Quite a bit of literature discuss various ways to deal with deviations from Kappa^2=2/3. Much of it hinges on how quickly the donor and acceptor can rotate as well over what range of angles. The heart of the problem is that it is very difficult to determine the shape of the distribution of Kappa^2. A good reference to start with is a new book chapter about 'the Kappa^2 problem' by Vogel et al (http://www.fretresearch.org/kappaSquaredChapter.pdf) and also Van der Meer "Kappa-squared: from nuisance to new sense" Reviews in Molecular Biotechnology 82 2002. 181 196.

A 1979 paper by Dale et al "THE ORIENTATIONAL FREEDOM OF MOLECULAR PROBES THE ORIENTATION FACTOR IN INTRAMOLECULAR ENERGY TRANSFER" gives a prescription for determining an range of Kappa^2 from anisotropy measurements of both donor and acceptor. However, I think the two reviews above may show some more precise modifications to this older method, as this older method has been criticized as yielding too large of a range.

I do not know of a means that allows you to "correct" your FRET histogram. Instead I think most methods will simply allow you to try to understand anomalously more or less efficient FRET due to deviations from Kappa^2~2/3 or inhomogenously broad FRET peaks due to the distribution of Kappa^2 (see e.g. Seidel et al. ChemPhysChem 2012, 13, 1060 – 1078, and J. Am. Chem. Soc. 2011, 133, 2463–2480).

Hope these references help.

Dear Naghmeh,

Aside from the educated advises Paul gave you, I find the relation you draw between no free rotation and broadening of FRET population vague and irrelevant. When you assert that the dyes don't freely rotate, you mean that in within their excited-state lifetime, they don't reach rotational relaxation. On one hand, fluorescence lifetimes is usually in the few nanoseconds (at least for single molecule fluorescence common organic dyes). On the other hand, single molecule bursts that build up your FRET histogram have durations of the order of the diffusion times through the excitation beam, usually in the milliseconds. Thus, there are, at most, 6 order of magnitude separation in time between dye rotational relaxation and single molecule bursts. Now, if in within excited-state lifetime, the dye don't reach full rotational relaxation, still they may reach it in times above it, nevertheless it is highly unlikely to have rotational relaxation times of more than 100 ns.

Any such possible source of inhomogeneity or heterogeneity that might lead to changes in FRET efficiencies will be averaged out already in the microseconds, hence bursts of duration in the milliseconds are expected to be narrow.

There are many reasons for FRET population broadening that are totally unrelated to not being 2/3. 

I also would like to recommend you to follow Helmut Grubmuller's MD simulation works on the effects of large dyes and various cases on deviations from the 2/3 rule (hint: in many cases in which the freely rotating rule is not followed, the value of does not deviate that much from 2/3. Since the Forster Radius, R0, in the Forster Efficiency-distance relation, depends on as the power of 1/6, these small deviations anyway become negligible in means of FRET efficiency.