An Ultrafast Spectroscopic and Quantum-Chemical Study of the Photochemistry of Bilirubin

Initial Processes in the Phototherapy for Neonatal Jaundice

Burkhard Zietz

Department of Chemistry Biophysical Chemistry Umeå University Sweden, 2006 The front cover shows a newborn baby undergoing phototherapy for neonatal jaundice at Umeå's university hospital, overlaid with two molecular structures: the calculated HOMO (highest occupied molecular orbital) superimposed on the bilirubin molecule and the geometry of a dipyrrinone model system, in the geometry of the conical intersection between the ground and first excited electronic states. Also shown is a plot of symbolic potential energy surfaces for the ground and excited electronic states. The picture of the Aurora Borealis on the back was taken just outside Umeå, and the light is caused by emission from nitrogen and oxygen molecules, as well as oxygen atoms, after having been excited by energetic particles (electrons and protons) from the sun.

© 2006 Burkhard Zietz ISBN 91-7264-010-3 Printed by Solfjädern Offset, Umeå, Sweden TO SEE A WORLD IN A GRAIN OF SAND AND A HEAVEN IN A WILD FLOWER HOLD INFINITY IN THE PALM OF YOUR HAND AND ETERNITY IN AN HOUR

William Blake (1757-1827) in "Auguries of Innocence"

Table of contents

Abstract vii Sammanfattning viii List of Papers ix Preface 1 1. Introduction 3 2. Bilirubin, Neonatal Jaundice and the Mechanism of Phototherapy 7 3. Experimental Methods 15 3.1 Femtosecond transient absorption spectroscopy 16 3.2 Fluorescence upconversion 21 3.3 Anisotropy measurements 24 4. Quantum Chemical Methods and Concepts 25 4.1 Basic quantum chemical concepts 25 4.2 The CASSCF method 31 4.3 Density functional methods (DFT) 32 4.4 Conical intersections 33 4.5 Exciton theory 35 5. Initial Photochemistry of Bilirubin (Summary of Results) 38 Conclusions 44 Future Outlook 45 References 46 Acknowledgements 51

v vi Abstract

Bilirubin is a degradation product of haem, which is constantly formed in all mammals. Increased levels of bilirubin in humans lead to jaundice, a condition that is very common during the first days after birth. This neonatal jaundice can routinely be treated by phototherapy without any serious side effects. During this treatment, bilirubin undergoes a photoreaction to isomers that can be excreted. The most efficient photoreaction is the isomerisation around a double bond ( Z-E-isomerisation), which results in more soluble photoproducts. The work presented in this thesis shows results of a femtosecond optical spectroscopy study, combined with quantum-mechanical investigations, of the mechanism of isomerisation of bilirubin. The spectroscopic research was conducted with bilirubin in organic solvents, and in buffer complexed by human serum albumin. This albumin complex is present in the blood, and has thus medical importance. Quantum-chemical calculations (CASSCF) on a bilirubin model were used to explain experimental results. The fluorescence decay observed with femtosecond spectroscopy shows an ultrafast component (~120 fs), which is explained by exciton localisation, followed by processes with a lifetime of about 1-3 ps. These are interpreted as the formation of a twisted intermediate, which decays with a lifetime of 10-15 ps back to the ground state, as observed by absorption spectroscopy. CASSCF calculations, in combination with the experimental results, suggest the ca. 1-3 ps components to be relaxation to the twisted S 1 minimum, followed by the crossing of a barrier, from where further relaxation takes place through a conical intersection back to the ground state. Time-dependent DFT calculations were utilised to analyse the absorption spectrum of bilirubin. Good agreement with the measured spectrum was achieved, and low-lying states were observed, that need further investigation. The theoretically obtained CD spectrum provides direct evidence that bilirubin preferentially binds to human serum albumin in the enantiomeric P-form at neutral pH.

vii Sammanfattning

Bilirubin är en nedbrytningsprodukt av hem som ständigt bildas hos alla däggdjur. En förhöjd bilirubinkoncentration i den mänskliga kroppen kan leda till gulsot, något som är mycket vanligt under de första dagarna efter födelsen (neonatal gulsot). Fototerapi används rutinmässigt som säker be- handlingsmetod, under vilken bilirubin genomgår en fotoreaktion till en isomer som kan utsöndras. Den mest effektiva fotoreaktionen är en Z-E- isomerisation, vilken leder till lösligare fotoprodukter. Arbetet som presenteras i denna avhandling visar resultaten av en kombin- erad femtosekund optisk-spektroskopisk och kvantmekanisk undersökning av mekanismen bakom bilirubins isomerisation. Den spektroskopiska studien genomfördes med bilirubin, löst i organiska lösningsmedel och i buffert i komplex med humant serumalbumin. Detta albuminkomplex finns i blodet, och är därför av medicinskt intresse. Kvantmekanistiska CASSCF- beräkningar på en bilirubinmodell användes för att förklara de experimentella resultaten. Det uppmätta fluorescence sönderfallet visar ultrasnabba komponenter (~120 fs). Dessa tolkas som excitonlokalisering, som följs av bildandet av ett vridet intermediat med en hastighetskonstant på ca. 1 ps -1(beroende på lösningsmedlet). Absorptionsmätningar visar att detta intermediat sönder- faller tillbaka till grundtillståndet med en livstid på 10-15 ps. CASSCF beräkningar, i kombination med de experimentella resultaten, ty- der på att sönderfallet med livslängden på ca. 1 ps är en relaxation till det vridna S 1-tillståndet. Reaktionsvägen därifrån antas passera en barriär till en konisk genomskärning, som möjliggör snabb relaxation till grundtillståndet. Tidsberoende DFT-beräkningar användes för att analysera bilirubins absorp- tionsspektrum, vilket gav bra överensstämmelse med uppmätta data. Dessu- tom hittades ett tillstånd med låg excitationsenergi, som kräver ytterligare studier. Med hjälp av det beräknade CD-spectret kunde det visas att bilirubin binder till albumin i P-formen vid neutralt pH.

viii List of Papers

The present thesis is based on the following papers: I B. Zietz , A. N. Macpherson and T. Gillbro: Resolution of ultrafast excited state kinetics of bilirubin in chloroform and bound to human serum albumin. Phys. Chem. Chem. Phys. 6 (2004) 4535-4537.

II B. Zietz and F. Blomgren: Conical intersection in a bilirubin model - a possible pathway for phototherapy of neonatal jaundice. Revised version submitted to Chem. Phys. Letters

III B. Zietz : Bilirubin's Optical Absorption and CD Spectra Analysed by Time-Dependent-DFT. Manuscript, revised version

IV B. Zietz and T. Gillbro: Initial Photochemistry of bilirubin probed by femtosecond spectroscopy. Manuscript

The following papers are not included in this thesis: – B. Zietz , V. I. Prokhorenko, A. R. Holzwarth and T. Gillbro: A comparative study of the energy transfer kinetics in artificial BChl e aggregates containing a BChl a acceptor, and BChl e-containing chlorosomes of Chlorobium phaeobacteroides . J. Phys. Chem. B 110 (2006); DOI: 10.1021/jp053467a

– W. Rettig, B. Zietz : Do twisting and pyramidalization contribute to the reaction coordinate of charge-transfer formation in DMABN and de- rivatives? Chem. Phys. Letters 317 (2000) 187–196

– T. Shutova, A. Villarejo, B. Zietz , V. Klimov, T. Gillbro, G. Samuels- son, G. Renger: Comparative studies on the properties of the extrinsic manganese-stabilizing protein from higher plants and of a synthetic peptide of its C-terminus. Biochim. Biophys. Acta 1604 (2003) 95– 104

ix x Preface

This thesis is organised as follows: Chapter 1 (Introduction) gives an overview over the subject, also relating it to adjacent research topics, as well as introducing the basic tools and concepts used in this work. Chapter 2 (Bilirubin, Neonatal Jaundice and Phototherapy) gives a more detailed presentation of the chemistry of bilirubin and phototherapy as well as the medical background. In the following Chapter 3 (Experimental Methods) , the methods of ultra-fast time-resolved spectroscopy are presented. The concepts of quantum chemistry, used to gain theoretical insight into the mechanism of phototherapy, are given in Chapter 4 (Quantum Chemical Methods) . The pages following (Acknowledgments) are used to express my gratitude to people who have joint me through the process of this work. The remainder is composed of published research papers and manuscripts, containing the main results of this work, in the following order: (I) " Resolution of ultrafast excited state kinetics of bilirubin in chloroform and bound to human serum albumin " describes the general phenomenon of the photochemistry of bilirubin on the ultrafast time scale. (II) " Conical intersection in a bilirubin model - a possible pathway for phototherapy of neonatal jaundice " tries to give an insight into the molecular mechanism on the atomic level of initial relaxation after photoexcitation. (III) " Bilirubin's Op- tical Absorption and CD Spectra Analysed by Time-Dependent-DFT " is aimed at understanding the nature of the absorption and the excited states of bilirubin, which form the basis for its photochemistry. More detailed results of the photochemistry of bilirubin and model compounds, both in solvent solution and bound to albumin, are presented in (IV) " Initial Photochemistry of bilirubin probed by femtosecond spectroscopy ".

1 2 Chapter 1

1. Introduction

Walk into any children's ward in a hospital, and you're likely to find newborn babies treated with phototherapy. Lying in bright blue, white or green light, almost naked, but with their eyes well protected, they receive a treatment where the medicine administered is neither pills nor drops, but light. This is to reduce the symptoms of neonatal jaundice. The process, discovered in the 1960's, is by far the most common treatment of jaundice for infants, and many parents have become familiar with it during the first days of their childrens' lives. The aim of the treatment is to lower the level of the toxic bilirubin - the pigment causing jaundice - and thus prevent it from dif- fusing into the brain. There, it might lead to kernicterus, and result in brain damage. During the last decades, much light has been shed – not just literally – on bilirubin and the processes going on during phototherapy. 1-4 Starting from the photoprocesses of bilirubin, to the processes leading to a reduction of it's concentration in the blood, a rather detailed picture has emerged. Bilirubin is formed constantly in the healthy humans (and all mammals) as a breakdown product of haem. Red blood cells, that transport oxygen to all organs and tissue, have a limited life span, and after their cell death, the haemoglo- bin is broken down. The haem ring is opened, and a water-soluble intermediate, biliverdin is formed. Enzymatic reduction of biliverdin leads to water- insoluble bilirubin. Despite not being soluble, it can be transported to the liver by binding to human serum albumin. In the liver, the normal degradation pathway involves addition of sugar groups, which lead to a soluble product. This is finally excreted into bile. The liver plays thus a vital role in the breakdown chain, and in cases of liver damage, or in newborns, where the active enzyme hasn't formed in high enough quantities yet, higher levels of bilirubin can occur, resulting in jaundice. For newborns, the condition usually abates within a few days (during which the enzyme is formed) and only requires treatment of the symptoms during that time.

