BH3NH3 dimer and BH3NH3 complexes of methane, hydrogen cyanide, ammonia, water, methanol, and hydrogen fluoride, are studied using the Moller-Plesset second-order perturbation theory and the 6-31++G** basis set to understand the features of dihydrogen bond. Complex binding energy is corrected for the basis set superposition error with the counterpoise method and for the zero point energy. Natural bond orbital analysis is used to discuss the charge transfer. Computed results indicate that dihydrogen bond does not occur in both BH3NH3 . . .CH4 and BH3NH3 . . .NH3 complexes. Apart from the B-H. . .delta-H-N hydrogen bond (H bond) found previously in the BH3NH3 crystal, the B-H...H-X (X=C,O,F) H bonds have been observed in BH3NH3 . . .HCN, BH3NH3 . . .H2O, BH3NH3 . . .CH3OH, and BH3NH3 . . .HF complexes. As for the complexes in which only dihydrogen bonds appear the strength of dihydrogen bonds ranges from -13.9 to -20.5 kJ/mol. While the formation of BH3NH3 complexes, the weakest B-N bond of BH3NH3 contracts (its stretch appears blueshifted), and both B-H and X-H bonds in the B-H. . .H-X H bonds elongate slightly owing to the charge transfer from sigma (B-H) to sigma*(X-H), and the B-H...H tends to be bent. The charge transfer is generally proportional to the second-order perturbation energy lowering (DeltaE(2)) due to the interaction of frontier orbitals in sigma --> sigma* and n --> sigma (*) cases, and the threshold value (1.5 kcal/mol) of DeltaE(2) as one of the indices for judging the existence of dihydrogen bonds is recommended.