Excitation-Emission Spectra: Mirror Image Rule

A fluorescence spectrum is generally a plot of the fluorescence intensity as a function of wavelength (expressed in nm). In fluorescence spectra, when spectral distribution of emission as a function of wavelength is scanned by holding the excitation wavelength constant (at a wavelength at which the molecule absorbs), an emission spectrum is obtained. Similarly, scanning of the excitation spectral distribution by holding emission wavelength fixed gives excitation spectrum. In other words, the emission spectrum corresponds to the variations of, the fluorescence intensity, IF, as a function of emission wavelength, λF, the excitation wavelength λE being fixed, whereas the excitation spectrum describes the variations of IF as a function of λE, the observation wavelength λF being fixed. In principle, excitation is equivalent to absorption for a pure molecule. In other words, the fluorescence excitation spectrum of a single fluorophore species in dilute solution is often identical to its absorption spectrum. The absorption/excitation spectra originate from the ground state and therefore, these spectra provide information regarding the electronic distribution in this state. Emission originate from excited states, and so the emission spectra reflect the electronic distribution within the excited states. If any modification of the electronic distribution in these states occurs such as due to a charge transfer that will modify the corresponding spectra. The width of a band in the absorption and emission spectra of a chromophore located in a solvent is a result of two effects: homogeneous and inhomogeneous broadenings. Homogeneous broadening arises due to the existence of a continuous set of vibrational sub-levels in each electronic state. Inhomogeneous broadening results from the fluctuations of the solvation-shell structure surrounding the chromophore.

Fluorescence emission spectrum is often the 'mirror image' of the excitation spectrum. This is known as the 'mirror image rule'. The absorption of radiation promotes the molecule mainly from the v=0 level of the ground electronic state, S0, to different vibrational levels in upper electronic state, S1. The vertical transition has the highest transition probability and intensity and the transitions to other vibrational levels occur with lower intensity. Therefore, instead of an electronic absorption occurring at a single, sharp line, electronic absorption consists of many lines each corresponding to the stimulation of different vibrations in the upper state. This gives rise to vibrational structure (or progression) in an electronic transition. Therefore, the excitation (absorption) spectrum structure reflects the vibrational levels of the upper S1 state. Because the fluorescence emission involves transition from v=0 of S1 state to various vibrational levels of S0 state, emission spectrum will also show a similar vibrational structure but reflecting the vibrational levels of the ground S0 state. Since the vibrational levels in the excited states and the ground states are similar, the vibrational structures in the excitation and emission spectra appear as mirror image of one another. Mirror image rule typically applies for S0↔S1 transitions. Though the vibrational structure are well resolved for small molecules in the gas-phase, in a liquid or solid, the electronic absorption spectrum is often a broad band with limited structure. The width of the band in the absorption or emission spectrum of a fluorophore depends on two effects: homogeneous and inhomogeneous broadening. Homogeneous broadening is the result of the existence of a continuous set of vibrational levels in each electronic state. However, if many of the vibrational modes are not active (e.g., pyrene, naphthalene), then a vibrational structure is observed. Inhomogeneous broadening of electronic spectra is caused due to the fluctuations in the structure of the solvent-shell surrounding the molecule undergoing electronic transition. The distribution of solute-solvent configurations and the consequent variation in the local electric field leads to a statistical distribution of the energies of the electronic transitions. These two effects cause the spectral lines to merge together leading to the formation of spectral band. In most cases, the extent of inhomogeneous broadening is greater than that of homogeneous broadening. When S0 → S2 or higher transitions take place, molecules reach the first excited singlet state, S1, via internal relaxation before emission which causes deviations from the mirror image rule as in the case of quinine sulfate. Further, it should be noted here that the mirror image relationship is generally observed when the interaction of the fluorophore excited state with the solvent is weak.

Stokes Shift

The Franck-Condon principle states that the heavy atom nuclei do not change their positions during the fast electronic excitation. This results in an initial geometry of the excited state which is usually not the energy minimum geometry. We know from the Franck-Condon principle that the molecule will most probably be excited to one of the higher vibrational states of the excited electronic state. The molecule in an excited vibrational energy level loses energy rapidly (in 10-12 s or less) and moves to a lower (and finally to the lowest) vibrational energy level in the same electronic state. This kind of vibrational relaxation occurs via the emission of infrared photons or via radiationless transitions by losing the vibrational energy as heat energy. Once the molecule is in the lowest vibrational level of the excited electronic state, S1, the molecule can return to the ground singlet state S0 through (i) internal/external conversion, (ii) fluorescence, or (iii) intersystem crossing and phosphorescence. In internal conversion, a form of radiationless relaxation, a molecule in the lowest vibrational level of an excited electronic state passes directly into a high vibrational energy level of a lower energy electronic state of the same spin state by losing the energy as heat. (Why? because, with the increase in electronic energy, the energy levels grow more closely spaced. It is more likely that there will be overlap between the high vibrational energy levels of Sn and low vibrational energy levels of Sn+1, making the transition between states highly probable.) Internal conversion is a transition occurring between states of the same multiplicity and it takes place at a time scale of 10-12 s (faster than that of fluorescence process) The external conversion involves the transfer of excess energy to the solvent or another component in the sample matrix. In fluorescence, the acquired electronic energy is lost via the emission of a photon while transition occurs from lowest vibrational level of first excited singlet (i.e., v=0 of S1) to one of the vibrational states of the ground singlet state, S0. This radiative process takes about 10-9 second. Since prior to the fluorescence emission a part of the vibrational energy was lost (during vibrational relaxation), the emitted light in fluorescence will have lower energy than the excitation light. If the absorption energy is Ea = hc/λa and emission energy is Eem = hc/λem, then Eem < Ea and λem λa where λa and λem are absorption and emission spectra peak wavelengths. Thus, the emission spectrum peak wavelength shifted to longer wavelengths compared to the absorption spectrum peak wavelength. The energy difference between the excited and emitted lights or the complete shift between the absorption and emission bands, (λa - λem) due to the radiation-less deactivation process is known as the "Stokes shift" (after Sir George Stokes who reported this shift for the first time in 1852). When two or more bands are present in the absorption and/or the emission spectra of a fluorophore, the Stokes shift is taken as the difference of the two most intense bands of the two spectra. We have noted above that the Stokes shift arises due to a variety of factors. Some of these factors are intrinsic to the fluorophore whereas some are due to interactions of the fluorophore with its environment. As a consequence the Stokes shift parameter can provide information on the excited states and its surrounding environment. For example, the Stokes shift increases with solvent polarity if the the dipole moment of a fluorescent molecule is higher in the excited state than in the ground state. This information can be used in the estimation of polarity using fluorescent polarity probe molecules. Here in order to demonstrate the Stokes shift and the mirror image transition relationship, two fluorophores, namely anthracene (in cyclohexane) and quinine sulfate (in aqueous 0.5 M H2SO4), have been chosen.