1 Basic Principles of Fluorescence Spectroscopy

1 1 Basic Principles of Fluorescence and Emission of LightAsfluorophores play the central role influorescence Spectroscopy and imaging wewill start with an investigation of their manifold interactions with light. Afluorophoreis a component that causes a molecule to absorb energy of a specific wavelength andthen re-remit energy at a different but equally specific wavelength. The amount andwavelength of the emitted energy depend on both thefluorophore and the chemicalenvironment of thefluorophore. Fluorophores are also denoted as chromophores,historically speaking the part or moiety of a molecule responsible for its color. Inaddition, the denotation chromophore implies that the molecule absorbs light whilefluorophore means that the molecule, likewise,emits light. The umbrella term usedin light emission is luminescence, whereasfluorescence denotes allowed transitionswith a lifetime in the nanosecond range from higher to lower excited singlet states the following we will try to understand why some compounds are colored andothers are not.

2 Therefore, we will take a closer look at the relationship of conjugationto color withfluorescence emission, and investigate the absorption of light atdifferent wavelengths in and near the visible part of the spectrum of variouscompounds. For example, organic compounds ( , hydrocarbons and derivatives)without double or triple bonds absorb light at wavelengths below 160 nm, corre-sponding to a photon energy of>180 kcal mol 1(1 cal J), or> eV(Figure ), that is, significantly higher than the dissociation energy of commoncarbon-to-carbon single a wavelength of 200 nm the energy of a single photon is sufficient toionize molecules. Therefore, photochemical decomposition is most likely to occurwhen unsaturated compounds, where all bonds are formed bys-electrons, areirradiated with photon energies> eV. Double and triple bonds also usep-electrons in addition to as-bond for bonding. In contrast tos-electrons, whichare characterized by the rotational symmetry of their wavefunction with respect tothe bond direction,p-electrons are characterized by a wavefunction having a nodeat the nucleus and rotational symmetry along a line through the of Fluorescence Spectroscopy and Sauer, J.

3 Hofkens, and J. EnderleinCopyright 2011 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 978-3-527-31669-4j1are usually weaker thans-bonds because their (negatively charged) electrondensity is further from the positive charge of the nucleus, which requires moreenergy. From the perspective of quantum mechanics, this bond weakness isexplained by significantly less overlap between the componentp-orbitals due totheir parallel orientation. These less strongly bound electrons can be excited byphotons with lower energy. If two double bonds are separated by a single bond, thedouble bonds are termed conjugated. Conjugation of double bonds furtherinduces a red-shift in the absorption (a so-called bathochromic shift). Allfluor-ophores that have a high absorption in the visible part of the spectrum possessseveral conjugated double 200 nm only the two lowest energy transitions, that is,n!p andp!p ,are achieved as a result of the energy available from the photons.

4 When samplemolecules are exposed to light having an energy that matches a possible electronictransition within the molecule, some of the light energy will be absorbed as theelectron is promoted to a higher energy orbital. As a simple rule, energetically favoredelectron promotion will be from the highest occupied molecular orbital (HOMO),usually the singlet ground state,S0, to the lowest unoccupied molecular orbital(LUMO), and the resulting species is called the singlet excited stateS1. Absorptionbands in the visible region of the spectrum correspond to transitions from the groundstate of a molecule to an excited state that is 40 80 kcal mol 1above the ground mentioned previously, in saturated hydrocarbons in particular, the lowest elec-tronic states are more than 80 kcal mol 1above the ground state, and therefore theydo not absorb light in the visible region of spectrum. Such substances are not that absorb in the visible region of the spectrum (these compounds havecolor) generally have some weakly bound or delocalized electrons.

5 In these systems,the energy difference between the lowest LUMO and the HOMO corresponds to theenergies of quanta in the visible (m)Wavenumber (cm-1)Frequency (Hz)Energy (kcal)-131011102110810-11109101910610-91 07101710410-7105101510210-5103101310010- 310101110-210-110-110910-41010-310710-61 0 GammaraysX- raysRadioMicrowaveIRVisibleUVFigure electromagnetic Basic Principles of Fluorescence SpectroscopyOn the other side of the electromagnetic spectrum, there is a natural limit to long-wavelength absorption and emission offluorophores, which is in the region of1mm [1]. A dye absorbing in the near-infrared (>700 nm) has a low-lying excitedsinglet state and even slightly lower than that, a metastable triplet state, that is, a statewith two unpaired electrons that exhibits biradical character. Even though nogenerally valid rule can be formulated predicting the thermal and photochemicalstability offluorophores, the occupation of low-lying excited singlet and triplet statespotentially increases the reactivity offluorophores.

