Theoretical study of  potential energy curves and vibrational levels of low-lying electronic states of SbS

Wang Xin-Yu; Wang Yi-Lin; Shi Qian-Han; Wang Qing-Long; Yu Hong-Yang; Jin Yuan-Yuan; Li Song

doi:10.7498/aps.71.20211441

Abstract

In this paper, highly correlated ab initio calculations are performed for accurately determining the electronic structures and spectroscopic features of the Λ-S and Ω low-lying electronic states of SbS . The potential energy curves for 27 Λ-S states of the first three dissociation asymptotes are constructed. Spectroscopic constants and vibrational states for all bound states are well determined. The calculated atomic states for both atoms are consistent with experimental data quite well. Several low-lying Ω electronic states are also investigated, and their respective spectroscopic constants and vibrational states are obtained and compared with those of corresponding Λ-S states, which indicates that the spin-orbit coupling effect gives rise to a minor influence on the electronic states of SbS. To verify our computational accuracy, the additional calculations for the low-lying electronic states of PS, AsS and BiS are also carried out. Our derived results are in reasonable agreement with available experimental data. In addition, vibrational spectra from the excited Ω states to the ground state of SbS are simulated, including bands of X(3/2)→X(1/2), 2(1/2)→X(1/2), 4(1/2)→X(1/2), 5(1/2)→X(1/2) and 6(1/2)→X(1/2). The X(3/2)→X(1/2) band is found in the mid-infrared region, while the others are located in the visible region. The predictive results provided in this paper are expected to serve as a guideline for further researches, such as assisting laboratorial detections and analyzing observed spectrum of SbS.

Keywords:

Authors and contacts

School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China

Corresponding author: Li Song, lsong@yangtzeu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11804031).

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References

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图 1 SbS的Λ-S态势能曲线　(a)二重、六重态; (b), (c)四重态

Figure 1. Potential energy curves of Λ-S states of SbS: (a) Doublet and sextet states; (b), (c) quartet states.

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图 2 SbS的Ω态势能曲线

Figure 2. Potential energy curves of Ω states of SbS.

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图 3 SbS的振动谱带

Figure 3. Vibrational transition bands of SbS.

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表 1 SbS的Λ-S态离解极限

Table 1. Dissociation relationships of the Λ-S states of SbS.

原子态	Λ-S态	ΔE/cm^–1
原子态	Λ-S态	实验值^[68]	计算值
$ {\text{Sb}}({}^4{{\text{S}}_{\text{u}}}) + {\text{S}}{(^3}{{\text{P}}_{\text{g}}}) $	${{\text{1}}^2}{\Sigma ^ + }$, ${{\rm X}^2}\Pi $ , ${{\text{1}}^4}{\Sigma ^ + }$, ${{\text{1}}^4}\prod $, ${{\text{1}}^6}{\Sigma ^ + }$, $ {1^6}\Pi $	0	0
$ {\text{Sb}}({}^4{{\text{S}}_{\text{u}}}) + {\text{S}}{(^1}{{\text{D}}_{\text{g}}}) $	${1^4}{\Sigma ^ - }$, ${1^4}\Delta $, $2{}^4\Pi $	9238.609	9346
$ {\text{Sb}}({}^2{{\text{D}}_{\text{u}}}) + {\text{S}}{(^3}{{\text{P}}_{\text{g}}}) $	${2^2}{\Sigma ^ + }$, ${3^2}{\Sigma ^ + }$, ${1^2}{\Sigma ^ - }$, ${1^2}\Delta $, ${2^2}\Delta $, $2{}^2\Pi $, $3{}^2\Pi $, $4{}^2\Pi $, ${1^2}\Phi $, ${2^4}{\Sigma ^ + }$, ${3^4}{\Sigma ^ + }$, ${2^4}{\Sigma ^ - }$, ${2^4}\Delta $, ${3^4}\Delta $, $3{}^4\Pi $, $4{}^4\Pi $, $5{}^4\Pi $, ${1^4}\Phi $	9854.018	10022

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表 2 SbS的Λ-S态光谱常数

Table 2. Spectroscopic constants of the Λ-S states of SbS.

