Excited state decay of organic fluorophoresAfter electronic excitation the molecule typically decays to the lowest vibrational level of the first excited singlet state, S_{1}. In far most cases, this happens nonradiatively in the order of picoseconds by a combination of internal conversion (IC) and vibrational relaxation. From S_{1} a number of decay processes can occur to the electronic ground state, S_{0}. If the oscillator strength of the S_{0}S_{1} transition is high the molecule may decay to the ground state via emission of radiation (fluorescence) and the molecule is thus termed a fluorophore.The fluorescence, however, "competes" with nonradiative decay processes such as IC, intersystem crossing (ISC), or a bimolecular quenching process such as FRET and collisional quenching. Each process is associated with a rate constant, k_{i}. The process with the largest value of k_{i} dominates the decay. The total rate of decay from the excited state, then, is typically given by that of a unimolecular process:
Assuming that the fluorescence intensity is proportional to the excited state population, [S_{1}], the intensity decay is exponential and given by: where I_{0} is the intensity at t = 0. If the sample possess more than one lifetime the intensity as a function of time is the sum of intensities from each decay: which is called a multiexponential decay. α_{j} is the preexponential factor and can be used to represent the fraction of fluorophores with lifetime τ_{j}. The amplitudeweighted lifetime of the fluorophore is then given by: Fluorescence decay models in DecayFit In the DecayFit freeware the implemented intensity decay models are listed in the Fit models listbox:
The intensity decay expression of the fit model selected in the listbox is shown below the listbox:
A description of each of the fit models is provided below.
1. single_exp
A singleexponential decay corresponding to a single lifetime. Only the lifetime is provided as fit parameter.
2. double_exp
A doubleexponential decay corresponding to two lifetimes. The sum of the preexponential factors is constrained to 1 which means that only one prefactor, a_{1}, is provided as fitting parameter while the other is set to be 1a_{1}.
3. triple_exp
A tripleexponential decay corresponding to three lifetimes. The sum of the preexponential factors are constrained to be a_{1}+a_{2}+a_{3} = 1.
4. four_exp
A fourexponential decay corresponding to four lifetimes. The sum of preexponential factors are constrained to be a_{1}+a_{2}+a_{3}+a_{4} = 1.
5. FRET
A decay model for analyzing FRET data. The model implements a Gaussian distance distribution between the donor (D) and acceptor (A) with the distribution center (Rmean) and Full Width at Half Maximum (FWHM) as fitting parameters. The critical distance, R_{0}, must be supplied as input and is not meant to be a fitting parameter (although this is possible by varying the min and max values).
Up to three lifetimes can be specified for the donor in absence of acceptor (tauD_{1}, tauD_{2}, tauD_{3}), each with a preexponential factor (a_{1}, a_{2}, a_{3}). These are not meant as fitting parameters but should be determined on a donoronly reference sample. If the donor has a single lifetime only set the min and max values of a2 and a3 to 0 (default). The fraction of donors not coupled to an acceptor, f, can also be included as a parameter, either constrained or loosely fitted. An additional component not involved in FRET with a lifetime 'tauB' and relative fraction 'b' can be included in the model. The fraction of the FRETcomponent in the decay, then, is 1b. Note: When using dynamic averaging, the DA distance is modelled using a single distance  the mean of the Gaussian distribution (Rmean).
6. lifetime_dist
A Gaussian lifetime distribution model. A mixture of two independent Gaussians can be used, each with a lifetime center and a lifetime distribution width (FWHM) as fitting parameters.
7. double_exp_uncon
A double exponential decay in which there is no constraint on the sum of preexponential factors.
8. triple_exp_uncon
A triple exponential decay in which there is no constraint on the sum of preexponential factors.