6 Therefore, it is likely thatfluorophores with long-wavelength absorption and emission will show less thermaland photochemical stability, due to reactions with solvent molecules such as dis-solved oxygen, impurities, and otherfluorophores. In addition, with increasingabsorption, that is, with a decreasing energy difference betweenS1andS0, thefluorescence intensity offluorophores decreases owing to increased internal con-version. That is, with a decreasing energy difference between the excited and groundstate, the number of options to get rid of the excited-state energy by radiationlessdeactivation increases. Hence, most known stable and brightfluorophores absorband emit in the wavelength range between 300 and 700 with conjugated doubled bonds (polymethine dyes) are essentiallyplanar, with all atoms of the conjugated chain lying in a common plane linked , on the other hand, have a node in the plane of the molecule andform a charge cloud above and below this plane along the conjugated chain(Figure ).

7 The visible bands for polymethine dyes arise from electronic transitionsinvolving thep-electrons along the polymethine chain. The wavelength of thesebands depends on the spacing of the electronic levels. The absorption of light byfluorophores such as polymethine dyes can be understood semiquantitatively byapplying the free-electron model proposed by Kuhn [2, 3]. The arrangement ofalternating single double bonds in an organic molecule usually implies that thep-electrons are delocalized over the framework of the conjugated system. As thesep-electrons are mobile throughout the carbon atom skeleton containing the alter-nating double bonds, a very simple theoretical model can be applied to such a systemin order to account for the energy of these electrons in the molecule. If one makes theCH CHNCHCHCHNCH3CH3H3CH3 CNH3CH3 CCH CH CH CH CH NCH3CH3CN C C C C C N C0LX elctron cloud elctron cloudV(a)(b)Figure (a) Limiting structures of a resonance hybrid of a simple positively charged cyanine dye.

8 (b) Thep-electron cloud of the cyanine dye as seen from the side in a simplified potential energy (V)trough of Absorption and Emission of Lightj3seemingly drastic assumption that the severalp-electrons that comprise the systemare non-interacting (presumably, if thep-electrons are delocalized over the C C C C C C framework, they spread out, minimizing repulsion betweenthem), then one can view the energetics of this system as arising from the simplequantum mechanical assembly of one-electron energy levels appropriate to theparticle in the box model. In this case, one considers the potential energy of theelectron as being constant throughout the length of the molecular box and then risingto infinity at each end of the conjugated portion of the molecule. As an example,consider a positively charged simple cyanine dye. The cation can resonate betweenthe two limiting structures shown in Figure , that is, the wavefunction for the ionhas equal contributions from both states.

9 Thus, all the bonds along this chain can beconsidered equivalent, with a bond order of , similar to the C C bonds that the conjugated chain extends approximately one bond length to theleft and right beyond the terminal nitrogen atoms, application of the Schroedingerequation to this problem results in the well known expressions for the wavefunctionsand energies, namely:yn ffiffiffiffiffiffiffiffiffiffiffiffiffif fiffiffiffiffiffiffiffiffiffiffi2 LsinnpxL randEn n2h28mL2wherenis the quantum number (n 1, 2, 3,..) giving the number of antinodes of theeigenfunction along the chainLis the length of the (one dimensional) molecular boxmis the mass of the particle (electron)his Planck s constantxis the spatial variable, which is the displacement along the molecular wavefunction can be referred to as a molecular orbital, and its respectiveenergy is the orbital energy. If the spin properties of the electron are taken intoaccount along with thead hocinvocation of Pauli s exclusion principle, the model isthen refined to include spin quantum numbers for the electron ( ) along with therestriction that no more than two electrons can occupy a given wavefunction or level,and the spin quantum numbers of the two electrons occupying a given energy levelare opposite (spin up and spin down).

10 Thus, if we haveNelectrons, the lower statesarefilled with two electrons each, while all higher states are empty provided thatNisan even number (which is usually the case in stable molecules as only highly reactiveradicals posses an unpaired electron). This allows the electronic structure forthep-electrons in a conjugated dye molecule to be constructed. For example, forthe conjugated molecule CH2 CH CH CH CH CH26p-electrons have to beconsidered. The lowest energy configuration, termed the electronic ground state,4j1 Basic Principles of Fluorescence Spectroscopycorresponds to the six electrons being in the lowest three orbitals. Higher energyconfigurations are constructed by promoting an electron from the HOMO withquantum numbern 3 to the LUMO withn 4. This higher energy arrangement iscalled the electronically excited singlet state. The longest wavelength absorption bandcorresponds to the energy difference between these two states, which is then given bythe following expression:DE ELUMO EHOMO h28mL2n2 LUMO n2 HOMO The energy required for this electronic transition can be supplied by aphoton of theappropriate frequency, given by the Planck relationship:E hn hc=lwherehis Planck s constantnis the frequencycis the speed of lightlis the the ground state of a molecule withNp-electrons will haveN/2 lowestlevelsfilled and all higher levels empty, we can writenLUMO N/2 1 andnHOMO N/2:DE h28mL2N 1 orl 8mchL2N 1 This indicates that to afirst approximation the position of the absorption band isdetermined only by the chain length and the number of delocalizedp-electrons.