Fluorescence is an emission phenomenon where an energy transition from a higher to a lower state is accompanied by radiation. Only molecules in their excited forms are able to emit fluorescence; thus, they have to be brought into a state of higher energy prior to the emission phenomenon.
We have already seen in Section 13.1.2 that molecules possess discrete states of energy. Potential energy levels of molecules have been depicted by different Lennard Jones potential curves with overlaid vibrational (and rotational) states (Figure 1). Such diagrams can be abstracted further to yield Jablonski diagrams (Figure2).
Fig1. Energy diagram for a diatomic molecule exhibiting rotation and vibration, as well as an electronic structure. The distance between two masses m1 and m2 (nuclear displacement) is described as a Lennard–Jones potential curve with different equilibrium distances (Req) for each electronic state. Energetically lower states always have lower equilibrium distances. The vibrational levels (horizontal lines) are superimposed on the electronic levels. Rotational levels are superimposed on the vibrational levels and not shown for reasons of clarity.
Fig2. Jablonski diagram. Shown are the electronic ground state ( S0 ), two excited singlet states (S1 , S2) and a triplet state ( T1 ). Only select vibrational levels ( v ) are illustrated. Solid vertical lines indicate radiative transitions, dotted lines show non-radiative transitions. Inset: Explanation of total spin S and multiplicity M . The total spin S is calculated as the sum of the individual electron spins. The multiplicity M is obtained as either 1 ( singlet state) or 3 ( triplet state).
In these diagrams, energy transitions are indicated by vertical lines. Not all transitions are possible; allowed transitions are defined by the selection rules of quantum mechanics. A molecule in its electronic and vibrational ground state ( S0 v0 ) can absorb photons matching the energy difference of its various discrete states. The required photon energy has to be higher than that required to reach the vibrational ground state of the first electronic excited state ( S1 v 0 ). The excess energy is absorbed as vibrational energy ( v > 0), and quickly dissipated as heat by collision with solvent molecules. The molecule thus returns to the vibrational ground state ( S1 v 0 ). These relaxation processes are non-radiating transitions from one energetic state to another with lower energy, and are called internal conversion (IC). From the lowest level of the first electronic excited state, the molecule returns to the ground state ( S0 ) either by emitting light (fluorescence) or by a non-radiative transition. Upon radiative transition, the molecule can end up in any of the vibrational states of the electronic ground state (as per quantum mechanical rules).
If the vibrational levels of the ground state overlap with those of the electronic excited state, the molecule will not emit fluorescence, but rather revert to the ground state by non-radiative internal conversion. This is the most common way for excitation energy to be dissipated and is why fluorescent molecules are rather rare. Most molecules are flexible and thus have very high vibrational levels in the ground state. Indeed, most fluorescent molecules possess fairly rigid aromatic rings or ring systems. The fluorescent group in a molecule is called a fluorophore .
Since radiative energy is lost in fluorescence as compared to the absorption, the fluorescent light is always at a longer wavelength than the exciting light ( Stokes shift). The emitted radiation appears as a band spectrum, because there are many closely related wavelength values dependent on the vibrational and rotational energy levels attained. The fluorescence spectrum of a molecule is independent of the wavelength of the exciting radiation and has a mirror image relationship with the absorption spectrum. The probability of the transition from the electronic excited to the ground state is proportional to the intensity of the emitted light.
The fl uorescence properties of a molecule are determined by properties of the molecule itself (internal factors), as well as the environment of the protein (external fac tors). The fluorescence intensity emitted by a molecule is dependent on the lifetime of the excited state. The transition from the excited to the ground state can be treated like a first-order decay process, i.e. the number of molecules in the excited state decreases exponentially with time. In analogy to kinetics, the exponential coefficient k r is called the rate constant and is the reciprocal of the lifetime: τ r = k r−1 . The lifetime is the time it takes to reduce the number of fluorescence-emitting molecules to 1/e of the original number, and is proportional to λ3 .
The effective lifetime τ of excited molecules, however, differs from the fluorescence lifetime τ r since other, non-radiative processes also affect the number of molecules in the excited state. τ is dependent on all processes that cause relaxation: fluorescence emission, internal conversion, quenching, fluorescence resonance energy transfer, reactions of the excited state and inter-system crossing.
The ratio of photons emitted and photons absorbed by a fluorophore is called the quantum yield Φ ( Equation 13.8 ). It equals the ratio of the rate constant for fluorescence emission k r and the sum of the rate constants for all six processes mentioned above.
The quantum yield is a dimensionless quantity, and, most importantly, the only absolute measure of fluorescence of a molecule. Measuring the quantum yield requires comparison with a fluorophore of known quantum yield. In biochemical applications, this measurement is rarely done. Most commonly, the fluorescence emissions of two or more related samples are compared and their relative differences analysed.