3 Introduction The photoprocesses leading to the reduction in bilirubin levels involve configurational ( E-Z-) isomerisation, formation of a structural isomer - lumirubin - by internal cyclisation, and photooxidation. The latter though, is likely to contribute only to a small extend. All of these reactions lead to more soluble products, which are directly excretable. The exact contributions of the above mentioned processes to phototherapy are not known, as quantitative measurements are very difficult. This has implications for the optimisation of process of phototherapy. Bilirubin shows a peculiar wavelength dependent photochemistry, with light of different colours yielding slightly different products, in contrast to most photoreactions, which are not wavelength-dependent. In practical terms, choice of the optimum light source for phototherapy is not straight forward, with blue light preferably forming E–Z-isomerisation products, and green light giving higher yields of lumirubin. The main process going on in phototherapy is twisting around a double bond in the bilirubin molecule. The twisted intermediate, which has a very short lifetime (on the order tens of picoseconds, 0.000 000 000 01 s), can either rotate backwards to the parent molecule (a Z-isomer), or it can continue twisting (to 180°), to form the E-isomer. Out of about eight excited molecules, only one forms the more soluble E-form, whereas seven return to the insoluble Z-form. To achieve efficient excretion by phototherapy, the molecules will thus have to be excited many times. The Z-E (or cis-trans) photoisomerisation, i.e. rotation about the double bond initiated by light, is a process of far wider biological importance than just phototherapy. Several functions in nature are only possible by capturing a photon and utilising it for signalling or making use of its energy. The probably best known process is vision, where the retinal molecule in rhodopsin absorbs light and twists to an isomeric form. This is followed by a change in the surrounding protein, giving a signal to the nervous system, sending a pulse to the brain. Another opsin molecule, melanopsin, is situated at the inner retina, not contributing to vision, but has been suggested to be a candidate for the regulation of circadian rhythms. 5 Plants sense light by phytochrome as a receptor, which triggers, among others, chlorophyll pro-

4 Chapter 1 duction. The molecule isomerising, biliverdin, is very similar to bilirubin. Even here, light triggers a photoisomerisation. A certain type of salt-water bacteria, Halobacterium salinarium , has developed a photosynthetic ma- chinery – bacteriorhodopsin – in which the same retinal molecule as used in vision, isomerises and acts as a light-driven proton pump, supplying the bacteria with energy. Bilirubin, being more than just a waste product of catabolism, has powerful antioxidant properties and acts as a major physiologic cytoprotectant. 6 Copying from nature's pool of inventions, the photoisomerisation holds promising applications even for technical applications. Optical switches can find a role not only in data storage, but also in future computers where elec- trical signals are replaced by light, which could lead to an enormous increase in speed. The photoisomerisation of bilirubin, combined with the wavelength dependent reactions, have allowed bilirubin to be used as an optical switch. 7 Serum albumin forms a noncovalent complex with bilirubin, which partly allows transportation through the blood stream, but also acts as a buffer for higher levels of bilirubin, thus delaying toxic effects, such as kernicterus. Binding has a marked influence on bilirubin's photochemistry, leading to regio- and stereospecific photoreactions caused by the protein template. The medical importance of bilirubin and albumin, as well as the complex they form, have resulted in a large amount of research on the binding mechanism. Despite that, no detailed picture on the molecular level has emerged. The information available has nonetheless made the bilirubin-albumin complex a model for other pigment-protein bound complexes. 8 Due to its optical properties, bilirubin can act as a probe inside the protein, and can be used to give information about the binding, electrostatic interaction and even changes in protein structure, e.g. upon changes in pH. Because of the extremely short time-scales involved in chemical reactions, following them in real-time demands methods with staggering time- resolution. A typical time-scale for the initial relaxation of bilirubin is 0.1 ps. This compares to one second, as one second compares to 300 000 years!

5 Introduction Laser-based methods are, however, able to give light pulses short enough to follow the reactions, by yielding absorption and fluorescence signals. The information obtained by the experimental laser spectroscopic methods are, though, not always easily understood. They don't give a picture of atoms or molecules moving, instead they present the response of the whole system to external light, in the form of optical time-resolved spectra and decay curves. Translating these into chemical models is a demanding challenge. To aid the interpretation, and as an independent source of information about possible reaction pathways, theoretical chemistry was employed. The approach used, electronic structure methods, tries to solve equations based on the position and energies of electrons and protons – quantum chemistry. This allows to predict the ability of molecules to interact with light (absorb- ing photons), but also to look at possible ways for the excited molecule to relax back to the ground state, either unchanged, or altered after some photoreaction.

6 Chapter 2

2. Bilirubin, Neonatal Jaundice and the Mechanism of Phototherapy

Bilirubin (BR) is an orange-yellow substance that you are only likely to see when getting a bruise. For people working in paediatric clinics, however, the yellow colour of the skin and sclera of the eyes is a familiar sight. Also liver diseases can lead to these typical symptoms, known as jaundice. For newborn babies, a phase of several days with mild neonatal jaundice is very common, and can nowadays be treated routinely by phototherapy. 1, 3, 4 The main origin of bilirubin is the breakdown of haem. Blood in humans, and all mammals, contains red blood cells, whose function is to supply every bit of tissue with oxygen. Being bound to the central iron atom of the haem complex, the oxygen can be carried from the lungs through the blood stream. The lifetime of blood cells, however, is limited to 90-120 days, and a complex mechanism exists for the breakdown (an overview of the catabolism

α CO + Fe 3+ + NaDP + HO O O OH NADPH + O 2 O O A B N N A B N N δ Fe β H H Haeme N N H C D oxygenase = D C N N N N D C H A γ B N N H O α H O O Biliverdin IX OH O O OH OH O + Haem OH NADPH + H Biliverdin IX α Biliverdin reductase NADP +

HO COOH OH O O OH O UDP-glucuronate OH COOH OH glucuronyltransferase OH O O O OH two separate steps OH O O C D N N A H H B N N C D H 2 UDP 2 UDP- H O N N glucuronic O Bilirubin IX α A acid B H H N N H H O O Bilirubin diglucuronide Figure 1: Schematic showing the catabolism of haem 7 Bilirubin, Neonatal Jaundice and the Mechanism of Phototherapy process is given in Figure 1). The haem complex is first oxidised by a mem- brane-bound enzyme, haem oxygenase, whereby the ring is opened regio- specifically at the α-position, and the iron atom removed. Oxidation of the α-carbon atom leads to carbon monoxide, which is exhaled, and the amount of CO produced can serve as a measure of red-cell catabolism. The ring- opening step leads to a water-soluble, linear tetrapyrrole, biliverdin IX α. In the next catabolic step, another enzyme, biliverdin IX α reductase, reduces the central double bond yielding bilirubin IX α. The π-conjugation, which in the case of biliverdin, extends over all pyrrole rings, is broken, yielding two nearly identical subunits. This breaking of the conjugation is clearly dis- played by a change in absorption, and consequently colour, from blue-green for biliverdin to intensely orange-yellow for bilirubin. This is impressively demonstrated by the colour shift in a bruise over the course of days. Surprisingly, bilirubin, despite possessing two propionic acid side chains, is very nonpolar, insoluble in water or methanol, but dissolves easily in chloroform. It also binds tightly to human serum albumin (HSA), which is an abundant blood plasma protein. The water-insolubility has major implications for the biochemistry, as a simple excretion via the kidneys is impossible. The aforementioned processes of haem degradation and bilirubin formation take place in the reticuloendothelial system (mainly in lymph nodes, bone marrow, and spleen). For bilirubin to become excretable, it has to be transported to the liver, which takes place by binding to albumin. In the regular pathway, the bilirubin is glucuronidated in the liver in two separate steps, i.e. two sugar molecule are enzymatically attached to bilirubin's propionic acid side chains. Due to the increased polarity, the bilirubin diglu- curonidate is water-soluble, and can be excreted via bile. The normal pathway, as presented above, can be disrupted. Typically, liver disease causes the activity of glucuronyl transferase to be lowered, resulting in a build-up of bilirubin in its unconjugated from (i.e. not carrying glu- curonide ester groups). This increase is referred to as hyperbilirubinemia, and is expressed in the yellowing of the skin and the whites of the eyes, the symptom being called jaundice or icterus. Another typical case of reduced enzyme activity, besides pathological liver conditions, is in the foetus' and 8 Chapter 2 newborn's liver. During pregnancy, the bilirubin formed in the foetus is transported via the placenta and catabolised by the mother's liver. After birth, bilirubin production, on a per kilogram basis, is more than doubled compared to the adult, as red blood cells are removed from the circulation. Combined with the lower activity of the hepatic system, this leads to bilirubin accumulating. Jaundice has been observed in ca. 60 % of infants within their first week after birth. The binding to albumin serves an additional function here. Besides transporting, it also acts as a buffer for bilirubin, delaying the onset of kernicterus, brain damage resulting from bilirubin passing through the blood-brain barrier. Bilirubin is neurotoxic, and higher concentrations can lead to permanent neural damage, even death. For this reason, bilirubin levels of newborns are monitored to ensure that no dangerous quantities are reached. For most children, the liver activity reaches levels high enough to cope with the bilirubin present within a short time, and no further action is needed. In many other cases, however, the bilirubin levels are reduced by phototherapy, which is by far the most common treatment today. 1, 2, 4 Alternative methods available for the treatment of neonatal hyperbilirubinemia include the treatment with porphyrins, as well as herbal cures. Tin mesoporphyrin acts as inhibitors for haem oxygenase, and can reduce the production of bilirubin for prolonged periods of time. 9 Huang et. al. 10 have recently shown 6,7-dimethylescultelin to be an active ingredient in an old Chinese herbal tea which is widely used to prevent and treat jaundice. Dimethylescultelin was discovered to regulate the constitu- tive androstane receptor (CAR) which is implicated in bilirubin clearance. This knowledge opens the possibility of a future pharmacological treatment based on the active ingredient of the traditional herbs. The discovery of the phototherapheutic process originates from an acciden- tal observation by a nurse in the 1950s, working with prematurely born babies. When these newborns were taken out on sunny days, a bleaching of the skin at the exposed parts was observed. 11 Further examination of the phenomenon revealed not only systematic bleaching of the skin, but also a con- comitant drop in plasma bilirubin levels. In later investigations, sunlight was replaced with artificial light sources, and phototherapy was born. It has be-

