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

Abstract

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 <R(2)> are also observed. The new knowledge of influence the beta value will be beneficial to design high-performance nonlinear optical (NLO) materials.