We investigate isotope effects in dihydrogen systems using the nuclear orbital plus molecular orbital (NOMO) theory, which simultaneously determines nuclear and electronic wave functions without the Born-Oppenheimer approximation. In order to estimate the vibrational averaging bond distances, the analytical energy gradients are used for the NOMO theory. The bond distances of three dihydrogen-bonded systems, namely H3NX+ XBeH, LiX XC2H and H2BX XF for X = H, D and T, are obtained. The X X bond distances decrease with respect to the substitution T D H, which is contrary to the behaviour of typical hydrogen bonds. This indicates that isotope effects strengthen the X X bond. This behaviour is analogous to the Ubbelohde effect observed in the solid phase.
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