9 Bilirubin, Neonatal Jaundice and the Mechanism of Phototherapy come routine, and to date millions of children have undergone the procedure, without serious side effects being known. The constitutional structure of bilirubin was determined by Fischer et. al. 12 (H. Fischer received the Nobel Prize in 1930 for his work on the constitu- tion of haemin and chlorophyll). Still unknown at that time were the stereo- chemistry of the C 4-C5 and C 15 -C16 carbon-carbon double bonds ( E or Z), the preference of the lactim or lactam structure, and the orientation of the

C5-C6 and C 14 -C15 single Z syn bonds (syn or anti). In 1976 5 O 4 6 the first crystal structure of H A B O 13, 14 1 N 21 N O BR was published , and a 22 H H H H 10 24 O N 23 N 19 refined structure appeared a D O C 14 15 H 18 few years later. These es- O 15 syn Z tablished BR to exist as a lactam in the 4 Z,15 Z- Figure 2 The structure of 4Z,15Z-Bilirubin IX α, including the six intramolecular hydrogen bonds, configuration, and taking the symbolised by broken lines. syn-orientation (see Figure 2). Also shown was the existence of six hydrogen bonds, keeping the molecule in a ridge-tile conformation. This bonding scheme explains the very low solubility of bilirubin in water and methanol, which is unexpected for a carboxylic acid. The polar groups are locked in intramolecular hydrogen bonds, and are thus not accessible for interaction with the solvent. This pat- tern of intramolecular hydrogen bonding is only possible in a ridge-tile shape, where one propionic acid group interacts with the pyrrole and lactam groups of the other half. M P The two intersecting planes take an angle of 90°.16 Force field calculations have revealed this conformation to be mini- mising non-bonded steric repulsion. 17 Calculations Figure 3 The M and P enantiomeric forms of bilirubin, 18 two minima in conformational space on the semiempirical 10 Chapter 2 and ab initio level 19 also yielded this structure as a minimum in conformational space. Within this conformation, two different enantiomers are possible, the M and P form (see Figure 3). 20 Due to exciton interaction (see Exci- ton theory, Chapter 4), these are chiral and show optical activity. As both have the same energy in most solvents, however, no net optical effect is observed. Fast interconversion occurs at room temperature with a rate of ~5.4 s -1 at 37°C, the barrier was determined to ~80 kJ/mol.21 In chiral solvents, 22 upon binding to a chiral template such as HSA, 23, 24 and cyclodextrins 25 or in modified chiral bilirubin compounds, 26, 27 one form can be stabilised over the other, leading to a net chirality, as seen in CD spectroscopy. Even several years after phototherapy had been routinely established, the exact mechanism was not fully understood. Photooxidation had been assumed to contribute to the reduction of bilirubin. An important step was the

O H discovery of the configurational E-isomer 5 4 O (see Figure 4a for structure), that was N 10 N H shown in bile of rats undergoing photo- H H O N 3 O O H therapy, and could also be shown to occur 16 N O 15 28 a H in humans. A different photoisomer,

O lumirubin (see Figure 4b), that also plays a * H O O O * role in therapy, was discovered shortly N H H H N 29 N N after. Whereas the formation of the for- b mer is reversible, the latter is stable. Both H O show increased water solubility, and con- O tribute to the reduction in BR plasma lev- Figure 4 Structure of ( a) 4 Z-15 E- Bilirubin IX α and ( b) 15 Z-lumirubin, els. * denotes chiral centres The two dipyrrinone subunits in the bilirubin molecule are connected by a methylene bridge, allowing for free rotation around the single bonds. This bridge leads to a disruption in the conjugation between the two halves (in contrast to biliverdin, where the conjugation extends over the whole molecule). The two units act therefore as two separate chromophores. As they are rather close (ca. 7Å centre-to- centre distance), changes in the electronic state by absorption of light in one chromophore is "felt" by the other. This interaction is known as exciton

11 Bilirubin, Neonatal Jaundice and the Mechanism of Phototherapy coupling, and is of importance in many biological systems, such as photosynthetic antenna systems. The absorption of the dimer behaves differently from the monomer, and leads to a broadened or shifted spectrum. The exact spectrum can be calculated and requires knowledge of the transition dipole moments and the geometrical arrangement of the molecule. The strength of the interaction can vary considerably, and has been classified based on practical criteria by Simpson and Peterson 30 (see Chapter 4). For bilirubin, the interaction energy amounts to ~1000 cm -1,22 and the width of the absorption for the half-bilirubin model xanthobilirubic acid has been measured as 2250 cm -1. As a result, bilirubin can neither be attributed to the strong or weak case, but instead has to be seen as an intermediate case. The absorption spectrum, shown in Figure 5, 1.0 Absorption Emission 1.0 of BR in of BR in shows a shoulder HSA/buffer CHCl 0.8 3 0.8 CHCl HSA/buffer 3 on the blue side Anisotropy 0.6 0.6 of the spectrum BR in CHCl 3 Emission for bilirubin dis- 0.4 Anisotropy 0.4 solved in chloro- 0.2 0.2 Norm. Absorption/Emission Norm. form, which is 0.0 0.0 even stronger

300 400 500 600 700 pronounced for Wavelength / nm albumin bound BR. This can be Figure 5 Absorption and fluorescence spectrum of bilirubin in chloroform and bound to human albumin The emission anisotropy for attributed to a BR in chloroform is also shown. changed interaction between the molecular halves, but may also be influenced by the protein surrounding. The effect of binding on the emission spectrum (also shown in Figure 5) is clearly visible, with a bathochromic shift of ca. 10 nm. Usually, photoreactions are not dependent on excitation wavelength. Bilirubin is an exception, as was first discovered on its dimethyl ester, 31 and later also on BR itself. 32-35 A recent study used exciton theory to analyse this wavelength dependence in terms of excitonic states.36 Also, a regiospecific-

12 Chapter 2 ity is observed when BR is bound to albumin. In serum albumin of humans and other primates, the 4 Z,15 E:4 E,15 Z ratio at a photostationary state is about 100:1, whereas photolysis in rat or rabbit serum gives a ratio of 1.3:1. 37 To explain this unusual behaviour, intramolecular energy transfer between the two coupled chromophores is assumed. Thus, independent of which half is excited at first, the energy will be trapped on the lower-energy half, and isomerisation on that half follows. McDonagh and Lightner confirmed this with a dihydrobilirubin, where one vinyl group is reduced to an ethyl group, and in organic solvents the isomer ratio is ca. 10:1, whereas upon binding to human albumin a reversal occurs, and the other half isomerises, the ratio being ~1:43. From the above it can also be concluded that binding to albumin has a marked influence on the absorption energy, being able to shift either of both of the chromophore halves' absorption energies. Numerous studies have been carried out to investigate the binding interaction between bilirubin and albumin, concentrating on, but not limited to, human albumin. 38-42 The exact binding site of has not been determined, but bilirubin is known to bind "somewhere in domain II".8 Results from a Ra- man study showed BR to bind mainly as the dianion, with the intramolecular hydrogen bonds intact, 43 and this dianion complex has also been shown to be stable at physiological pH and temperature. Protein complex formation by albumin could be imagined to restrict bilirubin's flexibility, and restrict isomerisation. Therefore, it is worth men- tioning that binding to albumin actually enhances isomer formation, with quantum yields for both configurational ( E-isomer) 36, 44, 45 and structural isomers (lumirubin) 46 being higher as compared to solutions of organic solvents. The same applies for the fluorescence yield, which is significantly increased. 45 Equivalent behaviour is seen for half-bilirubin model dipyrrinone compounds. 47 An increase in isomerisation quantum yield upon binding to protein has been observed earlier: the quantum yield for the 11-cis to all-trans-retinal isomerisation process is 0.67 in rhodopsin, the visual receptor in higher animals. In ethanolic solution, a value of 0.25 has been measured for the same chromophore. 48, 49

13 Bilirubin, Neonatal Jaundice and the Mechanism of Phototherapy Whereas a wealth of information on bilirubin's photochemistry had been gained from absorption, fluorescence and quantum yield measurements, little could be said about the time-scale of the ongoing processes. An important study, published in 1981 50 showed absorption difference spectra of bilirubin after excitation with a 0.5 ps pulse of ultraviolet light. This work revealed a decay time for the singlet state of ~20 ps at room temperature, and 35 ps at 2 °C. Time resolved fluorescence measurements 51, 52 gave a similar decay rate for the fluorescent state. These measurements where, however, conducted with a limited time resolution, and could not resolve the fastest processes. Based on time-resolved picosecond absorption experiments, as well as quantum yield effi- S E 1 ciency measurements and other n data, Lamola 45 proposed a reac- e tion scheme as shown in Figure r g 6. The excitation was supposed y S0 to lead to a twisted state with a rate constant of 1/20 ps -1,50 from Z E where reaction to the ground Figure 6 Potential energy diagram for bilirubin state could either go back to the bound to albumin as proposed by Lamola Z-isomer (80 % efficiency) or continued twisting could lead to the E-isomer (20 % efficiency). This was used to explained the observed fluorescence decay, for which a life time of ca. 20 ps had been found, and the ground state recovery seen in the picosecond absorption.

