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SbS电子基态及激发态势能曲线和振动能级的理论研究

王新宇 王艺霖 石虔韩 汪庆龙 于洪洋 金园园 李松

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SbS电子基态及激发态势能曲线和振动能级的理论研究

王新宇, 王艺霖, 石虔韩, 汪庆龙, 于洪洋, 金园园, 李松

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
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  • 运用多参考组态相互作用(MRCI+Q)方法, 对硫化锑(SbS)能量最低的3个Ʌ-S离解极限的所有电子态以及考虑自旋-轨道耦合效应后分裂所得的Ω态进行了计算. 得到27个Ʌ-S电子态及能量最低的12个Ω态的电子结构、光谱常数和振动能级等信息. Sb原子和S原子能级的计算值与实验值相符很好. 分析表明自旋-轨道耦合效应对光谱常数与振动能级的影响总体上并不显著. 对X(3/2)→X(1/2), 2(1/2)→X(1/2), 4(1/2)→X(1/2), 5(1/2)→X(1/2)及6(1/2)→X(1/2)跃迁的振动光谱进行了模拟与分析, 其中X(3/2)→X(1/2)谱带位于中红外波段, 其他谱带均位于可见光波段. 此外, 对氮族元素硫化物的电子态进行了验证计算, 计算结果与已有实验结果吻合较好, 体现了同族元素代换后相关物性的渐变规律性.
    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.
      通信作者: 李松, lsong@yangtzeu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11804031)资助的课题
      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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  • 图 1  SbS的Λ-S态势能曲线 (a)二重、六重态; (b), (c)四重态

    Fig. 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

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

    图 3  SbS的振动谱带

    Fig. 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}}}) $${{\text{1}}^2}{\Sigma ^ + }$, ${{\rm X}^2}\Pi $ , ${{\text{1}}^4}{\Sigma ^ + }$, ${{\text{1}}^4}\prod $, ${{\text{1}}^6}{\Sigma ^ + }$, $ {1^6}\Pi $00
    $ {\text{Sb}}({}^4{{\text{S}}_{\text{u}}}) + {\text{S}}{(^1}{{\text{D}}_{\text{g}}}) $${1^4}{\Sigma ^ - }$, ${1^4}\Delta $, $2{}^4\Pi $9238.6099346
    $ {\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 $
    9854.01810022
    下载: 导出CSV

    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ReDe/eVBe/cm–1ωe/cm–1ωeχe /cm–1Te/cm–1RMS/cm–1电子组态(组态系数)
    ${{\text{X}}^{\text{2}}}\Pi $2.21993.440.1348479.81.5100.5715σαβxαβyαβxα (72.77)
    ${1^4}\Pi $2.44811.840.1108343.61.17128840.6515σαβxαβyαxαyα (84.83)
    ${{\text{2}}^{\text{2}}}\Pi $2.43882.600.1117356.30.89167210.6415σαβxαβyβxαyα (52.26)
    ${{\text{3}}^{\text{2}}}\Pi $2.45132.160.1106341.80.97203060.8815σαβxαβyαxαyβ (31.90)
    ${1^4}{\Sigma ^ - }$2.33541.880.1218361.12.54218701.5315σαxαβyαβxαyα (83.08)
    ${4^{\text{2}}}\Pi $2.45541.490.1109341.11.97257962.8515σαβxαyαβyαβ (59.44)
    ${{\text{1}}^{\text{2}}}{\Sigma ^ + }$第一势阱2.46990.450.1089254.40.88261853.6415σαβ16σαxαβyαβ (52.15)
    ${1^{\text{2}}}{\Sigma ^ - }$2.37351.170.1179340.16.30283507.0315σαxαβyαβxβyα (61.23)
    ${1^{\text{2}}}\Delta $2.35451.040.1198343.52.51292711.8015σαxαβyαβxαyβ (60.01)
    ${1^2}\Phi $2.54971.450.1022265.11.96325086.6315σαβxαyαxαβyβ(50.92)
    ${2^{\text{2}}}{\Sigma ^ + }$2.36780.630.1185337.01.73332502.1915σαxαβyαβyαβ (38.05)
    15σαxαβyαβxαβ (38.05)
    ${1^4}\Delta $2.84620.340.0820188.32.40343890.8415σαβ16σαxαβyαyα (35.39)
    15σαβ16σαxαyαβxα (35.39)
    ${2^4}\Pi $3.35550.280.0590134.11.52347910.3815σα16σαxαβyβxαyα (27.31)
    ${3^{\text{2}}}{\Sigma ^ + }$3.04780.320.0715189.74.99365543.7915σαxαβyαβyαβ (16.85)
    15σαxαβyαβxαβ (16.85)
    ${2^4}{\Sigma ^ + }$3.45740.090.055687.11.80370470.8415σαxαyαβxαyαβ (14.08)
    15σαxαβyαxαβyα (14.08)
    ${2^4}{\Sigma ^ - }$第一势阱2.83560.060.0826184.46.87372601.0115σαβ16σαxαyαβyα (35.84)
    15σαβ16σαxαβyαxα (35.84)
    ${2^4}\Delta $3.95700.050.042495.37.03373390.9615σα16σαβxαyαβxα (17.70)
    15σα16σαβxαβyαyα (17.70)
    下载: 导出CSV

    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.

