Dear Giseppe
Thank you very much for your kind attention and the details were said by you 
about spin polarization of such systems.I am sorry for the delay to reply your 
comments. I was doing what proposed by you and Stefano to see the difference 
origin.
so in the following we can see the results obtained:
Quantum -Espresso:
ecutwfc = 70, ecutrho = 600,   (the cutoff has been increased as proposed by 
Stefano)Re 186.207  Re.pbe-mt_fhi.UPFO  15.999   O.pbe-rrkjus.UPFC 12.000    
C.pbe-rrkjus.UPFH 1.000     H.pbe-rrkjus.UPFI 126.90   I.pbe-mt_fhi.UPFP  
30.9737  P.pbe-mt_fhi.UPF
E=  -312.61421481 Ry (spin-unpolarized)E=  -312.66455244 Ry (spin-polarized, 
total magnetization=4.00 Bohr mag/cell

Firefly (Quantum Chemistry Code):
B3LYP/6-31++G**:P,C,O,H; LANL2DZ:Re,I  (the system optimized using this method)
E (S=0) = -1202.07856 HartreeE (S=1) = -1202.06949 E (S=2) = -1202.04809
B2PLYP/6-31++G**:P,C,O,H; LANL2DZ:Re,I (the energy of previous step was 
modified by adding the MP2 part as proposed by Giseppe)
E (S=0) = -1199.826275 HartreeE (S=1) = -1199.825679 E (S=2) = -1199.820273

As still could be seen the plane-wave calculation shows that the spin-polarized 
system is the ground state and quantum chemistry calculation using 
Gaussian-like basis sets shows the trend conversely. 

-------------------------------------------------Alex Granov?????????? 
??????-??????????? ???????? (MIPT)Moscow, Russia                                
           
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