  The recently reported precise experimental determination of the dipole
polarizability of the H_2^+ molecular ion ground state [P.L. Jacobson, R.A.
Komara, W.G. Sturrus, and S.R. Lundeen, Phys. Rev. A 62, 012509 (2000)] reveals
a discrepancy between theory and experiment of about 0.0007a_0^3, which has
been attributed to relativistic and QED effects. In present work we analyze an
influence of the relativistic effects on the scalar dipole polarizability of an
isolated H_2^+ molecular ion. Our conclusion is that it accounts for only 1/5
of the measured discrepancy.
