MP2, QCISD and CCSD calculations with the use of the Pople style 6-311++G(d, p) and 6-311++G(3df, 3pd) basis sets were performed for the proton bound homodimers such as (N-2)(2)H+, (H2CO)(2)H+ and (CH3OH)(2)H+ as well as for (FHF) and NH4+ ... NH3 systems. The calculations were performed up to the CCSD(T)/6-311++G(3df, 3pd)//CCSD/6-311++G(3df, 3pd) level. All systems analyzed may be treated as the Low Barrier Hydrogen Bonds or the truly symmetrical hydrogen bonds. It was found that the analyzed proton bound homodimers are the truly symmetrical systems if MP2 method is applied but more accurate methods show that the proton for such systems is often moved out from the central position. (C) 2010 Elsevier B.V. All rights reserved.