  High-order harmonic generation is investigated for H$_2^+$ and D$_2^+$ with
and without Born-Oppenheimer approximation by numerical solution of full
dimensional electronic time-dependent Schr\"{o}dinger equation under 4-cycle
intense laser pulses of 800 nm wavelength and $I$=4, 5, 7, 10 $\times 10^{14}$
W$/$cm$^2$ intensities. For most harmonic orders, the intensity obtained for
D$_2^+$ is higher than that for H$_2^+$, and the yield difference increases as
the harmonic order increases. Only at some low harmonic orders, H$_2^+$
generates more intense harmonics compared to D$_2^+$. The results show that
nuclear motion, ionization probability and system dimensionality must be
simultaneously taken into account to properly explain the isotopic effects on
high-order harmonic generation and to justify experimental observations.
