Formulas for the coefficients A 6 , A 8 , and A 10 determining the long-range asymptotic behavior Ead(R)∼-A6R-6-A8R-8-A10R-10 of the diagonal Born–Oppenheimer (adiabatic) correction Ead(R) to the potential energy of a diatomic molecule are derived using two standard definitions of Ead(R). The first one is based on the explicit separation of the center-of-mass and rotational coordinates from the total Hamiltonian of a system, while the second definition uses the Born–Handy expression in a laboratory system of coordinates. Expressions for the asymptotic coefficients resulting from both definitions are proved to be equivalent. The obtained formulas are used to compute the asymptotics of the adiabatic correction for the ground state of the hydrogen molecule and for the helium dimer in the lowest quintet and singlet states. In the latter case basis sets up to 8-tuple zeta quality were used to adequately account for the electron correlation effects.