14 Chapter 3

3. Experimental Methods

The smallest building blocks of interest in chemistry - atoms - are held together by the forces between nuclei and electrons to form molecules. A change in the field exerted by the electrons can lead to a different connec- tion between the atoms. Bonds are broken or created, a chemical reaction takes place. Due to the strong forces involved, contrasted by the low weight of the atoms, these processes happen on a very short time-scale. During cen- turies, chemical reactions have been studied, using a large range of methods. The actual process of the reaction, however, has not been seen. Instead, only the initial starting material, possibly some intermediates and the final products were observed. On a theoretical basis, the transition state theory was developed, which predicted the existence of an very short-lived high-energy compound (the transition state or activated complex), that forms from the reactants, and either can continue its way on the reaction path to form products, or decay back to reactants. Technological progress during the last decades, mainly in the field of laser technique, enabled the generation of ultra- short light pulses, first on the nano-, then pico- and femtosecond time-scale. With that technology, it was finally possible to "see" the transition state directly. 53, 54 The light pulses used are in the visible (and bordering) region(s) of the electromagnetic spectrum. Therefore, what is measured are optical absorption and fluorescence spectra of the compound investigated. No direct picture of the molecule it obtained, but interpretation of the spectra can often give a good description of the ongoing processes. New techniques, using very short-wavelength pulses (X-rays) are developed to gain direct information about the position of atoms relative to each other (as in X-ray diffrac- tion). This could be seen as the closest possible to a "photographic picture" of the transition state. An overview over the techniques used in this work, the time-resolved absorption (pump-probe) and fluorescence upconversion methods, will be given here.

15 Experimental Methods 3.1 Femtosecond transient absorption spectroscopy In steady-state (i.e. not time-resolved) absorption spectroscopy, a light beam is sent through a sample, and the (logarithm of the) ratio of the measured intensities of the light beams passing through the sample (I), and without passing the sample (I 0), is calculated as the absorbance A (also known as optical density OD):

I A OD lg 0 I This can either be done by first measuring the background and then the sample, or by using two beams simultaneously (two-beam spectrometer). The latter case increases stability and thus data quality by compensating for instability of the light source. A similar setup is used in the time-resolved method, with the major difference being that the focus is put on the time- dependent absorption. Therefore, a change in the sample has to be induced, and the development of the process is monitored following the perturbation. In lower time-scale methods, reactions can be initiated by mixing solutions, and the development of the system is monitored. On the ultra-fast time- scale, the only usable trigger to initiate a change or reaction is light itself. Therefore, a strong laser pulse excites (pumps) the sample, and a second pulse shortly afterwards measures the signal (probe). In order to be able to initiate a reaction or process, light has to be absorbed, and the probe-wavelength has to match the absorption spectrum of the sample. In most work, this requires coloured samples, that are able to absorb light in the visible (excitations in the UV-region are also possible and can e.g. be applied on proteins). A description of the setup used in this work follows, a layout is depicted in Figure 7. The pulses used to perform the pump-probe experiments were generated in a Ti:Sapphire amplifier (Spectra Physics Spitfire). The lasing 3+ medium, Ti:Sapphire, consists of Al 2O3 doped with Ti 2O3, and the Ti ion is responsible for the lasing action.

16 Chapter 3 PD 1 variable PD2 delay-line PC Mono - Chopper Pump chromator Sample Reference White-Light Signal Probe BS 50% Generation Sapphire CW Nd:YVO , ν-doubled 460-1000 nm Q-switched Millenia V Nd:YLF mode-locked Ti:Sapphire Amplifier (ν-doubled) Tsunami, 82 MHz, 800 nm 0.9 W, 70 fs Optical Parametric 5 kHz Amplifier 15 W (OPA) Regenerative Ti:Sapphire Amplifier 5% 5 kHz, 800 nm, 1.2 W, 90 fs 4ν (idler), 400- 600 nm BS 95% Figure 7 Scheme of the setup used for fs transient absorption (pump-probe) experiments; BS - beam splitter, PD - photo diode, ν-doubled - frequency-doubled The system is seeded by a mode-locked Ti:Sapphire amplifier (pulse energy ca. 10 nJ), pumped by a continuous wave (cw) frequency-doubled, diode- pumped Nd:YAG laser (Millennia V). The active material, Nd:YAG is 3+ made of yttrium aluminium garnet (YAG = Y 3Al5O12 ) doped with Nd . The energy for the amplifier is provided by pumping with a Q-switched Nd:YLF

(LiY 1.0-xNd xF4) laser, running at the second harmonic wavelength (Merlin). In the regenerative amplifier, the seed pulses are amplified ca. 20 000 times, to pulse energies of 200 µJ. Although this corresponds to a rather low average power, the energy is compressed in very short pulses (ca. 100 fs). Therefore, the energy during the pulse corresponds to ca. 1 GW! As such high energies can easily damage the internal optics of the amplifier, a technique called chirped pulse amplification is used. This technique is demon-

Stretcher Amplifier Compressor

Figure 8 Chirped pulse amplification

17 Experimental Methods strated in Figure 8. The low-energy seed pulse is stretched (increasing pulse length), amplified, and afterwards compressed to the original pulse length. Stretching and compressing the pulses is done with the help of gratings, which separate different wavelengths, that subsequently travel different path-lengths. The output of the amplifier is then split by a beam-splitter (ratio ca. 95:5), The major part is used to generate signal (1.2-1.6 µm) and idler (1.6-2.2 µm) pulses in an optical parametric amplifier (OPA). These pulses can be frequency doubled or quadrupled to generate the desired wavelength between 400 and 800 nm. The output used in the experiments here (quadrupled idler, ca. 460 nm) were in some experiments compressed in a double pass prism compressor to reduce the pulse length. The weaker part of the amplifier output beam is attenuated and focused onto a sapphire plate. Thereby, white light is generated, covering a region from ca. 460-1000 nm, which is used as probe pulse. This white light is split into the signal and reference beam, both of which pass through the sample, but only the signal beam overlaps in space and time with the pump-pulse. After the sample, both beams are directed through a monochromator, and their signal detected by photodiodes. The signal observed, ∆Α , is calculated according to the following equation:

I I A log sig log sig Iref pump Iref no pump in which I sig and I ref are the signal intensities measured at the signal and reference photodiodes, respectively. Pump and no pump refer to conditions where the pump beam reaches the sample, or is blocked by the chopper. Due to these background corrections and the stability arising from the solid state lasers, low absorbance difference values down to ca. 50 µOD can be measured. The system allows measurement of absorption decays (intensity dependence on time) as well as transient spectra (intensity dependence on wavelength). The speed of light in optical components such as lenses and prisms is depending on wavelength, and longer wavelengths are travelling faster than shorter ones, leading to a group velocity dispersion, or chirp. The effect can be substantial, up to more than one ps, and thus requires compen-

18 Chapter 3

0.0003 ESA ESA

0.0000 S1 SE GSB

Absorbance -0.0003

∆ GSB SE

-0.0006 S0

Wavelength

Figure 9 Symbolic transient absorption spectrum, with the different possible contributions: GSB = ground state bleaching, ESA = excited state absorption, SE = stimulated emission; the line symbolises the sum of the contributions, and would correspond to the measured spectrum at one chosen time. A simple energy level scheme is also shown sation. When measuring transient spectra, the setup corrects automatically for the chirp, by adjustment of the delay-line according to the wavelength used. A schematic transient absorption spectrum is shown in Figure 9. In steady-state spectra, the only contribution is (apart from artefacts such as light scattering) the absorption of light. In time-resolved spectra, the difference in absorbance between an excited (signal) and a non-excited sample (reference) is taken as ∆ Absorbance. Here, different contributions to the spectrum can occur. The molecules that were excited by the pump beam to a higher (excited) state, such as S 1, are not available for the same excitation by the probe beam, as long as no relaxation back to the ground state has occurred. A negative absorbance is recorded (compared to the reference), which is seen as ground state bleaching (GSB in Figure 9). Absorption from the excited state is also possible (e.g. S 1→S2 or S 2→S3, more generally

S1→Sn), usually at a different wavelength than the ground state absorption, which is expressed as a positive ∆A signal (ESA). Furthermore, the excited sample can emit light by stimulated emission, i.e. the incoming photon of the probe beam causes an excited state molecule to relax to the ground state, with the emission of an additional photon. This is seen as stimulated emission (SE), and usually occurs in the range where steady-state fluorescence is 19 Experimental Methods observed. The exact contributions change over time, as the molecule can vibrationally or electronically relax or photoreact and the depicted symbolic spectrum corresponds only to one fixed time. Thus, usually a range of spectra at different delay times are recorded. Alternatively, measurement of

0 2 4 0 20 40 60 80 100 120

0.008 0.008 BR in CHCl 3 λ =560 nm ex 0.004 0.004 λ = 453 nm BR in CHCl ex 3 λ =560 nm 0.000 ex 0.000 λ Absorbance = 453 nm ex Absorbance ∆ ∆

-0.004 -0.004

0.001 0.001 0.000 0.000

residuals -0.001

residuals -0.001 0 2 4 0 20 40 60 80 100 120 Time (ps) Time (ps)

Figure 10 Typical transient absorption decay curved (open circles), together with the best fit to the experimental data. The residuals are also shown below the graphs. The system is bilirubin in CHCl 3 at early times (left), and the complete plot (right). ∆Absorbance with changing delay times yields kinetic curves, such as seen in Figure 10. Even here, positive and negative signals can occur. These kinetic traces can be fitted to multi-exponential decay functions (with up to n independent decays) of the general form n t

i A RF t shift Amp Amp i e BG i 1 in which RF is the response function of the system, usually taken as a Gaus- sian function (which can describe the laser pulse well), shift is the time shift from time-zero, Amp is the sum amplitude and Amp i are the individual amplitude components of the signal. BG represents the background, usually a fixed value, obtained by the fitting procedure (i.e. a floating background). As the laser pulse is not infinitively short (i.e. not a δ-function), the response function is convoluted with the exponential function, this is indicated in the equation by the convolution integral ⊗. From these fits, lifetimes are obtained which are

20 Chapter 3 the inverse of the rate constants of the reaction. A negative amplitude is obtained when a rise occurs, i.e. the signal grows with time. This can, for instance, be the case in energy transfer processes, where the laser pulse excites a molecule or a part of a molecule, and the energy then is transferred to another molecule or another part of the same molecule. In this situation, a gradual build-up of the second state is observed, which ideally matches the decay of the first state, from which the energy is transferred. In all transient absorption measurements in this work, the angle between pump and probe beam was set to 54.7° (magic angle, see below).

