Raman and infrared spectra of complex low energy tetrahedral carbon allotropes from first-principles calculations

Hui Wang; Ze-Yu Zhang; Xiao-Wu Cai; Zi-Han Liu; Yong-Xiang Zhang; Zhen-Long Lv; Wei-Wei Ju; Hui-Hui Liu; Tong-Wei Li; Gang Liu; Hai-Sheng Li; Hai-Tao Yan; Min Feng

doi:10.1088/1674-1056/ab9613

Journals >Chinese Physics B >Volume 29 >Issue 9 >Page > Article

Chinese Physics B
Vol. 29, Issue 9, (2020)

Raman and infrared spectra of complex low energy tetrahedral carbon allotropes from first-principles calculations

Hui Wang^1、†, Ze-Yu Zhang¹, Xiao-Wu Cai², Zi-Han Liu¹, Yong-Xiang Zhang^1、3, Zhen-Long Lv¹, Wei-Wei Ju¹, Hui-Hui Liu¹, Tong-Wei Li¹, Gang Liu¹, Hai-Sheng Li¹, Hai-Tao Yan¹, and Min Feng⁴

Author Affiliations

¹Henan Key Laboratory of Photoelectric Energy Storage Materials and Applications, School of Physics Engineering, Henan University of Science and Technology, Luoyang 47023, China

²First High School of Luoyang City, Luoyang 471001, China

³Institute of Microelectronics of Chinese Academy of Sciences, Beijing 100029, China

⁴School of Physics, Nankai University, Tianjin 300071, China

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DOI: 10.1088/1674-1056/ab9613 Cite this Article

Hui Wang, Ze-Yu Zhang, Xiao-Wu Cai, Zi-Han Liu, Yong-Xiang Zhang, Zhen-Long Lv, Wei-Wei Ju, Hui-Hui Liu, Tong-Wei Li, Gang Liu, Hai-Sheng Li, Hai-Tao Yan, Min Feng. Raman and infrared spectra of complex low energy tetrahedral carbon allotropes from first-principles calculations[J]. Chinese Physics B, 2020, 29(9): Copy Citation Text

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Fig. 1. Primitive cell of (a) Pbam-32, (b) P6/mmm, and (c)

I4¯3d

. They are composed of tetrahedra network, which is the characteristic of sp³ hybridization. The numbers of panels (a) and (b) refer to fivefold, sixfold, sevenfold, and eightfold topological carbon rings.

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Calculated Raman spectra of powder sample at 300 K with 532-nm excitation light. There are obvious peaks in the middle frequency region from 600 cm−1 to 1150 cm−1 except for diamond.

Fig. 2. Calculated Raman spectra of powder sample at 300 K with 532-nm excitation light. There are obvious peaks in the middle frequency region from 600 cm⁻¹ to 1150 cm⁻¹ except for diamond.

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Fig. 3. Vibrational modes of principle peaks of Pbam-32.

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Fig. 4. Vibrational modes of principle peaks of P6/mmm.

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Fig. 5. Vibrational modes of principle peaks for

I4¯3d

. We only give carbon wireframe here for clarity.

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Fig. 6. Calculated electronic band structures of (a) Pbam-32, (b) P6/mmm, and (c)

I4¯3d

. The energy of the highest occupied state is set to be zero.

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Structure	a/Å	b/Å	c/Å	Atomic positions	Energy/(eV/atom)
Pbam-32	8.193 8.303*	8.145 8.865*	2.484 2.511*	4h (0.088 0.499 1/2)	0.10
				4h (0.837 0.341 1/2)
				4h (0.575 0.555 1/2)
				4h (0.480 0.276 1/2)
				4g (0.729 0.351 0)
				4g (0.850 0.580 0)
				4g (0.174 0.979 0)
				4g (0.586 0.245 0)
P6/mmm	9.738 9.855*	9.738 9.855*	2.471 2.497*	6l (0.093 0.185 0)	0.13
				6m (0.145 0.290 1/2)
				12p (0.828 0.336 0)
				12q (0.090 0.410 1/2)
	10.126 10.289*	10.126 10.289*	10.126 10.289*	12b (0 3/4 5/8)	0.14
				16c (0.757 0.743 0.257)
				16c (0.852 0.648 0.352)
				48e (0.893 0.555 0.584)
				48e (0.450 0.381 0.705)
				48e (0.254 0.417 0.426)

Table 1. Calculated crystal parameters of Pbam-32, P6/mmm, and

I \bar{4} 3 d

. Integer fractions represent atomic positions fixed by symmetry. Their energy values relative to diamond are listed in the last column. Data with * is cited from Ref. [7].

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Structure	Point group	Raman active	Infrared active	Both Raman- and infrared-active	Silent
Pbam-32	D2h	16Ag+16B1g+8B2g+8B3g	7B1u+15B2u+15B3u		8Au
P6/mmm	D6h	6A1g+6E1g+12E2g	3A2u+11E1u		2A1u+6A2g+4B1g+6B1u+2B2g+6B2u+6E2u
	Td	11A1+23E		35T2	12A2+35T1

