Fluorescence requires electron transition or electron redistribution, first after light absorption and then after the relaxation of the molecule from the excited singlet state to the ground singlet state with emission of light. Redistribution of electron density caused by an electron transition occurs on a much faster scale than the reorientation of the nuclei (Franck-Condon principle). This results in an altered dipole moment of the excited fluorophore (or a reorientation of the fluorophore dipole moment) upon excitation (of the molecule). This in turn leads to an energetically unfavorable Franck-Condon state of the excited molecule. This requires that the system relaxes (to a lower energy state) through reorientation of the solvent molecules (envelope) surrounding the fluorophore. The reorientation of the solvent envelope by reorganizing solvent molecules around the fluorophore is known as the 'solvent relaxation'. The fluorescence lifetime (1-10 ns) is longer than the solvent relaxation time (10-100 ps) for a liquid solvent at room temperature. Therefore, the emission spectra of the flourophores are often representative of the solvent relaxed state. The degree of reorientation of the solvent molecules is dependent on the physical and chemical properties of the solvent and the fluorophore. Electronic excitation of molecules such as substituted aromatic compounds typically results in an increase in the dipole moment of the molecules with respect to the ground state. Such molecules exhibit high sensitivity to the solvent polarity change. Non-polar fluorophores such as the unsubstituted aromatic hydrocarbons are much less sensitive to the solvent polarity.

The solvent relaxation introduces an additional red shift to the Stokes shift, the difference between the absorption and emission energies (often expressed as difference in absorption and emission wave numbers). One should recall that the Stokes shifts caused due to the loss of energy result from several dynamic processes such as dissipation of vibrational energy as heat energy, reorientation of the solvent molecules around the excited state dipole, redistribution of electrons in the solvent molecules as a result of the altered dipole moment of the excited fluorophore, and fluorophore-solvent interactions.

No single theory can quantitatively interpret the solvent dependent emission spectra. Solvent-dependent Stokes shifts have been described in terms of 'general and specific solvent effects'. 'Specific solvent effects' result from direct solvent-fluorophore interactions such as hydrogen bonding, acid-base chemistry, charge transfer interactions, and complex formation. On the other hand, 'general solvent effects' refer to the solvent dependent spectral shifts that originate from the interaction between the fluorophore and the entire set of surrounding solvent molecules and do not involve any chemical interactions or specific solvent-flurophore interactions. In such cases, the energy between the ground state and excited state is affected by the dipole interaction between the solvent and the fluorophore which is function of the solvent refractive index and dielectric constant. The 'general solvent effects' on emission spectra is often interpreted in terms of dipole interaction theory of Lippert and Mataga. The Lippert-Mataga equation describes the Stokes shift in terms of the change in the dipole moment upon excitation and the energy of a dipole in in solvents of various dielectric constants (ε) or refractive indices (n).

The Lippert-Mataga equation is given by:

\begin{equation} \Delta v = v_{abs} - v_f = 2 \Delta f ( \Delta \nu )² / hca³ + const.

\end{equation} \begin{equation} \Delta f = [( ε - 1) /(2 ε + 1)] - [(n² - 1)/(2n² + 1)] \end{equation}

where Δv is the Stokes shift (in wave-numbers), the difference in energy between the absorption and emission maxima; vabs and vf are the wave-numbers of absorption and emission peaks, respectively, h is Planck's constant, c is the speed of light, a is the Onsager cavity radius in which the chromophore resides, and M = Me - Mg is the difference between the fluorophore excited- and ground-state dipole moments, Δf is the orientational polarizability of solvent, ε is the dielectric constant, and n is the refractive index of the solvent. The term "const." includes the Stokes shift that results from the dynamic processes like vibrational relaxation and internal conversion effects.

The plot of Δv (= vabs - vf ) versus Δf should be a straight line. The slope is given by the following expression: 2(ΔM)²/hca³. Observations of Stokes shift is used to assess the environment polarity. Further, this method is used for determination of excited state dipole moments. To calculate ΔM one needs to know a, the Onsager cavity radius, of the solute (fluorophore). An approximate value of a (cavity radius) can be calculated from the following relationship:

\begin{equation} a (in A^o)= 10⁸ (3M /4πqN)^{1/3} \end{equation} where M is the molecular weight and q the density in g/cc of the solute and N Avogadro's constant.

One should note that the effects of the refractive index differ from those of the dielectric constant. The refractive index is a property of the electrons of the solvent molecules, whereas the dielectric effects include both electronic and molecular orientation effects. Because, the refractive index (n) is dependent on the motion of electrons within the solvent molecules (which instantaneously occurs during light absorption), an increase in n results in decrease in energy loss and stabilization of the ground and excited state. Since the dielectric constant (ε) is dependent on both the electronic and the molecular motions, an increase in ε also will result in stabilization of the ground and the excited states. The decrease in energy of the excited state occurs only after the reorientation of the solvent dipoles and is time dependent. Therefore an increase in ε results in larger energy loss (larger energy loss between vabs and vf).

The Lippert-Mataga equation works fairly well for non-protic solvents whereas protic solvents (e.g., water, ethanol) tend to give greater than the predicted Stokes shifts, because of several assumptions made in the derivation of the Lippert-Mataga equation. For example, it assumes a fluorophore as a point dipole in a spherical cavity. This assumption does not seem to be a very obvious approximation for many fluorophore-solvent systems. Further, it takes only the continuum dielectric properties, such as the dielectric constant and the refractive index, as a measure of the solvation energy and ignores specific solvent interactions which is not completely satisfactory.

Table 1. Refractive Indices and Dielectric Constants of the Solvents and Corresponding Absorption and Emission Spectra Wavelengths of Curcumin.