3.2 Fluorescence upconversion A system excited by light can relax in several ways, i.e. return to a more stable state. It can photo-react, the light energy is then used to start a chemical reaction, or there may be processes to stepwise dissipate the energy to the surrounding in form of vibrational and rotational energy (i.e. produce heat), corresponding to internal conversion. An alternative and common process is fluorescence, where the electrons return to the ground state by emitting light. A typical time-scale for fluorescence of a molecule in its singlet state is in the nanosecond region. A macroscopic sample, excited by a laser pulse, contains on the order of 10 10 -10 15 molecules. Thus, although, the average lifetime is unchanged, a very great number of molecules will emit photons directly after excitation (for example, in the first picosecond). These photons, if collected by lenses or mirrors, can be used to combine with a light pulse split off the laser pulse that originally excited the sample. Scanning with variable delay in between these pulses allows to gain information about the development of the system on the ultra-fast time-scale. For the laser pulse to combine with the photons of the fluorescence, several conditions have to be fulfilled. The combination of two photons to form one photon with different energy is a non-linear process, and can only take place in certain materials with special optical properties (non-linear crystals, such as BBO ( β-BaB 2O4). Also, high light intensities are needed. This is ensured not only by using lasers with high output power. Due to the pulsed nature of the light, the light power is concentrated in short intervals, whereas the av-

21 Experimental Methods erage intensity is comparably low. Focusing the beam also ensures high spatial intensities. From the two light pulses, a higher energy (shorter wavelength) photon is obtained by the non-linear combination process, usually in the UV-region (with the excitation and fluorescence in the visible region). The upconversion technique, also known as sum-frequency generation technique, allows detection on the fastest time-scales, only limited by the pulse length of the lasers used. A scheme of the system used in this work is given in Figure 11, and a detailed description can be found in ref 55. A tuneable, mode-locked Ti:Sapphire laser (Spectra Physics Tsunami), pumped by an argon ion laser, gave pulses of ca. 60 fs pulse length, tuneable between 710 and 1080 nm, covering the red and near-infrared region. By frequency doubling with a BBO crystal as doubling medium, the blue and green regions of the spectrum (ca. 360-540 nm) became accessible. A beam splitter was used to separate the frequency doubled and fundamental beams. The sample was kept in a rotating cell, avoiding fast bleaching that otherwise could occur due to the high repetition rate. After passing through the sample, the pump beam was blocked. The fluorescence from the sample was collected and, together with the gate pulse, after passing through a variable

Ar + Laser, ~10 W, 514.5 nm ( ν-doubled)

Ti:Sapphire Laser Tsunami 1 W, 710-1080 nm, 82 MHz, ~60 fs 0.3 mm BBO

Sample Photon Mono- Coun- chromator ter PC PMT

Figure 11 Setup of the laser system used for fluorescence upconversion 22 Chapter 3 delay line, focused onto a 0.5 mm BBO crystal. The upconverted signal was collected and passed through a prism. Pump beam residuals were removed by an iris, the signal was passed through a UV filter and focused onto the slits of a monochromator (ISA H10 UV). For signal detection, a Peltier- element cooled photomultiplier (Hamamatsu R4220P) was utilised, and a gated photon counter (Stanford Research Systems SR400) was used for signal counting. The desired wavelength was chosen by adjusting the monochromator, the angles of the mixing crystal and prism, as well as choice of UV filters. Typical decay curves can be seen in Figure 12, together with the response function and a least square fit to the measured data. Data evaluation was performed with the SPECTRA programme, allowing for a variable background, a shift in the excitation time (time zero), and a sum of up to six exponential. The "square root" noise model was chosen for fluorescence experiments (photon noise). Control of the delay line (by the PC) allowed for different step sizes during one measurement, thus greatly increasing the dynamic range by collecting data in typically 10 fs steps at early decay times, and up to two picoseconds at very long times. For least square fitting, the data were extrapolated (typically 4096 points per decay), and weighted according to the step size to give equal weight to each measured point.

Upconversion decay 4000 Upconversion decay 4000 Fit to data Fit to data Response function Response function 3000 3000

2000 2000 Counts Counts per second 1000 Countssecond per 1000

0 0

-400 -200 0 200 400 600 800 0 2 4 6 8 10 Time in femtoseconds Time in picoseconds

Figure 12 Typical decay kinetics as measured by fluorescence upconversion (bilirubin in CH 2Cl 2)

23 Experimental Methods 3.3 Anisotropy measurements Light as an electromagnetic wave can be described by electric oscillations in a plane situated perpendicular to a plane of magnetic oscillations. The inter- sectional line between these two planes is the direction of propagation. Normal light, as arriving from the sun or emitted by light bulbs, has no preferred direction due to the averaging of all possible directions. In contrast, laser light possesses a preferred direction, which can be utilised for selected excitation and detection. This allows, besides monitoring light intensities, to gain additional information on orientational changes due to e.g. energy transfer. Commonly, two different measurements are performed, one with a parallel and one with a perpendicular orientation between the two beams. From that, the anisotropy is calculated according to: I t I t r t I t 2 I t

From the parallel and perpendicular polarisation measurements, the iso- tropic signal (that is devoid of all polarisation effects) can be calculated:

I t 2 I t I t iso 3 Alternatively, a single measurement with a polarisation of 54.7° (magic angle) also is void of anisotropic effects. A measured value of 0.4 for the anisotropy is a sign for the absorption and emission dipole being in line, a decay within few hundreds of femtoseconds or a few picoseconds can arise from energy transfer between two units (rotational depolarisation effects usually play only a minor role at such short times). Assuming a final anisotropy value r ∞ smaller than 0.4, the angle θ between the donor and acceptor transition dipole moments can be calculated with the following equation:

3cos 2 1 r 5

24 Chapter 4

4. Quantum Chemical Methods and Concepts

4.1 Basic quantum chemical concepts One of the greatest scientific achievements of the 20th century, the development of quantum theory, has allowed chemists to gain a detailed understanding of the mechanism of chemical reactions. It allows interpretation and predictions on the smallest level, on the scale of electrons, neutrons and protons. The main aim in quantum chemistry is to solve the Schrödinger equation,

H E and through it to obtain a wave function Ψ which, in principle, contains all properties of the molecule in question, including its energy E. 56 Ĥ is the Hamiltonian, an operator working on the wave function. The terms appear- ing in the Hamiltonian contain the kinetic energy of the nuclei and electrons, and the potential energy resulting from interaction between them, and among electrons and nuclei:

H Tnuc Tel V el_nuc Vel V nuc Although strictly valid, an exact (analytic) solution to the Schrödinger equation is only possible for the smallest of atoms, hydrogen. Numerical, i.e. approximate solutions have to be found otherwise. The main difficulty in practice, when using quantum chemical methods, is the complexity of the problem, as there are usually tens, often hundreds of atoms involved. This results in interaction between hundreds or thousands of particles, leaving a vast computational challenge. To simplify the problem, assumptions have to be made. A very basal assumption is based on the fact that electrons are about 2000 times lighter than protons. This leaves the nuclei (whose mass is even larger due to neutrons) relatively inert to changes, whereas electrons can adopt nearly instantaneously (timescale less than 1 fs). As a result, the nuclei can be seen as fixed, and the electrons adopt to the field resulting from them. This is known as the Born-Oppenheimer-approximation and

25 Quantum-Chemical Methods and Concepts forms a basis of our understanding of chemical bond formation and dissociation, as well as molecular dynamics. By calculating energies for several nuclear positions in space, potential energy curves for two-atomic molecules can be constructed. The minimum position corresponds to the most stable equilibrium position. For molecules with more than two atoms, hypersurfaces result from the large number of possible orientations of nuclei towards each other, and a potential energy curve can be seen as a section through such a many-dimensional surface. Under the assumption of the Born-Oppenheimer approximation, a separation of the wave function into a nuclear and an electronic part becomes possible: 57

el nuc All common electronic structure methods concentrate on solving the electronic part of the Schrödinger equation, the Hamiltonian of which consists of the following parts:

Hel Tel Vel_nuc V el V nuc

The aim now is to find an electronic wave function, Ψel (r 1, r 2, . . .) , as a function of all electrons. In the orbital approximation, the complete wave function is a product of one-electron functions - the orbitals, i.e.

el 1 r 1 2 r2 ...

LCAO approximation and basis sets To construct the one-electron functions for a molecule in the LCAO- approximation (linear combination of atomic orbitals), atomic orbitals χi are combined to form molecular orbitals (MOs), with corresponding weighting factors c p:

r cp p r p In reality, instead of using atomic basis functions, basis sets are used. To combine, for instance, two s-orbitals to describe a σ-bond, the two principle s-functions are augmented with further s-orbitals and p-, d-, f- and even more orbitals (polarisation functions). In special cases, such as the descrip- 26 Chapter 4 tion of ions, diffuse functions are also added. These are useful in describing for instance long-range interactions. A very efficient way of expressing the electron distribution (i.e. the orbital shape) is to use Slater type orbitals, functions with an e –ζr radius dependence of electron density ( ζ is connected to the effective nuclear charge). These give analytic expressions for one- electron functions that can be fitted to calculated (numerical) atomic orbitals. In praxis, however, these are not very efficient to handle, and are sur- passed by Gaussian type orbitals (with an e –ζr² dependence) in their suitabil- ity for computational treatment. As a result, although a larger number of orbital functions is required for a good description, the computational de- mand is greatly reduced.

