High-order harmonic generation is investigated for H$_2^+$ and D$_2^+$ withand without Born-Oppenheimer approximation by numerical solution of fulldimensional electronic time-dependent Schr\"{o}dinger equation under 4-cycleintense 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 forD$_2^+$ is higher than that for H$_2^+$, and the yield difference increases asthe harmonic order increases. Only at some low harmonic orders, H$_2^+$generates more intense harmonics compared to D$_2^+$. The results show thatnuclear motion, ionization probability and system dimensionality must besimultaneously taken into account to properly explain the isotopic effects onhigh-order harmonic generation and to justify experimental observations.
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