>Do you mean that automatic SCF procudure performed by GAMESS do not result to the correct electronic structure?
Yes. This is not limited to Gamess/Firefly: AFAIK, most packages will have some trouble doing it (though I seem to recall that Gaussian has a special guess procedure which may make it less troublesome)
>As I understand (please correct me if I get wrong) if I have spin populations (alpha minus beta) like the following (for MULT=2):
> ATOMIC SPIN POPULATION (ALPHA MINUS BETA)
>it is incorrect because I should have ~ -4 at one Fe and ~ +4 at the another one or something like this.
>Or for MULT=5 I should not get the following:
>But I should obtain +5 -5 and +4 at three irons.. or like this. How can I validate that it is true? Is there some experimental results that say that spin density at iron atoms of Fe-S clusters should be such assymmetric?
There is a long line of results from EPR/Mossbauer spectroscopies and magnetic susceptibility measurements establishing this picture. You may want to read (among others) the following (computational) refs., which contain citations of the relevant experimental results:
Louis Noodleman and Evert Jan Baerends (1984) "Electronic structure, magnetic properties, ESR, and optical spectra for 2-iron ferredoxin models by LCAO-X.alpha. valence bond theory " Journal of the American Chemical Society, 106 , 2316-2327 DOI:10.1021/ja00320a017
Noodleman, L., Peng, C. C. Y. Y., Case, D. A. A., Mouesca, J.-M., N, L., & Mouesca, L. (1995). Orbital interactions, electron delocalization and spin coupling in iron-sulfur clusters. Coordination Chemistry …, 144, 199–244. doi:10.1016/0010-8545(95)07011-L
Guigliarelli and Bertrand (1999) "Application of EPR Spectroscopy to the Structural and Functional Study of Iron-Sulfur Proteins", Adv. Inorg. Chem, 47, 421-497
Torres, R. A., Lovell, T., Noodleman, L., & Case, D. A. (2003). Density functional and reduction potential calculations of Fe4S4 clusters. Journal of the American Chemical Society, 125(7), 1923–1936. doi:10.1021/ja0211104
Sharma, Sandeep, et al. "Low-energy spectrum of iron–sulfur clusters directly from many-particle quantum mechanics." Nature chemistry 6.10 (2014): 927-933.