“…The zigzag DWCNT here is denoted by (m 1 , 0)À(m 2 , 0), where (m 1 , 0) is the inner tube, and (m 2 , 0) is the outer tube. It has been pointed out that the distance between the two coaxial zigzag tubes of DWCNT(m 1 , 0)À(m 2 , 0) is close to 3.3 Å (the interlayer distance in bulk graphite) when m 2 Àm 1 ¼ 9 to form a more stable zigzag DWCNT [37], and this fact also agrees with the recently obtained ultra-thin DWCNTs [28]. In order to study the carbon chains encapsulated in DWCNTs (C chain @DWCNTs) with different inner and outer tubes, totally eight zigzag DWCNTs, including (7, 0)-(16, 0), (8, 0)-(16, 0), (8, 0)-(17, 0), (8, 0)-(18, 0), (9, 0)-(17, 0), (9, 0)-(18, 0), (9, 0)-(19, 0) and (10, 0)- (19,0), are selected to form the C chain @DWCNTs in this paper.…”