summary: fluorescence lifetime calculation



 Hello,
 It is summary of replies on my question that was sent one week ago:
 Initial question was: "I am interested in prediction of fluorescence
 lifetime of organic molecules. Is there any reasonable approach to
 calculate this value or make approximate estimation. I suppose I may
 use difference of energies between ground and exited singlet state.
 Please send on my mail as I am not subscriber. Thank you."
 I took several answers (thank you very much!!!) those are very
 promising (!):
 *******************************************************
 1. "Najeeb Said" <najeeb.said.,at,.uk.amershambiosciences.com>:
 Although some semi-empirical methods allow you to predict wavelength
 of a photon emitted from the excited state
 (http://www.accelrys.com/cerius2/zindo.html), these methods
 will not
 tell you if an efficient non-radiative relaxation pathway to the
 ground state is present e.g. cis/trans isomerisation or electron
 transfer. Ab-initio calculations on the excited state are required to
 determine this and these are computationally expensive. As an example
 see (Ultrafast Radiationless Deactivation of Organic Dyes: Evidence
 for a Two-State Two-Mode Pathway in Polymethine Cyanines;
 Sanchez-Galvez, A et al; J. Am. Chem. Soc., 122 (12), 2911 -2924,
 2000).
 The calculation of fluorescence lifetime is an even more challenging
 area. As I mentioned earlier, depopulation of the excited state can
 occur by via fluorescence, internal conversion, electron transfer and
 other processes. These competing processes can be described as a
 series of rate constants i.e.
 K(depop) = K(fluorescence) + K(non-fluorescence)
 Where K(non-fluorescence) = K(internal conversion) + K(electron
 transfer) + K(other pathways).
 To determine the fluorescent lifetime (1/ Kfluorescence) of a
 compound, you would need to follow the trajectory of its excited state
 along a reaction co-ordinate (time). When you consider that a typical
 organic dye has a fluorescent lifetime in the nanosecond region and a
 typical timestep in these calculations is in the fentosecond scale
 (Jolibois, F et al. J. Am. Chem. Soc.; 2000; 122; 5801-5810), the
 calculation of fluorescent lifetimes of organic dyes is beyond our
 capabilities.
 The area of fluorescence modelling is a fascinating, but challenging
 area. Can you please send a summary of your answers to this list.
 Regards,
 Najeeb Said
 =================
 Amersham Biosciences
 The Maynard Centre
 Cardiff, UK
 *******************************************************
 2. Sergei Tretiak <serg.,at,.markov.chem.rochester.edu>
 Hi Ifir,
 You could calculate the radiative lifetime "tau" with formulae
 k_rad=4/3 * E^3 d^2/c^3 where k is the radiative decay rate (1/tau), c
 is the speed of light, E is the difference between ground and exited
 singlet state energies and d is the transition dipole moment
 associated with this transition.
 Practical expression is
 tau[ns]=6000/d^2[Debye]/E^3[eV]
 The transition dipole is well defined, it is dipole moment associated
 with optical transition between states, i.e. d_ge=<\psi_e| D | \psi_g>,
 where \psi_e and \psi_g are excited and ground state electronic
 wavefunctions and D is the dipole moment operator (note that you have
 x, y and z components of d and their vector's sum).
 It does not associated with ground or excited state dipoles given by
 d_gg=<\psi_g| D | \psi_g > and d_ee=<\psi_e| D | \psi_e >, but
 closely
 related to the oscillator strength f for a given optical transition
 f=2/3 * d^2 * E_e, where E_e is the transition frequency.
 Note that this way you are going to calculate the radiative decay rate
 only, internal conversion (e.g. to triplet), energy and electron
 transfer channels will not be accounted for. The total depopulation
 rate would be the sum of all these rates.
 Best,
 Sergei
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 *******************************************************
 3. Qadir <Qadir.,at,.cermm.concordia.ca> (Centre de Recherche en de
 Modélisation Moléculaire)
 Well, the problem is really complicated, and one can not really get
 anything from considering just energies between ground and exited
 states. At least you have to consider transition moments and the
 energy gap (i.e. one needs to calculate the oscillator strength, which
 is something like f=1/3*TD^2*deltaE). Using this may be you can make
 some correlations between fluorescence lifetime and calculated
 properties. I am sure there are some rigorous way to calculate
 fluorescence lifetime but I don't think it is too easy...
 *******************************************************
 Ok, now I see there is practical approach to the problem. It should be
 tried! If anyone will have good experience with with expression please
 send message to this board and to me.
 Best regards,
 Ilfir
 mailto:ilfir.,at,.bgumail.bgu.ac.il
 http://ilfir.cjb.net