Λ-S态	R_e/Å	D_e/eV	B_e/cm^–1	ω_e/cm^–1	ω_eχ_e /cm^–1	T_e/cm^–1	RMS/cm^–1	电子组态(组态系数)
${{\text{X}}^{\text{2}}}\Pi $	2.2199	3.44	0.1348	479.8	1.51	0	0.57	15σ^αβ7π_x^αβ_y^αβ8π_x^α (72.77)
${1^4}\Pi $	2.4481	1.84	0.1108	343.6	1.17	12884	0.65	15σ^αβ7π_x^αβ_y^α8π_x^α_y^α (84.83)
${{\text{2}}^{\text{2}}}\Pi $	2.4388	2.60	0.1117	356.3	0.89	16721	0.64	15σ^αβ7π_x^αβ_y^β8π_x^α_y^α (52.26)
${{\text{3}}^{\text{2}}}\Pi $	2.4513	2.16	0.1106	341.8	0.97	20306	0.88	15σ^αβ7π_x^αβ_y^α8π_x^α_y^β (31.90)
${1^4}{\Sigma ^ - }$	2.3354	1.88	0.1218	361.1	2.54	21870	1.53	15σ^α7π_x^αβ_y^αβ8π_x^α_y^α (83.08)
${4^{\text{2}}}\Pi $	2.4554	1.49	0.1109	341.1	1.97	25796	2.85	15σ^αβ7π_x^α_y^αβ8π_y^αβ (59.44)
${{\text{1}}^{\text{2}}}{\Sigma ^ + }$第一势阱	2.4699	0.45	0.1089	254.4	0.88	26185	3.64	15σ^αβ16σ^α7π_x^αβ_y^αβ (52.15)
${1^{\text{2}}}{\Sigma ^ - }$	2.3735	1.17	0.1179	340.1	6.30	28350	7.03	15σ^α7π_x^αβ_y^αβ8π_x^β_y^α (61.23)
${1^{\text{2}}}\Delta $	2.3545	1.04	0.1198	343.5	2.51	29271	1.80	15σ^α7π_x^αβ_y^αβ8π_x^α_y^β (60.01)
${1^2}\Phi $	2.5497	1.45	0.1022	265.1	1.96	32508	6.63	15σ^αβ7π_x^α_y^α8π_x^αβ_y^β(50.92)
${2^{\text{2}}}{\Sigma ^ + }$	2.3678	0.63	0.1185	337.0	1.73	33250	2.19	15σ^α7π_x^αβ_y^αβ8π_y^αβ (38.05)
								15σ^α7π_x^αβ_y^αβ8π_x^αβ (38.05)
${1^4}\Delta $	2.8462	0.34	0.0820	188.3	2.40	34389	0.84	15σ^αβ16σ^α7π_x^αβ_y^α8π_y^α (35.39)
								15σ^αβ16σ^α7π_x^α_y^αβ8π_x^α (35.39)
${2^4}\Pi $	3.3555	0.28	0.0590	134.1	1.52	34791	0.38	15σ^α16σ^α7π_x^αβ_y^β8π_x^α_y^α (27.31)
${3^{\text{2}}}{\Sigma ^ + }$	3.0478	0.32	0.0715	189.7	4.99	36554	3.79	15σ^α7π_x^αβ_y^αβ8π_y^αβ (16.85)
								15σ^α7π_x^αβ_y^αβ8π_x^αβ (16.85)
${2^4}{\Sigma ^ + }$	3.4574	0.09	0.0556	87.1	1.80	37047	0.84	15σ^α7π_x^α_y^αβ8π_x^α_y^αβ (14.08)
								15σ^α7π_x^αβ_y^α8π_x^αβ_y^α (14.08)
${2^4}{\Sigma ^ - }$第一势阱	2.8356	0.06	0.0826	184.4	6.87	37260	1.01	15σ^αβ16σ^α7π_x^α_y^αβ8π_y^α (35.84)
								15σ^αβ16σ^α7π_x^αβ_y^α 8π_x^α (35.84)
${2^4}\Delta $	3.9570	0.05	0.0424	95.3	7.03	37339	0.96	15σ^α16σ^αβ7π_x^α_y^αβ8π_x^α (17.70)
								15σ^α16σ^αβ7π_x^αβ_y^α8π_y^α (17.70)