Electron spin Elementary particles can be grouped into two categories, fermions (which follow the Fermi-Dirac-statistics, having half spin values) and bosons (having integer spin and following the Bose-Einstein-statistics). 56 The former are the basic building blocks of matter, whereas the latter are the carriers of forces (the photon, e.g. carries the electromagnetic force). For fermions, an exchange of two identical particles requires the change of sign of their wave function, known as the Pauli-principle. Put in a simplified way, it states that two fermions have to differ in at least on quantum number. Thus, two electrons in one orbital have to differ in their spin values, α and β. The one- α β electron wave functions therefore takes the form ψ1 (r 1) or ψ1 (r 1). In contrast, photons do not need to differ in their quantum numbers, as can bee seen in intense monochromatic laser radiation, where a great number of photons are in the same state. Practically, a simple product form of the wave function

el 1 r 1 2 r2 ... that does not satisfy the Pauli-principle, is replaced with a Slater determinant:

27 Quantum-Chemical Methods and Concepts

1 1 1 2 1 3 ... 1 N 1 2 3 ... N 1 1 1 1 1 el 1 2 3 ... N N! 2 2 2 2

Z 1 Z 2 Z 3 ... Z N

Here, as required, exchange of two electrons results in a change in sign of the wave function.

The Hartree-Fock-Method and the Self-Consistent Field The electronic Hamilton operator from above can be written as a sum of one-electron and two-electron operators, plus the nuclear potential energy operator:

H el h g Vnuc Tel Vel_nuc Vel V nuc

Applying each of these operators on the Slater determinant (wave function) gives:

E h g V , were Ψ|ĥ|Ψ and Ψ | ĝ| Ψ stand for the one-electron and two-electron contributions, respectively. The two-electron integral contains two contributions, one being the Coulomb integral J, which corresponds to the classical interaction due to the charge of the electrons. It is always positive and leads to an increase in energy (destabilisation). The other contribution is the exchange integral K, which can be seen as a correction to the Coulomb integral. Not having any classical counterpart, it takes the spin correlation into account. For two electrons with the same spin, the probability of finding both at the same point in space is zero. For opposite spins, however, there is a higher probability of finding the second electron in close proximity to the first (which is the basis for Hund's rule of maximum multiplicity). The exchange integral, being positive, reduces the Coulomb energy from J to J-K. Based on the above, the Hartree-Fock equations can be formulated. The overall energy is

28 Chapter 4

E 2 i 2Jij K ij i j

Here,

H backbone 2 J j 1 K j 1 i 1 i i 1 j j

56 and the Coulomb and exchange integrals J ij and K ij are:

* Jij i 1 J j 1 i 1 d 1

* K ij i 1 K j 1 i 1 d 1

The Coulomb and exchange operators Ĵ and Kˆ are given by:

1 * 1 J j 1 0 d 2 j 2 j 2 4 r12

1 * 1 K j 1 i 1 0 d 2 j 2 i 2 j 1 4 r12 The variational principle can now be used to optimise the orbitals. Accord- ing to this, all possible wave functions will have an energy at least as high as the true energy: E trial = Ψ|Ĥel |Ψ ≥ E true . The problem arising is, that in order to calculate the energy, a wave function is required. Therefore, an itera- tive procedure is used, starting with some guess wave function (which can be e.g. a Hückel guess function).

Electron correlation and configuration interaction Due to approximations in the above described methods, solving the self- consistent-field calculations with the Hartree-Fock-procedure gives an energy E HF which is higher than the true energy of the system. The difference is defined as the correlation energy E corr :

Ecorr E HF Eexact , where the true energy E exact can be estimated with very high accuracy methods. There are two main contributions which, however, can not be completely separated, the dynamic and static correlation.

29 Quantum-Chemical Methods and Concepts After arriving with a set of orbitals for a molecule, the ground state is obtain by filling the lowest energy orbitals with electrons, according to the Aufbau- principle. This set of orbitals, partly filled with electrons, is known as a configuration. For closed-shell molecules at equilibrium geometry, it gives usually a reasonable description of the molecule. For excited states (being of interest in spectroscopy), electrons are taken from the filled, low lying orbitals, and placed into higher ones. In most cases, however, one configuration is not giving an adequate description of the properties of this excited state. Also, molecules far away from the equilibrium geometry, such as in dissociation processes and bond formations as well as transition states, are poorly described. The static correlation stems from the fact that a single configuration does not give a good description of the state. Instead several configurations with similar energy start mixing, and contribute to the correct picture of that state. The form of the Slater determinant excludes the possibility of electrons of the same spin being at the same orbital, i.e. close in space. For electrons with different spin, however, the determinant underestimates the fact that electrons try to avoid each other, it thus neglects local electron-electron- interaction, and takes only the total interaction into account. This is known as dynamic correlation. Together, the static and dynamic correlation lead to a higher energy than the one actually observed for the system. To overcome the correlation problem and minimise the correlation energy, several methods are available. Perturbation theory (such as second and higher order Møller-Plesset, MP2, MP3,...) reduces the dynamic part of the correlation energy. Configuration interaction 58 is used to minimise the static electron correlation. This is done by combining different configurations, the ground state (i.e. all electrons in the lowest energy orbitals) and excited configurations, were electrons are taken from the lowest orbitals and placed in - formerly empty - higher lying orbitals. Optimising the weighting factors in a linear combination to reach the lowest possible energy results in weights, which are highest for those configurations of greatest chemical importance. The most commonly used method, configuration interaction singles (CIS) includes only single excitations, i.e. lifting only one electron per configura-

30 Chapter 4 tion. An extension (CISD) also takes double excitations into account. Due to the large number of possible variations (excitations), including all possible configurations (full configuration interaction) is only possible for the smallest of systems, as single atoms or small molecules. Thus, although the method recovers the complete static correlation energy, it is not applicable to larger systems, such as many of the systems of biological importance.

4.2 The CASSCF method Closely related to the configuration interaction method is the complete active space self consistent field (CASSCF) method. 59 It is also based on the multiconfigurational approach, but during a CASSCF calculation, not only the weighting factors in the linear combination, but also the orbitals them- selves are optimised to the current conditions. To minimise computational cost, a subset of orbitals is chosen, based on chemical reasoning, such as a group of π-orbitals, some of which will be filled and the remaining empty. Within this subset, known as the active space, a full configuration interaction is done, creating all possible excitations from the filled into the empty orbitals. Subsequently, the energy is minimised by optimising the orbitals and weighting factors simultaneously. In a typical calculation, thousands or even hundreds of thousands of electronic configurations are taken into account. Although most of the static correlation can be recovered by the CASSCF method, it does not describe dynamical correlation effects well. In a further development, perturbation theory of second order has been included, with the CASSCF wave function as the zeroth-order starting point. 60 It has become known as CASPT2 (complete active space with second order perturbation theory). The CASSCF/CASPT2 method is second to none in its ability to describe awkward chemical systems. It is (together with closely related multiconfigurational approaches) the only method able to give a quan- 60 titatively correct picture of the Cr 2 molecule, containing no less than six (weak) bonds, and very recently the properties of a uranium dimer have been calculated by means of the CASSCF/CASPT2 method. 61, 62

31 Quantum-Chemical Methods and Concepts 4.3 Density functional methods (DFT) As stated earlier, the wave function contains all information necessary to describe a system. A physical parameter (an observable Ω) is obtained by applying the corresponding operator on the wave function:

< > * d

Thus only the square of the wave function is connected to physical observables, whereas the wave function itself does not have any physical meaning. As the wave function often is complex, having a real and an imaginary part, taking the complex conjugate (indicated by the asterisk) ensures that the square is void of imaginary parts. Walter Kohn was able to show that all information related to physical quantities is contained in the electron density ∗ ρ, which can be calculated as the square of the wave function ρ = ψ ψ. This forms the basis for density functional (DFT) methods, which have grown greatly in importance over the last decade. The electron density ρ, which has the form of a matrix, takes the role of the wave function, and instead of using the latter to obtain expectation values (observables), the density matrix is evaluated:

tr tr

Here, tr symbolises the trace of the matrix. The main advantage that DFT methods offer, are greater accuracy at reduced computational cost, partly, because a part of the electron configuration is included. A reduction of computational costs allows treatment of larger molecules, especially those of biological importance. The significance of Kohn's work, on which the DFT methods are based, was stated by the award of the Nobel price in 1998. In its time-dependent form (TD-DFT), these methods allow calculations of excited states, and thus the prediction (and analysis) of optical spectra. In this thesis, DFT methods were used to calculate the optical spectra of bilirubin and model compounds.

32 Chapter 4 4.4 Conical intersections The vast majority of all reactions are thermal reactions, where the reaction barrier is low enough to be crossed at ambient temperatures, or where an increase of temperature will be sufficient to enable the reaction. In many cases, catalysts lower the reaction barrier, and open otherwise impossible reaction paths. This is especially true for biochemical reactions, where en- zymes as highly specialised catalysts enable reactions at ambient or body temperature. All of these reactions proceed on the lowest electronic potential surface (adiabatic reactions), all the reactants, intermediates and products are in their lowest electronic state at all times during the reaction. With modern quantum chemical tools, the reaction paths can be calculated rather accurately for even moderate size molecules (hundreds of atoms). In contrast, photoreactions are triggered by excitation with light, and the reactants are excited into higher electronic state, from where the reaction proceeds. Since the photoproducts accumulate as ground state products, a surface crossing has to take place during the reaction (nonadiabatic reactions). Figure 13 shows two potential energy surfaces for the ground and first excited electronic state, together with possible photoprocesses. In many reactions, the molecule moves to a minimum of the excited state surface, which corresponds to a maximum of the ground state surface. Here, the surfaces can come rather close (avoided crossing), or they can actually cross (called conical intersection due to the topology of a double cone). Until a few decades ago, it was widely believed that intersections result from point group symmetry, and that states of the same symmetry avoid one another (noncrossing rule, which strictly only applies for two-atomic molecules). Following from that, true conical intersections were assumed to be extremely rare. Theoretical and computational advances in recent years, have however shown true conical intersections to be common, 63 and playing an important role in some of natures most important processes, such as energy transport in photosynthesis and the initial photoprocess of vision.

