Dear Professor Shahab, 

Thanks for your answer, 

We know people use 0.01 as criteria but what can one say if we have an approximately continuous range of oscillator strengths(e.g.  f_1~0.0099 f_2=0.0089  f_3=0.0105 f_4=0.0101.........)

Is that make sense to neglect S_1 and consider S_3 as the first excited states?

and also my other question is this...what is the role of these dark states in fluorescence of a molecule?  (we can use dark S_1 as an excited state which starts fluorescence?)

Mr. Taghipour,

You could pay attention to:

http://www.fc.up.pt/pessoas/mjramos/EMTCCM-2016/EMTCCM_MalgorzataBiczysko_3.pdf