Diffusion Processes with Hidden States from ... - FU Berlin, FB MI

4.2 Fluorescence SpectroscopyAfter absorption of light with an energy h·ν of an appropriate frequency ν the molecule is excitedfrom the ground state S 0,0 to a higher oscillation state S i,k , while the subsequent emission of lightoccurs from the vibrational ground states S i,0 and T i,0 into the ground states S 0,k (”Kascha-Rule”).The relaxation of the molecule from the higher vibrational states to the vibrational ground statesoccur without emission of radiation either through ”Internal Conversion” (IC), or through ”Intersystem Crossing” (ISC). IC is the relaxation of the molecule without change of spin under releaseIC ISCof thermal radiation (S i,k → S1,0 ), while ISC is a change of the spin orientation (S i,k → T j,k ). TheFluorescenceemission of light without change of spin is called fluorescence (S 1,0 → S 0,k ), while the statePhosphorescencerelaxation from the triplet states with change of spin is called phosphorescence (T 1,0 →S 0,k ). The spin change at phosphorescence leads to an enormously longer lifetime of the tripletstates compared to the singlet states which explains the long decay phase of Phosphorescence.In general the Fluorescence spectrumis shifted to higher wavelengthscompared to the absorption spectrum,a phenomenon denoted by theterm ”Stokes-shift”.This is easily understandable by thefollowing observation: imagine amolecule, suspended in an environmentat room temperature or evenat the physiological temperature of37 ◦ C and now consider the molecule,absorbing a photon with a certainwavelength λ a (frequency ν a ). Dueto thermal fluctuations in the systemthe molecule is permanently vibrating,and is rarely arranged in theground state S 0,0 and the vibrationalground state of the excited states S i,0 .Figure 4.2: Stokes-shift of the emitted wavelength relativeto the absorbed wavelength.Due to this fact the molecule cannot absorb photons with energies, exactly the same as the gapenergies between the ground state S 0,0 and the vibrational ground state of the excited states S i,0 .The subsequent emission of fluorescence photons is occurring after relaxation without radiationof light from vibrational excited states S i,k into the vibrational excited states S i,0 , and thereafter itrelaxes with emission of light into the vibrational ground states S 0,k or into the ground state itself.For this reason the energy of the fluorescence photon E f is lower than the energy of the absorbedphoton E a , thus the wavelength λ f higher than the wavelength λ a .4.2 Fluorescence SpectroscopyWe have learned in the last section that Fluorescence is the relaxation of a molecule to the groundstate under emission of a photon after excitation. The energy of the fluorescence photons is belowthe energy of the excitation photons [35].63