33 Quantum-Chemical Methods and Concepts

Franck-Condon- point

S minimum 1 Conical intersection Energy Fluorescence Absorption

S minimum 0

Figure 13 Symbolic potential energy surfaces and possible photoprocesses In the representative example in the figure, excitation would first lead to barrierless relaxation to the S 1 minimum. From there, the molecule can relax by red-shifted fluorescence (shorter distance between the surfaces from the

S1 minimum) and return to the same ground state minimum, i.e. no photoreaction occurred. Alternatively, passing over the barrier in an activated process to the next minimum leads to a conical intersection. This would require additional energy, and the barrier could experimentally be observed by monitoring the reaction at different temperatures. Accumulation of molecules in the S 1 minimum would lead to a build-up of an intermediate, the lifetime of which would be, among other factors, dependent on the barrier height. After a molecule has crossed the barrier, a very fast downhill relaxation to the ground state takes place. The nature of the ground state surface determines the result of the photoreaction, with a possible path back to the reactant, and possibly another path leading to a different photoproduct. In cases where the ground and excited state potential energy surfaces are very close, they start interacting, and the system cannot be correctly de-

34 Chapter 4 scribed as moving on only one potential energy surface, the Born- Oppenheimer-approximation breaks down. This is a great challenge for computational chemistry, and only in recent years has a general description of many photoreactions become possible. This description involves the multiconfigurational approach, as described earlier. In the reaction in phototherapy of neonatal jaundice, a conical intersection is assumed to be of great importance, enabling an efficient reaction path from the excited to the ground state.

4.5 Exciton theory

Imagine two chromopho- Monomer Dimer res that are close to each 1 other, but not in van der 2 1 2

1 2 + ES 2 2V Waals contact (with their ES – ES 1 1 electrons well localised to Energy 2 1 2 either chromophore). The levels field exerted by the electrons on one chromophore GS GS will be sensed by the electrons on the other one. Absorption During the absorption ν0 ν0±V process, the transition ν ν dipole moment leads to a λ λ major rearrangement of Figure 14 Energy levels and symbolic absorption spectra for a monomer and a chromophore of interacting dimers; electrons, and this will GS = ground state, ES = excited state effect the electrons on the other unit and vice versa. Therefore, the electrons are not completely independent, and the system becomes coupled. The biggest term in the interaction stems from the dipole-dipole interaction, and in most cases all higher multipole-multipole interactions are neglected. Assuming a single absorption for the monomeric unit, the interaction will lead to a splitting yielding one lower and one higher energy absorption (see Figure 14). The absorption spectrum can broaden, as seen in the figure, with a shoulder occurring. The

35 Quantum-Chemical Methods and Concepts net effect in this example, integrated over the absorption band, would correspond to a red shift. The interaction energy V is strongly dependent on the distance between the dipoles, but also on their orientation, and can be calculated as: 64

2 µ µ 1 µ 1 µ2 3 µ R R µ V 1 2 1 12 12 2 4 3 4 3 5 0 R 0 R 12 R12 r r r µ µ µ where the dipole moment vectors are given by 1 and 2 (µ = | |), the dis- r tance and the vector between the two chromophores by R and R12 , respectively, and ε0 is the permittivity in free space. The angle dependence is expressed as κ = (cos α - 3·cos θ1 cos θ2), in which α is the angle between the chromophores, and θ is the angle between the transition dipoles and the line between the chromophore centres (i.e. the line that represents the distance R). Both, the upper and lower excitonic state take part in the absorption, but the intensity of the transition (the dipole strength) can vary. This depends on the orientation, and some extreme cases can be pointed out: for an in-line arrangement (head-to-tail or head-to-head), all intensity is situated at lower energies, resulting in a bathochromic (red) shift of the observed spectrum. For a parallel arrangement, the higher energy component possesses all dipole strength, which is expressed in a hypsochromic shift of the spectrum (i.e. at shorter wavelengths). In a perpendicular assembly, no interaction will occur, whereas all other cases lead to a broadened spectrum, with both components actively contributing to the absorption.64 Simpson and Peterson 30 put forward practical criteria to distinguish between different types of interaction, dividing into strong and weak coupling, where the exciton is envisaged as being free (delocalised over all interacting chromophores) or localised, respectively. The former case is encountered when the splitting energy 2V is much larger than the band width of the monomer absorption (taken as the full width at half maximum of the absorption spectrum, ∆ε), and vice versa for the weak case: 65

36 Chapter 4 strongcoupling weak coupling 2V 2V 1 1

For strongly coupled excitons, the energy transfer times are in the femtosecond region, on the time scale of molecular vibrations, and the energy can therefore not be seen as localised, as it is constantly travelling back and forth. For the weakly coupled case, transfer times amount to picoseconds 65 , and the energy is "hopping" between single units. As a further case, Förster or resonance energy transfer can be classified as the very weak coupling limit. These transfer rates are at least one order of magnitude lower than for the weak case.

37 Initial Photochemistry of Bilirubin

5. Initial Photochemistry of Bilirubin (Summary of Results)

A possible photoreaction scheme for bilirubin, as had been proposed earlier (see Chapter 2 and Figure 6), was able to explain many details of bilirubin's behaviour. However, several facts where not fully in agreement with this model. The similar lifetimes observed for the albumin bound molecule and the chloroform solution were not consistent with the big difference observed in the fluorescence quantum yield for these two systems. An increase in the radiative strength upon binding to albumin by an order of magnitude or more would have been required. A calculation of the radiative lifetime, based on the absorption spectrum, gave natural lifetimes of about 1 ns. Combined with the quantum yield, the expected lifetimes were not matched by the measured decay time of ca. 20 ps. Therefore, we studied the time- resolved fluorescence with greatly increased time resolution by the upconversion method, and found lifetimes shorter by at least one order of magnitude than previously reported. The fast decay was in good agreement with the fluorescence quantum yields, and the more than ten times higher quantum yield for the BR-albumin complex compared to BR in chloroform was reflected in slower decay times for the former. It became also clear that the slower decay components for BR-albumin, although having small amplitudes, were the main contributors to the steady state fluorescence. Meas- urement of time-resolved absorption spectra could confirm the ca. 20 ps lifetime found earlier, 50 but additional ultrafast components were found (Pa- per I). Bilirubin's very fast, sub-picosecond decay of the fluorescence observed in a range of solvents, contrasted by the natural lifetime of about 1 ns, requires the existence of very efficient de-excitation channels. Without these, relaxation to the nearest minimum on the excited state surface would be followed by fluorescence lasting about 1000 times longer than actually observed. To find a mechanistic explanation, quantum chemical methods were applied. Twisting of the exocyclic double bond had already been pointed out as an

38 Chapter 5 important relaxation pathway. 45, 66 Preliminary calculations, using DFT methods, showed a decrease in the energy gap between ground and first excited state upon twisting of the double bond. A strong decrease of the energy gap will lead to potential energy surfaces coming close, a situation where DFT methods are not reliable, and a multiconfigurational approach is required. Therefore, the CASSCF method was used to look for an avoided crossing or conical intersection between the two surfaces. A method developed by Bearpark et. al. 67 allows a direct search for the location of the lowest energy point on a potential surface crossing. The excited state energy is minimised simultaneously with the energy gap between the two surfaces, leading to the geometry of the (avoided) crossing. We were able to find a conical intersection for a bilirubin model (dipyrrinone), that showed a ca. 90° twisted C-C-double bond (see Figure 15 and Paper II). Interestingly, even the exocyclic single bond was highly twisted. This is remarkable, as an isomerisation mechanism, called Hula- Twist, 68, 69 had been suggested, which involved

Figure 15 Structure of the simultaneous twisting of a single and adjacent bilirubin model dipyrrinone at double bond. In contrast to the conventional one- the geometry of the conical intersection between the bond-flip isomerisation picture, where large parts ground and excited state of the molecule need space for rotation, Hula- Twist offered a volume-conserving mechanism, which could explain efficient isomerisation in e.g. proteins. The energetic location of the calculated conical intersection for our model was ca. 50 kJ/mol under the Franck- Condon-point, and a potential decay path through the intersection could be suggested. The transient absorption measurements showed complicated kinetics. A stimulated emission sub-picosecond decay in the region of the steady-state fluorescence, overlapping with excited state absorption growing on the same time-scale. This absorption, caused by a "dark" state intermediate, showed a lifetime of ca. 15 ps, which matched the ground state recovery (Paper IV). In further theoretical work, search for characteristic points in order to gain more information on the excited state topography, the S 1 minimum was lo-

39 Initial Photochemistry of Bilirubin cated. The geometry was somewhat close to the one of the conical intersection, with twisted exocyclic bonds, with an energetic location ca. 50 kJ/mol below the conical intersection, and ca. 100 kJ/mol under the Franck- Condon-point (Paper II). Based on that, is could be suggested that fast relaxation from the Franck-Condon-region after optical excitation proceeds to the S 1 minimum, which corresponds to the dark state intermediate. From the excited state minimum, fluorescence could occur, this would, however, be expected in the infrared region (>1000 nm). As an alternative process to fluorescence, the molecules have to overcome a barrier in an activated process. After passing the barrier, direct relaxation through the conical intersection would return the molecules to the ground state. The twisted nature of the conical intersection allows relaxation to either the E- or Z-isomer. Investigation of bilirubin in comparison with half-bilirubin model compounds (xanthobilirubic acid, XBR, and its methyl ester, MeXBR) with the fluorescence upconversion method yielded valuable information about the fastest observed processes. In nonpolar solvents (chloroform, dichloromethane and tetrahydrofuran), the fluorescence decay of BR was considerably faster than for the half-models, fast lifetime components of ca. 100-150 fs, with amplitudes of ca. 50 %, were observed for bilirubin, but not for XBR and MeXBR. Neither were they seen in solution of BR in alkaline methanol, were the decay between XBR and BR became rather similar. It was concluded that these fast lifetimes could be attributed to the interaction between the chromophore halves in bilirubin, where the excitation, first delocalised over both halves, is transferred to one half, i.e. exciton localisation (Paper IV). The fact that no comparable lifetime can be seen in alkaline methanol was explained by the less rigid structure of BR, which is deproto- nated at high pH, leading to a different interaction between the two halves. The assumed energy transfer (localisation) would be expected to result in a decay of anisotropy, which was seen for bilirubin in several solvents. Figure 16 shows the time-resolved anisotropy for BR in chloroform and tetrahydrofuran. Achieving a good signal to noise ration is a great challenge, but a ultrafast decay is clearly visible in both cases. By comparison to the overlaid fluorescence decay curves, it can bee seen that most of the anisotropy de-

40 Chapter 5 cays during the time of the instrument response function (i.e. during the rise of the signal). An estimation of the time-scale yielded a component of ca. 100-200 fs, which is in fair agreement with the fast decay component of ca. 120 fs.

