In a combining reaction: A + B => C, the electronic energy change can be calculated using familiar formula: E(C) - (E(A) + E(B)); in which all species are considered at the same level of theory. However, in computational calculations, the product C consists of A and B molecular fragments giving rise to the fact that C inherits a phase bases combined from two sets of primitive functions of A and B with many new integrals appear. This results the fact that C is lower in energy than it really is as referring to the reference energy of reactant well (A and B). This phenomena is sometimes called borrowed basis set, and the arisen error is the "Basis Set Superposition Error (BSSE)" The counterpoise calculation help to correct such error.
# B3LYP/6-31G(d) countepoise=2
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0 1 0 1 0 1
O(Fragment=1) -1.38994389 -0.12369108 -0.10907897
H(Fragment=1) -1.24220750 0.02800549 -1.04543473
H(Fragment=1) -1.90618392 0.59933806 0.25468619
H(Fragment=2) -2.10434580 -1.36111307 0.06985319
O(Fragment=2) -2.58061384 -2.18606124 0.18913972
H(Fragment=2) -3.42541682 -2.13625554 -0.26410119
grep "BSSE energy" dimer.out
. Result is something like: Counterpoise: BSSE energy = 0.019154309097
Ref: