The nitrogen edge-doped effect on the static first hyperpolarizability of the supershort single-walled carbon nanotube

The nitrogen edge-doped effect on the structure, dipole moment, and first hyperpolarizability of the supershort single-walled carbon nanotube (5, 0) has been studied systematically. For the nitrogen edge-doped effect on the structure, the mean diameter on the nitrogen-doped side (D(u)) decreases as the number of doped-nitrogen (n) increases (4.044 (1) > 3.991 (2) > 3.941 (3) > 3.891 (4) > 3.844 A (5)). Significantly, the nitrogen edge-doped effects on the dipole moment and first hyperpolarizability are revealed for the first time and these new effects are dramatic for the supershort single-walled carbon nanotube (5, 0). Among the beta(0) values of these seven nitrogen-doped structures, the largest beta(0) (3155 au) is larger by almost 450 times than the very small beta(0) (7 au) of undoped structure (D(5h)). For nitrogen-doped structures, the order of the beta(0) values is 3155 (1) > 2677 (2A) approximately 2817 (2B) > 1465 (3A) approximately 1458 (3B) > 670 (4) > 254 au (5), which shows two interesting relationships between the beta(0) value and nitrogen-doped number: (1) the smaller the nitrogen-doped number, the larger the beta(0) value. (2) The structures with the same number of doped-nitrogen have almost the same beta(0) values (1465 for 3A and 1458 au for 3B). As for the frequency-dependent beta (-omega; omega, 0) and beta (-2omega; omega, omega), the dependence on the nitrogen-doped number (n) is similar to the case of static beta(0). For beta (-2omega; omega, omega) values at omega = 0.005 au are 3220 (1) > 2720 (2A) approximately = 2862 (2B) > 1480 (3A) approximately = 1477 (3B) > 676 (4) > 256 au (5). In addition, the important monotonic dependences of the beta value on the D(u) and electronic spatial extent are also observed. The new knowledge of influence the beta value will be beneficial to design high-performance nonlinear optical (NLO) materials.