0.35 0.35 BR in CHCl3 12000 Anisotropy r(t) BR in THF

4500 Counts Numberof Fluorescence Decay Anisotropy r(t) Perpendicular Fluorescence Decay Perpendicular Counts of Number 0.30 Parallel 8000 3000 Parallel 0.30 Anisotropy Anisotropy 1500 4000 0.25

0 0 0.0 0.4 0.8 0.25 0.0 0.4 0.8 Time (ps) Time (ps)

Figure 16 Time-resolved anisotropy decays for BR in chloroform and tetrahydrofuran; the measured decay curves, from which the anisotropy was calculated, are shown in grey. The exciton interaction, leading to a higher and lower energy level (blue and red shifted in the spectrum, respectively), was probed by exciting at shorter and longer wavelengths than the absorption maximum. This would mainly excite the higher and lower states. Interestingly, no difference in the emission kinetics could be observed in dichloromethane. The conclusion drawn was that excitonic relaxation at least in this solvent is extremely fast (tens of femtoseconds at most), and could not be resolved with the existing time resolution. Even aside from the fast (~120 fs) component, bilirubin shows a complex kinetic behaviour, with more than one fluorescence decay time. This is also observed for XBR and MeXBR, in all solvents investigated. Excitation of a single conformation would be expected to lead to a mono-exponential decay. A possible explanation is the existence of several ground-state conformers in solution. Although being stabilised by hydrogen bonds, the bilirubin molecule is not rigid. 70, 71 which is also seen in the fast interconversion of the P- and M-form. 21 Thus, after excitation to the Franck- Condon-state, the molecules start relaxing from different points on the excited state surface. After relaxation to the intermediate, however, the structures equilibrate, and the relaxation from the S 1 minimum is mono- exponential.

41 Initial Photochemistry of Bilirubin In another theoretical project (Paper III), the optical absorption and circular dichroism (CD) spectra of bilirubin and model compounds XBR and semirubin 72, 73 were calculated by means of time-dependent DFT. As a start, the molecular structure was optimised, and very good agreement with nearly all data from the crystal structures was obtained, approaching experimental accuracy. This was an improvement over previous structure calculations, based on the AM1 18 and Hartree-Fock 19 method (the latter with the 3-21G basis set). The time-dependent calculations, utilising three different func- tionals, gave excitation energies in good general agreement to the observed absorption. For the half-bilirubin model XBR, very good agreement was seen, the comparison with BR was partly complicated due to limited experimental data (the solution spectra are very broad and the main absorption bands are overlaid). A finding that still needs to be resolved are the calculated low-energy absorptions found by all three DFT methods. These may possibly be spurious states which are known to occur for some density func- tionals. In a very recent article, Granucci et. al.16 also found low lying absorption states for bilirubin, which were analysed as charge-transfer states. Time-dependent DFT methods has been shown to give inaccurate results for excited states involving significant charge-transfer-components. 74 The experimental verification is impeded by the low oscillator strength for those absorptions, combined with there rather close location to the main transitions of large intensity. Using a method developed to calculate chiroptical properties by time-dependent DFT, 75, 76 the CD spectra of bilirubin could be calculated from first principle. This allowed a direct assignment of the P-form binding to human albumin at neutral pH, in line with experimental results on bilirubin models that were synthesized with known configuration. 27 Furthermore, the effect of hydrogen bonding on the electronic spectra was separated from the excitonic interaction. This was done by calculating absorption of two different absorption spectra of semirubin, one with and one without intramolecular hydrogen bonds. As could be seen from the results, the hydrogen bonding can have medium effects on the absorption spectra, with shifts of about 10 nm occurring.

42 Chapter 5 These calculations, being confirmed to give reliable results, open the possibility to calculate for instance CD spectra of different bilirubin conformers or isomers, possibly even in a protein environment (use of ONIUM), or with the possible addition of charged centres (point charges). To test whether the relaxation from the Franck-Condon region is a barrierless process, we have performed a series of temperature-dependent measurements. Nitrogen gas, cooled by conducting through liquid nitrogen or

BR in CHCl at BR-HSA in 3 1.0 buffer/ethylene glycol (50%/50%) -20°C 1.0 at ca. 1.0 1.0 +20°C -9°C +20°C +35°C +40°C 0.5 0.5 0.5 0.5 Norm. Intensity Norm. Norm.Intensity 0.0 0.0 0 2 4 0.0 0.4 0.8

0.0 0.0

0 4 8 0 50 100 150 200 250 Time (ps) Time (ps)

Figure 17 Fluorescence upconversion results for bilirubin in chloroform (left) and the BR- HSA complex (right) at different temperatures, the inset shows an increased time-resolution heated with hot water, was blown on the rotating sample cuvette, situated in a home-built housing. With this equipment, temperatures between ca. -50 and +40°C could be achieved. The results for bilirubin in chloroform are shown in Figure 17. The decays are, within the very low noise, virtually identical, the same result was obtained in tetrahydrofuran. Thus no barrier has to be overcome by the molecules to relax from the initially excited state. Measurements of bilirubin bound to albumin, however showed a marked dependence on temperature, with considerably faster and slower decays occurring at elevated and lower temperatures, respectively. As can be seen in the inset in the right panel of Figure 17, the fast components are not effected, and the observed changes take place in the medium long components. Thus, changes in temperature have no consequence for the excitonic interaction, as expected. The component that is most effected is thus the twisting around the double bond. A temperature dependence of the fluorescence decay was also observed for BR solutions in alkaline methanol

(1%NH 4OH/MeOH). Interestingly, the half-bilirubin compound XBR also

43 Initial Photochemistry of Bilirubin showed a clear temperature dependence in methanol, and surprisingly even in chloroform (where none was observed for BR).

Conclusions The isomerisation process of bilirubin in organic solvents and bound to human serum albumin was reinvestigated, using femtosecond fluorescence and absorption spectroscopy, combined with quantum-mechanical calculations. Ultrafast exciton localisation takes place within ca. 120 fs in nonpolar solvents, followed by deactivation of the initially excited state and a build-up of an intermediate, interpreted as the S 1 minimum. This transient state is likely to relax to the ground state, after crossing a barrier, through a conical intersection, in which the exocyclic double and single bonds are twisted. The initial relaxation is barrierless for bilirubin in nonpolar solvents, but a barrier is introduced upon binding to human albumin.

44 Future Outlook

Phototherapy for neonatal jaundice had been empirically discovered, and over the course of its existence, steady progress has yielded a wealth of information that is important not just on therapeutical aspects. However, many questions remain. Within this project, the photochemistry of bilirubin was studied by fluorescence and absorption spectroscopy and with quantum chemical methods. Future investigation on the experimental side should focus on ultrafast absorption measurements of the albumin-complex of bilirubin, and the temperature dependence of the reaction. Also, half-bilirubin model compounds as XBR offer an interesting field of investigation for time-resolved absorption spectroscopy. Theoretical calculations, based on the CASSCF method, have hitherto been used to identify single points on the excited state energy surface for a bilirubin model. An extension of these calculations can give valuable information by studying a complete reaction path, starting from the Franck- Condon-point. By that, it should be possible to tell if the conical intersection is crossed by all molecules, or if other deactivation channels are available. Quantitative improvements of the calculations can be achieved by including dynamic correlation, i.e. the use of the CASPT2 method. The space-conserving Hula-Twist mechanism, suggested for the isomerisation of a range of molecules of biological interest, including bilirubin, could be tested by synthesising model compound, where the single-bond is locked, and the isomerisation would require a single-bond flip around the double bond.

45 References

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50 Acknowledgements

Many people have joined me on my way during my PhD studies, not least through a lot of ups and downs, and I would like to exrpress my gratitude to them. First, I would like to thank Tomas Gillbro for giving me the possibility to start my PhD studies in his group. Gerhard, immer dabei, immer aktiv - Du mischt Dich in vieles ein, und bist immer bereit, anderen zu helfen. So manch langes Gespräch, und so manche Pizza. Warum sie nicht in der Skuleskogenhütte auftauchten, musst Du mir noch erklären! Jakub, you have helped me to get going with the laser system, and introduced me to a lot of other things in Umeå - thanks! Alisdair, your knowledge about fluorescence upconversion and lasers is impressive. Anita, du tar dig an många olika problem - och hitta en lösning. Vad vore avdelningen utan dig? Bäst att inte tänka på det! Charlotte, vieles habe ich von Dir gelernt, nicht zuletzt, dass es noch soviel mehr zu erleben und zu leben gibt! Tomas: fågelskådning, cykling, skidåkning, många prattimmar eller en tur i Abiskos polarnatt - vad var viktigast? Kanske allt ihop - tack! Erik, det har väl inte blivit inte så många kWh vindenergi (än?), men vägen är målet, och kul och spännande var det. Ska inte glömma att tacka för all korrekturläsning. Dorit, habe Deine Hunde mögen gelernt - hatte ich eine Wahl ☺? Danke für alle Spaziergänge mit den kleinen, und die Abendessen, wobei natürlich auch Alex erwähnt werden muss! Es tut immer gut, Gedanken aus der ganz anderen Richtung zu hören. Beate, Du hast meinen Start im neuen Land am aktivsten mitbekommen. Ohne Dich hätte ich mich sicher schwerer eingelebt. Ich bewundere Deine Begeisterungsfähigkeit! There are a lot of things to be grateful for, simply too many to mention: but thank you for simply being around to: Tatiana and Nick (thank you for proof-reading), Jürgen, Angela, Sara F., Elena, Darius, Laura and Madeleine, Staffan, Vahid, Katarina och natürligtvisst ockå Lovisa. Rune, du har alltid himla många idér när det gäller utelivet. En fin vårvinter-skidtur blev det! Ett stort tack också till tryckeriet Solfjädern, speciellt Ann - din kompetens är be- tryggande!

Manche Personen um einen nimmt man vielleicht als zu selbstverständlich hin, einfach weil sie immer da sind: Ein herzlichen Dank an meine Eltern, Geschwister und Ver- wandten! 51