First-principles study on the mechanics, optical, and phonon properties of carbon chains<xref rid="cpb_27_11_117101fn1" ref-type="fn">*</xref><fn id="cpb_27_11_117101fn1"><label>*</label><p>Project supported by the National Natural Science Foundation of China (Grant No. 11672087), the Strategic Programs for Innovative Research (SPIRE), the Computational Materials Science Initiative (CMSI), and the Yukawa International Program for Quark-Hadron Sciences at YITP, Kyoto University, Japan.</p></fn>

First-principles study on the mechanics, optical, and phonon properties of carbon chains**

Project supported by the National Natural Science Foundation of China (Grant No. 11672087), the Strategic Programs for Innovative Research (SPIRE), the Computational Materials Science Initiative (CMSI), and the Yukawa International Program for Quark-Hadron Sciences at YITP, Kyoto University, Japan.

Li Jin-Ping^{1, †}, Meng Song-He¹, Lu Han-Tao², Tohyama Takami³

(color online) (a) The total energy and (b) the band gap of polyyne as a function of the fractional coordinate without geometry optimization.