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表 3 XS (X = N, P, As, Sb, Bi)自由基电子基态${{\text{X}}^{\text{2}}}\Pi $的光谱常数

Table 3. Spectroscopic constants of the ground state ${{\text{X}}^{\text{2}}}\Pi $of XS (X = N, P, As, Sb, Bi) radicals.

		R_e/Å	D_e/eV	ω_e/cm^–1	B_e/cm^–1
	理论值^[35] ^a	1.515	—	1220.5	0.7542
	理论值^{[40] b}	1.5058	—	1202.4	0.742
NS	理论值^{[46] c}	1.4962	4.8504	1216.17	0.77323
	理论值^{[47] d}	1.498	—	1220.9	0.7715
	实验值^[9]	1.495(7)	—	—	0.7736(4)
	实验值^[11]	1.4938(2)	—	—	—
	理论值^{[36] e}	1.944	—	735.6	0.2836
	理论值^[40] ^b	1.9148	—	728.0	0.292
	理论值^{[43] f}	1.879	—	732.0	0.2936
PS	理论值^{[48] g}	1.8972	4.5272	741.0	0.2979
	理论值^{[52] h}	1.918	—	708	—
	实验值^[15]	1.92	—	739.5	0.29
	实验值^[18]	1.900(7)	—	—	—
	实验值^[21]	1.8977405(45)	—	739.13 (42)	0.2975216 (14)
	本文工作	1.9014	4.41	739.5	0.2960
	理论值^{[53] i}	—	4.15(13)	—	—
	理论值^[40] ^b	2.0395	—	559.2	0.181
AsS	理论值^[44] ^j	2.045	3.94	—	—
	理论值^{[49] k}	2.0180	4.0554	565.19	0.18472
	实验值^[28]	2.0174	—	567.94	0.18476
	本文工作	2.0208	3.83	564.4	0.1839
SbS	本文工作	2.2199	3.44	479.8	0.1348
BiS	本文工作	2.3118	3.12	424.9	0.1135
注: ^aMRSDCI/modified basis sets; ^bCAS-ACPF/cc-pVQZ; ^cMRCI+Q/AV5Z+CV+DK; ^dMRCI+Q/aug-cc-pV5Z; ^eMRSDCI/modified basis sets; ^fMRCI/aug-cc-pV5Z; ^gMRCI+Q/56+CV+DK; ^hMRCI/modified basis sets; ⁱObtained from the RKR method; ^jMP2(full)/6-31G(d); ^kMRCI+Q/Q5+CV+DK.

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表 4 SbS自由基Ω态的离解极限

Table 4. Dissociation relationships of the Ω states of SbS.

原子态	Ω态	ΔE/cm^–1
原子态	Ω态	实验值^[68]	本文计算值
$\rm {{Sb} }({}^4{ {{S} }_{ {3/2} } }) + {{S} }{(^3}{ {{P} }_2})$	7/2, 5/2(2), 3/2(3), 1/2(4)	0	0
$\rm{{Sb} }({}^4{ {{S} }_{ {3/ } 2} }) + {{S} }{(^3}{ {{P} }_1})$	5/2, 3/2(2), 1/2(3)	396.055	410.46
$\rm {{Sb} }({}^4{ {{S} }_{ {3/2} } }) + {{S} }{(^3}{ {{P} }_0})$	3/2, 1/2	573.640	605.81

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表 5 SbS自由基的Ω态光谱常数

Table 5. Spectroscopic constants of the Ω states of SbS.

