Raman and infrared spectra of complex low energy tetrahedral carbon allotropes from first-principles calculations**Project supported by the National Natural Science Foundation of China (Grant Nos. U1404111, 11504089, 61874160, 61675064, and 11404098), the Fund for Young Key Teacher of Henan Province, China (Grant No. 2016GGJS-059), and the Henan Provincial Major Scientific and Technological Projects, China (Grant No. 182102210289).

Abstract

Up to now, at least 806 carbon allotropes have been proposed theoretically. Three interesting carbon allotropes (named Pbam-32, P6/mmm, and ) were recently uncovered based on a random sampling strategy combined with space group and graph theory. The calculation results show that they are superhard and remarkably stable compared with previously proposed metastable phases. This indicates that they are likely to be synthesized in experiment. We use the factor group analysis method to analyze their Γ -point vibrational modes. Owing to their large number of atoms in primitive unit cells (32 atoms in Pbam-32, 36 atoms in P6/mmm, and 94 atoms in ), they have many Raman- and infrared-active modes. There are 48 Raman-active modes and 37 infrared-active modes in Pbam-32, 24 Raman-active modes and 14 infrared-active modes in P6/mmm, and 34 Raman-active modes and 35 Raman- and infrared-active modes in . Their calculated Raman spectra can be divided into middle frequency range from 600 cm−1 to 1150 cm−1 and high frequency range above 1150 cm−1. Their largest infrared intensities are 0.82, 0.77, and 0.70 (D/Å)2/amu for Pbam, P6/mmm, and , respectively. Our calculated results provide an insight into the lattice vibrational spectra of these sp3 carbon allotropes and suggest that the middle frequency Raman shift and infrared spectrum may play a key role in identifying newly proposed carbon allotropes.