Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2021 / Paper 2A / Section B / 22 / a

For the absorption spectrum, pass a scanned monochromatic beam through the solution and a matched solvent reference. Record the incident and transmitted intensities and calculate the absorbance $A(\lambda )={\log }_{10}[I_0(\lambda )/I(\lambda )]$, using an appropriate blank and concentration to avoid saturation.

For the fluorescence emission spectrum, excite at a fixed wavelength within an absorption band, collect emission away from the incident beam, commonly at $90^{\circ }$, and scan an emission monochromator. Correct the detected signal for wavelength-dependent detector sensitivity, subtract solvent/background light and exclude scattered excitation light. The two plotted vertical scales have been independently normalized; their equal peak heights do not imply equal absorption and emission rates or unit fluorescence quantum yield.

Vibrational and solvent relaxation remove energy before emission, producing a Stokes shift. Absorption initially excites a vertical transition from the populated ground-state vibrational levels to excited-state vibrational levels. Vibrational relaxation and solvent rearrangement then bring the molecule near the relaxed lowest excited singlet level before fluorescence. Emission ends in vibrationally excited levels of the electronic ground state, so the emitted photon generally has less energy and a longer wavelength. This explanation does not require a change of electronic multiplicity.

The approximate mirror relationship follows from the Franck-Condon principle when the ground and excited electronic states have similar vibrational frequencies and comparable potential shapes displaced along the active coordinates. Absorption samples $S_0,v\simeq 0\to S_1,v^{\prime }$ overlaps, while relaxed emission samples $S_1,v^{\prime }\simeq 0\to S_0,v$ overlaps. For displaced harmonic potentials, the corresponding overlap intensities form similar progressions on opposite sides of the transition between the lowest vibrational levels of the two electronic states.

The symmetry is approximate and is most naturally compared on an energy or wavenumber axis. A wavelength axis is nonlinear in photon energy, and solvent response, frequency changes, differing transition strengths and instrumental corrections can spoil an exact mirror image.

For a fluorescence excitation spectrum, hold the emission detector at a fixed wavelength within the fluorescence band and scan the excitation wavelength. Correct for the incident photon flux and instrumental response at each excitation wavelength.

For one emitting molecular species with an approximately excitation-independent fluorescence yield, it should follow the absorption spectrum. In a dilute sample the detected emission is proportional to the photons absorbed, $I_{\mathrm{exc}}(1-10^{-A}){\varphi }_F\simeq I_{\mathrm{exc}}(\ln 10)A{\varphi }_F$. Without the dilute approximation it follows absorptance rather than absorbance exactly. Impurities, photochemistry or multiple emitting states could invalidate that correspondence.