Ω态	R_e/Å	D_e/eV	B_e/cm^–1	ω_e/cm^–1	ω_eχ_e/cm^–1	T_e/cm^–1	RMS/cm^–1
X(1/2)	2.2195	3.62	0.1348	476.3	1.36	0	2.36
实验值^[7]	—	—	—	480	1.2	—
X(3/2)	2.2201	3.36	0.1348	477.3	1.97	2025	2.25
实验值^[7]	—	—	—	470	1.6	—
2(1/2)	2.4527	1.93	0.1104	341.4	0.43	13646	2.70
3(1/2)	2.4538	1.90	0.1103	342.2	0.62	13888	2.28
2(3/2)	2.4503	1.86	0.1106	346.5	1.17	14123	0.30
1(5/2)	2.4537	1.83	0.1103	344.6	1.16	14346	0.38
3(3/2)	2.4428	2.56	0.1113	364.7	1.46	17632	2.94
4(1/2)	2.4467	2.48	0.1110	367.3	2.46	18340	9.74
4(3/2)	2.4524	2.18	0.1105	339.7	0.41	21413	3.17
5(1/2)	2.4560	2.13	0.1101	342.8	1.03	21610	2.17
6(1/2)	2.3462	1.95	0.1207	352.3	1.41	22947	6.01
5(3/2)	2.3476	1.91	0.1205	356.6	2.74	23268	8.04

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表 6 XS (X = N, P, As, Sb, Bi)自由基Ω基态的光谱常数

Table 6. Spectroscopic constants of the ground Ω state of XS (X = N, P, As, Sb, Bi) radicals.

Ω态		R_e/Å	D_e/eV	ω_e/cm^–1	B_e/cm^–1	T_e/cm^–1
NS
X(1/2)	理论值^{[46] a}	1.4962	4.8562	1216.43	0.77320	0
	理论值^{[51] b}	1.4976	4.7586	1213.30	—	0
	实验值^[12]	1.4955	—	1219.14	0.7730	0
	实验值^[13]	1.4955	—	1218.97	0.7730	0
	实验值^[14]	1.4931	—	1218.1	0.7758(11)	0
X(3/2)	理论值^{[46] a}	1.4962	4.8446	1215.93	0.77326	223.64
	理论值^{[51] b}	1.4975	4.7412	1213.02	—	221.67
	实验值^[12]	1.4901	—	1218.90	0.7777	223.15
	实验值^[13]	1.4901	—	1218.90	0.7777	222.98
	实验值^[14]	1.4884	—	1218.0	0.7807(2)	220.4
PS
X(1/2)	实验值^[19]	1.899	—	739.54(2)	0.29724(5)	0
	本文工作	1.9015	4.40	738.8	0.2960	0
X(3/2)	实验值^[19]	1.897	4.566	739.45(2)	0.29765(5)	321.93
	本文工作	1.9014	4.37	738.6	0.2960	324.8
AsS
X(1/2)	实验值^[24]	—	—	567.9(4)	0.18476	0
	本文工作	2.0206	3.89	565.6	0.1839	0
X(3/2)	实验值^[24]	2.0174	—	566.1(3)	0.18492	—
	实验值^[25]	2.0216(3)	—	562.40(16)	0.18408(4)	—
	本文工作	2.0210	3.78	563.3	0.1838	893.3
SbS
X(1/2)	本文工作	2.2195	3.62	476.3	0.1348	0
X(3/2)	本文工作	2.2201	3.36	477.3	0.1348	2025.0
BiS
X(1/2)	理论值^{[45] c}	2.365	—	407	—	0
	实验值^[29]	2.3194	—	408.71	0.11301	0
	实验值^[30]	2.3122(10)	—	404.68(8)	0.11371(10)	0
	实验值^[31]	2.3188(1)	—	408.67(7)	0.113063(10)	0
	实验值^[32]	—	—	408.66(3)	—	0
	本文工作	2.3131	3.58	429.5	0.1134	0
X(3/2)	理论值^{[45] c}	2.361	—	404	—	7076
	实验值^[31]	2.31525(13)	—	403.95(21)	0.113411(13)	6905.02(18)
	实验值^[32]	2.31489(11)	—	404.501(94)	—	—
	本文工作	2.3191	2.87	413.8	0.1128	5781
注: ^a MRCI+Q/AV5Z+CV+DK+SO; ^b MRCI+Q/56+CV+DK+SO; ^c MRDCI+Q/modified basis sets.

