We use density matrix theory to numerically simulate the orientation of LiH molecules induced by laser pulses with two different envelope shapes. The results show that the envelope shape of the terahertz single-cycle laser pulse (SCP) has significant effects on molecular orientation degree and duration. When a SCP with adjusted laser field amplitude and carrier envelope phase is used to steer the molecular orientation, a larger orientation degree can be obtained by the Gaussian-shaped SCP, while a longer orientation duration can be realized by the sin 2 -shaped SCP.When combined with the two-color femtosecond laser pulse, the sin 2 -shaped SCP is better than Gaussian-shaped SCP, either in improving orientation degree and duration or in stability and controllability shown with increasing temperature. The optimal molecular orientation can be realized under the combination of the two-color femtosecond laser pulse and sin 2 -shaped SCP which has the appropriate delay time: the maximal orientation degree reaches 0.801 at 0 K and 0.450 at 20 K, the maximal orientation duration is 31.3% of the rotational period at 0 K.

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