Quenching of the spontaneous emission that follows photochemical excitation can be treated as an elementary chemical reaction.
Vibrational deactivation: the transition associated with an electronic absorption band produces a higher electronic state. The molecule is also often left in one of the higher vibrational states of the new electronic state. For molecules in solution, molecular collisions are very effective in removing the excess vibrational energy, probably by one vibrational level step at one time. This energy goes into the motion of the molecules of the solvent and is not detected as emitted radiation. A typical time required for the dissipation of excess vibrational energy by such a process is of the order of 10-10 s. when this time is compared with a typical vibrational period of 10-13 s, many vibrations, say a thousand; occur while the excess vibrational energy is being lost.
The potential energy for a given electronic state is functioning of all the internal coordinates of the molecule, and for polyatomic molecules the potential energy would have to be represented by a surface in this much dimensional space. A representative arrangement of potential curves is determined sufficiently.
The occurrence of a crossing potential energy surface with that initially reached by the absorption process allows a second type of radiationless process to occur. This process can lead to the return of the excited molecule to its ground electronic state. When potential surfaces or two potential curves cross over the molecule to an excited electronic state, to change over into a different electronic state. The crossing of the potential curves facilitates this process, which is known as internal conversion. At the crossover point, the geometry and the potential energies of the two electronic states are equal.
For polyatomic molecules, potential curves often exist with suitable relative postions so that combinations of vibrational deactivations and internal conversions can return the molecule to its ground state before any emission process has had a chance to occur. Other molecules, however, either do not have such crossing potential curves or have electronic states in which the molecules becomes trapped. In such cases emission does occur.
The effect of spontaneous emission can be written, in view of the treatment of the rate equation:
[dNm/dt]spont = Aml Nm
Since Aml plays the role of a constant, it is related to the half-life for spontaneous emission by:
t ½ = In 2/Aml
For spontaneous emission from a state that is reached directly by the absorption of radiation, the spontaneous coefficient Aml is related to the coefficient for induced absorption coefficient ∫ ∝ dv. These relations give:
Aml = (8∏hv3)/c3B = 8∏v2/c2N∫ ∝ dv
Fluorescence and the quenching of fluorescence: if the efficiency of nonradioactive processes that return the molecule to its ground state is not too great, various emission processes can occur. One type of process produces an emission band like that of the observation that the emission band generally appears at longer wavelengths, i.e. lower energy, than the absorption band suggests that vibrational deactivation within the potential curve of the upper electronic state is essentially state is essentially complete before much emission occurs. The emission transaction rather than the exact reverse of the absorption transition is to be drawn.
The relations that have been developed can be used to calculate lifetimes of excited states, as determined by spontaneous emission, for any absorption band for which v at the band center and ∫ ∝ dv are known. In general, lifetimes are longer for upper as the energy separation between the states becomes smaller.
The calculated lifetimes are for states reached directly by the absorption process. The emitting state, however, is often reached by rapid nonradioactive process. Then the lifetime of the spontaneously emitting state will not be related to the intensity of the absorption band. The relation however, will be a general guide to the lifetime due to the emission process.
Any decrease to the efficiency of collisional deactivation, e.g. by freezing in a glass to occur to a significant extent. Many absorption bands are less intense, i.e. occur with a smaller integrated absorption coefficient, than that cited for typical, completely allowed transitions. Emissions correspondingly longer half life, one finds in practice that spontaneous emission can be observed with a half life in to the microsecond range or even up to about 10-4 s in cases where the value of Aml is small enough and nonradioactive processes are relatively ineffective.