Table 2. Γ -point optical vibrational modes of Pbam-32, P6/mmm, and

I \bar{4} 3 d

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Pbam-32			1234	B1g	235.4	1329	E2g	0.34	1040	A1	170
Freq	Sym	R.A.	1244	B2g	15.4	1357	A1g	34.9	1053	T2	64.2
418	B3g	4×10−4	1283	B3g	4.4				1077	T2	164
441	Ag	2.5	1290	Ag	288.7	Freq	Sym	R.A.	1080	E	0.46
451	B2g	0.15	1303	B1g	82.2	445	A1	2.0	1085	T2	26.2
465	B1g	0.017	1305	Ag	158.5	473	T2	2.9×10−2	1095	A1	22.6
469	Ag	7.5	1309	B3g	329.7	484	T2	9.0×10−3	1117	T2	8.0
489	B3g	0.12	1310	B2g	56.4	516	E	4.2×10−3	1126	E	0.78
505	B2g	2.6×10−3	1312	B1g	15.4	527	T2	0.55	1131	T2	70.3
594	Ag	3.4	1336	Ag	60.2	535	E	0.13	1110	T2	6.8
671	B3g	2.6×10−3	1361	B1g	82.9	569	E	0.58	1144	E	0.83
672	B2g	0.11	1462	Ag	107.6	616	T2	2.7	1156	A1	186
675	B1g	1.3×10−2	1464	B1g	11.2	631	T2	2.8×10−2	1163	E	0.51
688	B1g	1.8×10−2	P6/mmm			657	T2	2.9	1168	T2	240
709	B2g	0.15	Freq	Sym	R.A.	692	E	1.4×10−3	1176	T2	2.1×10−2
710	B1g	2.5	360	E1g	8.2×10−2	702	A1	1.9	1196	E	19.5
747	B3g	2.2×10−2	408	E2g	0.14	710	T2	0.55	1201	A1	386
788	Ag	10.0	581	E1g	1.1	723	T2	5.1	1216	T2	53.1
795	B1g	3.8	584	E2g	4.8×10−2	734	E	1.3×10−3	1223	E	5.8
847	Ag	30.8	617	E1g	3×10−4	759	T2	15.7	1225	T2	72.7
903	B1g	1.7	631	A1g	6.0	773	A1	1.1	1239	E	10.7
989	B1g	0.26	652	E2g	15.2	780	E	5.4	1251	T2	191
1001	Ag	178.3	744	E2g	9.0×10−2	788	T2	8.3×10−2	1257	E	98.4
1059	Ag	15.9	865	A1g	93.7	819	T2	3.6	1269	T2	10. 3
1093	Ag	11.3	926	E2g	3.4	827	T2	13.2	1276	T2	3.0
1107	B3g	29.9	1029	A1g	134	865	T2	29.1	1277	A1	39.7
1113	B1g	81.1	1059	E2g	11.9	874	A1	18.6	1277	E	13.4
1130	B1g	7.0	1141	E1g	7.4	880	E	0.86	1289	T2	171
1143	Ag	73.2	1154	E2g	37.2	910	T2	5.3	1293	E	86.4
1154	B2g	0.44	1200	A1g	32.1	923	E	0.95	1304	T2	20.9
1173	Ag	51.0	1205	E2g	0.34	932	E	3. 9	1319	A1	11.8
1176	B1g	79.1	1222	E1g	96.7	953	E	1.9×10−2	1320	E	2.9
1186	B2g	2.7	1228	E1g	6.7	979	T2	42.6	1321	T2	18.2
1190	B3g	100.5	1236	E2g	0.14	995	A1	269	1328	T2	199
1202	Ag	16.9	1280	A1g	422	998	E	23.6	1334	T2	4.0×10−3
1207	B1g	3.7	1295	E2g	65.3	999	T2	90.5	1345	E	0.46
1226	Ag	257.7	1314	E2g	116	1038	T2	286

Table 3. Calculated values of frequency (Freq, in unit cm⁻¹) and Raman activity (R.A., in units Å⁴/amu) of Raman-active mode.

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Pbam-32			1166	B2u	21	1047	E1u	0.04	865	T2	1.2
Freq	Sym	I.I.	1189	B2u	22	1079	A2u	0.18	910	T2	14
374	B3u	0.20	1194	B3u	8.5	1084	E1u	4.1	979	T2	0.23
403	B2u	2.6	1210	B2u	0.07	1125	E1u	77	999	T2	4.0
544	B2u	0.01	1214	B1u	23	1185	A2u	17	1038	T2	24
559	B1u	4.2	1215	B2u	1.8	1259	E1u	8.7	1053	T2	2.0
575	B1u	2.1	1227	B3u	16	1284	E1u	5.8	1077	T2	27
586	B3u	0.35	1235	B1u	3.5	1311	E1u	5.6	1085	T2	23
613	B2u	0.71	1257	B3u	4.8	1330	E1u	0.19	1117	T2	70
657	B3u	1.8	1260	B1u	2.8				1131	T2	0.04
690	B1u	2.1	1271	B2u	14	Freq	Sym	I.I.	1140	T2	0.69
708	B2u	4.3	1278	B3u	0.25	473	T2	0.50	1168	T2	1.7
802	B3u	0.09	1307	B3u	1.1	484	T2	0.01	1176	T2	5.4
823	B3u	0.11	1322	B2u	12	528	T2	2.0	1216	T2	0.54
874	B2u	4.8	1342	B2u	14	616	T2	0.17	1225	T2	2.3
910	B2u	1.1	1352	B3u	82	631	T2	0.42	1251	T2	3.3
917	B3u	38	P6/mmm			657	T2	5.4	1269	T2	2.7
934	B3u	0.17	Freq	Sym	I.I.	710	T2	0.81	1276	T2	13
1008	B2u	7.4	472	E1u	1.2	723	T2	1.0	1289	T2	1.5
1074	B3u	1.9	496	A2u	2.9	759	T2	2.5	1304	T2	9.9
1081	B1u	0.70	692	E1u	0.10	788	T2	0.01	1321	T2	2.1
1098	B2u	10	788	E1u	1.6	819	T2	0.73	1328	T2	0.50
1117	B3u	9.4	966	E1u	3.2	827	T2	0.02	1334	T2	46

Table 4. Calculated frequency and infrared intensity (I.I., in units (D/Å)²/amu×10⁻²) of infrared-active mode.

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