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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.
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Keywords:
- SbS /
- electronic structure /
- spin-orbit coupling effect /
- spectroscopic constants
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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.
图 2 SbS的Ω态势能曲线
Figure 2. Potential energy curves of Ω states of SbS.
图 3 SbS的振动谱带
Figure 3. Vibrational transition bands of SbS.
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 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 Re/Å De/eV Be/cm–1 ωe/cm–1 ωeχe /cm–1 Te/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 15σαβ7πxαβyαβ8πxα (72.77) ${1^4}\Pi $ 2.4481 1.84 0.1108 343.6 1.17 12884 0.65 15σαβ7πxαβyα8πxαyα (84.83) ${{\text{2}}^{\text{2}}}\Pi $ 2.4388 2.60 0.1117 356.3 0.89 16721 0.64 15σαβ7πxαβyβ8πxαyα (52.26) ${{\text{3}}^{\text{2}}}\Pi $ 2.4513 2.16 0.1106 341.8 0.97 20306 0.88 15σαβ7πxαβyα8πxαyβ (31.90) ${1^4}{\Sigma ^ - }$ 2.3354 1.88 0.1218 361.1 2.54 21870 1.53 15σα7πxαβyαβ8πxαyα (83.08) ${4^{\text{2}}}\Pi $ 2.4554 1.49 0.1109 341.1 1.97 25796 2.85 15σαβ7πxαyαβ8πyαβ (59.44) ${{\text{1}}^{\text{2}}}{\Sigma ^ + }$第一势阱 2.4699 0.45 0.1089 254.4 0.88 26185 3.64 15σαβ16σα7πxαβyαβ (52.15) ${1^{\text{2}}}{\Sigma ^ - }$ 2.3735 1.17 0.1179 340.1 6.30 28350 7.03 15σα7πxαβyαβ8πxβyα (61.23) ${1^{\text{2}}}\Delta $ 2.3545 1.04 0.1198 343.5 2.51 29271 1.80 15σα7πxαβyαβ8πxαyβ (60.01) ${1^2}\Phi $ 2.5497 1.45 0.1022 265.1 1.96 32508 6.63 15σαβ7πxαyα8πxαβyβ(50.92) ${2^{\text{2}}}{\Sigma ^ + }$ 2.3678 0.63 0.1185 337.0 1.73 33250 2.19 15σα7πxαβyαβ8πyαβ (38.05) 15σα7πxαβyαβ8πxαβ (38.05) ${1^4}\Delta $ 2.8462 0.34 0.0820 188.3 2.40 34389 0.84 15σαβ16σα7πxαβyα8πyα (35.39) 15σαβ16σα7πxαyαβ8πxα (35.39) ${2^4}\Pi $ 3.3555 0.28 0.0590 134.1 1.52 34791 0.38 15σα16σα7πxαβyβ8πxαyα (27.31) ${3^{\text{2}}}{\Sigma ^ + }$ 3.0478 0.32 0.0715 189.7 4.99 36554 3.79 15σα7πxαβyαβ8πyαβ (16.85) 15σα7πxαβyαβ8πxαβ (16.85) ${2^4}{\Sigma ^ + }$ 3.4574 0.09 0.0556 87.1 1.80 37047 0.84 15σα7πxαyαβ8πxαyαβ (14.08) 15σα7πxαβyα8πxαβyα (14.08) ${2^4}{\Sigma ^ - }$第一势阱 2.8356 0.06 0.0826 184.4 6.87 37260 1.01 15σαβ16σα7πxαyαβ8πyα (35.84) 15σαβ16σα7πxαβyα 8πxα (35.84) ${2^4}\Delta $ 3.9570 0.05 0.0424 95.3 7.03 37339 0.96 15σα16σαβ7πxαyαβ8πxα (17.70) 15σα16σαβ7πxαβyα8πyα (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.Re/Å De/eV ωe/cm–1 Be/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: a MRSDCI/modified basis sets; b CAS-ACPF/cc-pVQZ; c MRCI+Q/AV5Z+CV+DK; d MRCI+Q/aug-cc-pV5Z; e MRSDCI/modified basis sets; f MRCI/aug-cc-pV5Z; g MRCI+Q/56+CV+DK; h MRCI/modified basis sets; i Obtained from the RKR method; j MP2(full)/6-31G(d); k MRCI+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 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 Re/Å De/eV Be/cm–1 ωe/cm–1 ωeχe/cm–1 Te/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 Re/Å De/eV ωe/cm–1 Be/cm–1 Te/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 Gv Bv 108Dv Gv Bv 108Dv Gv Bv 108Dv 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
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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 Gv Bv 107Dv Gv Bv 107Dv v Gv Bv 108Dv 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.
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