/D0 CI. At room temperature, when the molecule has enough vibrational energy, this barrier can be easily overcome and the intersection is reached within 200 fs. The thermally equilibrated ground-state population is then restored within a few picoseconds upon intra- and intermolecular vibrational relaxation and vibrational cooling. The whole process is associated with the electron transfer from the nitrogen centers to the phenyl ring and back. As the temperature is lowered, < 3 kcal mol-1 barrier located on the way to the CI comes into play and the lifetime of the D1 state becomes long enough for fluorescence to be a competing deactivation pathway.
(ii) By analyzing the D1/D0 CI responsible for the ultrafast non-radiative deactivation of
WB at room temperatures, we have also contributed to the general understanding of how CIs control the charge (electron transfer) in open shell systems. We have shown that CI of WB is characterized by the crossing of the states with very different electronic distributions. In particular, the excited state evolution is characterized by the displacement of the unpaired electron from initially delocalized position, on two C=NMe2 bonds, to the phenyl bridge and, 125
finally, to a single -NMe2 group. This last event is driven by a twisting deformation of the -NMe2 group carrying the radical center. The CI is reached when such a group is fully twisted. Upon decay the electronic structure changes by moving a single electron from a doubly occupied π- orbital of the phenyl ring into the singly occupied π-orbital of the twisted. During the D0 relaxation (i.e. after decay at a D1/D0 CI) the unpaired electron moves back to the bridge. It then delocalizes on the two C=NMe2 bonds upon twisting of the -NMe2 back to the original planar configuration. The torsion of the NMe2 group required to reach the conical intersection in WB
points to a twisted intramolecular charge transfer phenomenon associated with the D1 to D0 decay.
(iii) Having understood the origin of the barrier-controlled fluorescence lifetime in WB, we investigated the possibility of the excited state lifetime increase in such a complex biological system as rhodopsin. In particular, we have demonstrated the role of the ab initio multiconfigurational quantum chemistry for in silico design of rhodopsin proteins with augmented fluorescence efficiencies, taking the well-studied bovine rhodopsin (Rh) as a model system. Using state-of-the-art CASPT2//CASSCF/6-31G*/AMBER protocol at the hybrid quantum mechanics/molecular mechanics (QM/MM) level, we have extensively investigated the photochemical reaction paths in wild-type Rh and its Rh5 analogue produced by incorporating the C11=C12 reactive bond in a cyclopentene ring. The comparative analysis of these paths helped to unravel the origin of experimentally observed three-order of magnitude increase of the fluorescent lifetime: from ca. 100 fs in Rh to 85 ps in Rh5. Our results have shown that
f fluorescence observed in Rh5 (λ max = 620 nm) is due to a previously unreported locally excited intermediate close in the geometry and electronic structure to the Franck-Condon point. The same calculations have predicted the existence of a second red-shifted fluorescent intermediate 126 with a full charge-transfer character at ca. 980 nm, which, at the best of our knowledge, has not been spectroscopically investigated. According to our calculations, the S1 lifetime of the locally excite intermediate is controlled by a small (ca. 2 kcal/mol) energy barrier separating it from the charge-transfer one. The analysis of the transition state, corresponding to this barrier, and the flatness of the S1 potential energy surface of Rh5 relative to Rh, have suggested the intramolecular origin of the barrier that can be explained by the resonance theory and Hammond postulate. Additional CASPT2//CASSCF/6-31G*/AMBER calculations have been performed for
Rh5 chromophore in the gas phase to confirm the intramolecular origin of the barrier and to show that flat S1 energy surface of Rh5 is mainly a consequence of its reaction coordinate (i.e. of the structural changes imposed by the protein cavity). In conjunction with this information, the analysis of the properties and decay path of the locally excited intermediate has provided information useful for engineering rhodopsin variants with augmented fluorescence efficiencies.