We study tunneling ionization of aligned ${\mathrm{H}}_2^{+}$ in strong near-circular laser fields numerically and analytically. The calculated attoclock offset angles differ for different alignments. By developing a strong-field model to quantitatively describe the alignment-related effects of two-center interference and near-nucleus Coulomb potential during tunneling, we can reproduce this phenomenon. We show that both effects significantly affect the offset angle and corresponding ionization time delay of aligned molecules. This model enables us to analytically separate these two effects, allowing us to clearly identify the Coulomb-induced time delay corresponding to dynamic time. Overall, there is an angle difference of about $1^{\circ }$ and a time-delay difference of about 5 as between the two typical cases of parallel and perpendicular alignments. This can be attributed to the subtle difference in the laser-dressed near-nucleus Coulomb potential in these cases. For more complex molecules such as ${\mathrm{N}}_2$, our simulations show that the wave function of the valence electron also plays an important role in the alignment-dependent offset angle and time delay. Our results may be useful for probing attosecond tunneling dynamics of aligned molecules.

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• Atomic & molecular processes in external fields
• Multiphoton or tunneling ionization & excitation
• Single- and few-photon ionization & excitation