Subject: summary: fluorescence lifetime calculation

From: [email-masked]
Date: Wed, 18 Sep 2002 16:22:58 +0200

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 (!):

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1. "Najeeb Said" <[email-masked]>:

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

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2. Sergei Tretiak <[email-masked]>

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 <[email-masked]> (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...

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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:[email-masked]
http://ilfir.cjb.net