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表 7 SbS的Λ-S及其对应Ω态的振动能级、转动常数和离心畸变常数(单位: cm^–1)

Table 7. Vibrational energy levels, rotational constants and centrifugal distortion constants for the Ω and its respective Λ-S states of SbS (in cm^–1).

v	G_v	B_v	10⁸D_v	G_v	B_v	10⁸D_v	G_v	B_v	10⁸D_v
	X(1/2)			X(3/2)			${\text{X}}{}^2\Pi $
0	205.3	0.1350	4.30	200.7	0.1349	4.37	212.4	0.1351	4.18
1	682.7	0.1345	4.32	673.6	0.1344	4.39	696.4	0.1344	4.38
2	1156.9	0.1340	4.32	1143.1	0.1338	4.40	1171.8	0.1339	4.40
3	1628.2	0.1334	4.33	1609.4	0.1332	4.41	1642.2	0.1334	4.32
4	2096.6	0.1329	4.35	2072.6	0.1327	4.44	2110.0	0.1328	4.28
5	2561.9	0.1323	4.39	2532.6	0.1321	4.48	2575.7	0.1323	4.31
	3(3/2)			4(1/2)			${2^2}\Pi $
0	160.5	0.1118	4.32	165.5	0.1113	4.44	153.7	0.1119	4.42
1	519.5	0.1114	4.31	517.2	0.1109	4.44	508.8	0.1114	4.38
2	876.8	0.1109	4.29	866.9	0.1104	4.42	862.3	0.1108	4.37
3	1232.5	0.1105	4.29	1214.7	0.1100	4.43	1214.1	0.1104	4.33
4	1586.4	0.1101	4.32	1560.6	0.1095	4.46	1564.3	0.1099	4.34
5	1938.3	0.1097	4.34	1904.3	0.1090	4.49	1912.9	0.1095	4.35
	4(3/2)			5(1/2)			${3^2}\Pi $
0	169.7	0.1106	4.58	170.6	0.1103	4.59	163.4	0.1108	4.73
1	512.3	0.1101	4.59	511.8	0.1098	4.60	501.1	0.1102	4.54
2	852.6	0.1096	4.59	850.7	0.1093	4.60	839.6	0.1096	4.57
3	1190.7	0.1091	4.60	1187.4	0.1089	4.61	1176.7	0.1091	4.58
4	1526.5	0.1086	4.62	1521.9	0.1084	4.63	1512.0	0.1086	4.61
5	1860.0	0.1081	4.62	1854.0	0.1079	4.64	1845.0	0.1081	4.64
	6(1/2)			5(3/2)			${1^4}{\Sigma ^ - }$
0	131.6	0.1204	5.73	128.3	0.1203	5.80	151.1	0.1215	5.33
1	479.4	0.1197	5.60	473.6	0.1196	5.72	517.9	0.1214	5.42
2	826.2	0.1190	5.66	817.0	0.1189	5.75	881.0	0.1204	6.22
3	1170.2	0.1183	5.85	1157.7	0.1182	5.86	1230.6	0.1194	6.24
4	1510.2	0.1177	5.91	1494.9	0.1175	5.91	1571.7	0.1186	5.89
5	1846.6	0.1171	5.66	1828.6	0.1169	5.82	1909.2	0.1179	5.87
	2(1/2)			3(1/2)			$1{}^4\Pi $
0	170.1	0.1106	4.55	170.3	0.1106	4.55	160.2	0.1111	4.73
1	514.3	0.1102	4.55	514.0	0.1101	4.56	499.2	0.1104	4.56
2	856.3	0.1097	4.56	855.5	0.1096	4.57	838.7	0.1099	4.63
3	1196.0	0.1092	4.57	1194.7	0.1091	4.58	1176.2	0.1094	4.65
4	1533.5	0.1087	4.58	1531.6	0.1086	4.59	1511.4	0.1089	4.67
5	1868.7	0.1082	4.58	1866.2	0.1081	4.60	1844.2	0.1084	4.69
	2(3/2)			1(5/2)
0	168.8	0.1108	4.56	170.4	0.1105	4.57
1	513.4	0.1103	4.57	513.2	0.1100	4.58
2	855.6	0.1098	4.58	853.6	0.1095	4.58
3	1195.5	0.1093	4.59	1191.7	0.1090	4.60
4	1533.0	0.1088	4.60	1527.5	0.1085	4.61
5	1868.2	0.1083	4.61	1860.8	0.1080	4.62

DownLoad: CSV

表 8 XS (X = P, As, Bi)自由基Ω基态的振动能级、转动常数和离心畸变常数(单位: cm^–1)

Table 8. Vibrational energy levels, rotational constants and centrifugal distortion constants for the ground Ω state of XS (X = P, As, Bi) radicals (in cm^–1).

v	G_v	B_v	10⁷D_v	G_v	B_v	10⁷D_v	v	G_v	B_v	10⁸D_v
	PS X(1/2)			PS X(3/2)				AsS X(3/2)
0	368.4	0.29550	1.91	368.2	0.29551	1.91	3	1952.3	0.18108	7.90
	—	0.29649^a	1.85^a	—	0.29695^a	1.9^a		—	0.18116(8)^b	8.6(5)^b
1	1101.3	0.29394	1.92	1100.8	0.29394	1.92	4	2501.2	0.18024	7.93
	—	0.29469^a	1.7^a	—	0.29543^a	1.8^a		—	0.18033(4)^b	8.7(8)^b
2	1828.2	0.29237	1.92	1827.2	0.29237	1.92	5	3046.0	0.17939	7.93
	—	0.29333^a	1.9^a	—	0.29385^a	2.0^a		—	0.17950(4)^b	8.8(7)^b
3	2549.0	0.29078	1.92	2547.6	0.29078	1.92	6	3587.0	0.17853	7.89
	—	0.29161^a	1.85^a	—	0.29223^a	1.95^a		—	0.17865(5)^b	9.1(9)^b
4	3264.0	0.28918	1.92	3262.2	0.28917	1.93	7	4124.1	0.17765	7.85
	—	0.29015^a	1.9^a	—	0.29065^a	1.8^a		—	0.17782(4)^b	9.7(8)^b
5	3973.2	0.28756	1.93	3971.0	0.28755	1.93
	—	0.28855^a	2.0^a	—	0.28933^a	1.8^a			BiS X(1/2)
6	4676.7	0.28595	1.94	4674.0	0.28594	1.94	0	213.9	0.11344	3.19
	—	0.28710^a	1.9^a	—	0.28740^a	2.0^a		—	0.112764(5)^c	3.34(4)^c
7	5374.2	0.28434	1.95	5371.0	0.28432	1.95	1	641.0	0.11302	3.19
	—	—	—	—	0.28653^a	1.7^a	2	1065.6	0.11260	3.19
8	6065.7	0.28273	1.96	6061.9	0.28271	1.96	3	1488.0	0.11218	3.20
	—	—	—	—	0.28416^a	2.0^a
注: ^a为文献[19]实验值; ^b为文献[25]实验值; ^c为文献[29]实验值.

DownLoad: CSV

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