    ReDe/eVωe/cm–1Be/cm–1
    理论值[35] a1.5151220.50.7542
    理论值[40] b1.50581202.40.742
    NS理论值[46] c1.49624.85041216.170.77323
    理论值[47] d1.4981220.90.7715
    实验值[9]1.495(7)0.7736(4)
    实验值[11]1.4938(2)
    理论值[36] e1.944735.60.2836
    理论值[40] b1.9148728.00.292
    理论值[43] f1.879732.00.2936
    PS理论值[48] g1.89724.5272741.00.2979
    理论值[52] h1.918708
    实验值[15]1.92739.50.29
    实验值[18]1.900(7)
    实验值[21]1.8977405(45)739.13
    (42)
    0.2975216
    (14)
    本文工作1.90144.41739.50.2960
    理论值[53] i4.15(13)
    理论值[40] b2.0395559.20.181
    AsS理论值[44] j2.0453.94
    理论值[49] k2.01804.0554565.190.18472
    实验值[28]2.0174567.940.18476
    本文工作2.02083.83564.40.1839
    SbS本文工作2.21993.44479.80.1348
    BiS本文工作2.31183.12424.90.1135
    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.
    下载: 导出CSV

    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)
    00
    $\rm{{Sb} }({}^4{ {{S} }_{ {3/ } 2} }) + {{S} }{(^3}{ {{P} }_1})$5/2, 3/2(2),
    1/2(3)
    396.055410.46
    $\rm {{Sb} }({}^4{ {{S} }_{ {3/2} } }) + {{S} }{(^3}{ {{P} }_0})$3/2, 1/2573.640605.81
    下载: 导出CSV

    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ReDe/eVBe/cm–1ωe/cm–1ωeχe/cm–1Te/cm–1RMS/cm–1
    X(1/2)2.21953.620.1348476.31.3602.36
    实验值[7]4801.2
    X(3/2)2.22013.360.1348477.31.9720252.25
    实验值[7]4701.6
    2(1/2)2.45271.930.1104341.40.43136462.70
    3(1/2)2.45381.900.1103342.20.62138882.28
    2(3/2)2.45031.860.1106346.51.17141230.30
    1(5/2)2.45371.830.1103344.61.16143460.38
    3(3/2)2.44282.560.1113364.71.46176322.94
    4(1/2)2.44672.480.1110367.32.46183409.74
    4(3/2)2.45242.180.1105339.70.41214133.17
    5(1/2)2.45602.130.1101342.81.03216102.17
    6(1/2)2.34621.950.1207352.31.41229476.01
    5(3/2)2.34761.910.1205356.62.74232688.04
    下载: 导出CSV

    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ReDe/eVωe/cm–1Be/cm–1Te/cm–1
    NS
    X(1/2)理论值[46] a1.49624.85621216.430.773200
    理论值[51] b1.49764.75861213.300
    实验值[12]1.49551219.140.77300
    实验值[13]1.49551218.970.77300
    实验值[14]1.49311218.10.7758(11)0
    X(3/2)理论值[46] a1.49624.84461215.930.77326223.64
    理论值[51] b1.49754.74121213.02221.67
    实验值[12]1.49011218.900.7777223.15
    实验值[13]1.49011218.900.7777222.98
    实验值[14]1.48841218.00.7807(2)220.4
    PS
    X(1/2)实验值[19]1.899739.54(2)0.29724(5)0
    本文工作1.90154.40738.80.29600
    X(3/2)实验值[19]1.8974.566739.45(2)0.29765(5)321.93
    本文工作1.90144.37738.60.2960324.8
    AsS
    X(1/2)实验值[24]567.9(4)0.184760
    本文工作2.02063.89565.60.18390
    X(3/2)实验值[24]2.0174566.1(3)0.18492
    实验值[25]2.0216(3)562.40(16)0.18408(4)
    本文工作2.02103.78563.30.1838893.3
    SbS
    X(1/2)本文工作2.21953.62476.30.13480
    X(3/2)本文工作2.22013.36477.30.13482025.0
    BiS
    X(1/2)理论值[45] c2.3654070
    实验值[29]2.3194408.710.113010
    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2.31313.58429.50.11340
    X(3/2)理论值[45] c2.3614047076
    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2.31912.87413.80.11285781
    注: a MRCI+Q/AV5Z+CV+DK+SO; b MRCI+Q/56+CV+DK+SO; c MRDCI+Q/modified basis sets.
    下载: 导出CSV

    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).

    vGvBv108DvGvBv108DvGvBv108Dv
    X(1/2)X(3/2)${\text{X}}{}^2\Pi $
    0205.30.13504.30200.70.13494.37212.40.13514.18
    1682.70.13454.32673.60.13444.39696.40.13444.38
    21156.90.13404.321143.10.13384.401171.80.13394.40
    31628.20.13344.331609.40.13324.411642.20.13344.32
    42096.60.13294.352072.60.13274.442110.00.13284.28
    52561.90.13234.392532.60.13214.482575.70.13234.31
    3(3/2)4(1/2)${2^2}\Pi $
    0160.50.11184.32165.50.11134.44153.70.11194.42
    1519.50.11144.31517.20.11094.44508.80.11144.38
    2876.80.11094.29866.90.11044.42862.30.11084.37
    31232.50.11054.291214.70.11004.431214.10.11044.33
    41586.40.11014.321560.60.10954.461564.30.10994.34
    51938.30.10974.341904.30.10904.491912.90.10954.35
    4(3/2)5(1/2)${3^2}\Pi $
    0169.70.11064.58170.60.11034.59163.40.11084.73
    1512.30.11014.59511.80.10984.60501.10.11024.54
    2852.60.10964.59850.70.10934.60839.60.10964.57
    31190.70.10914.601187.40.10894.611176.70.10914.58
    41526.50.10864.621521.90.10844.631512.00.10864.61
    51860.00.10814.621854.00.10794.641845.00.10814.64
    6(1/2)5(3/2)${1^4}{\Sigma ^ - }$
    0131.60.12045.73128.30.12035.80151.10.12155.33
    1479.40.11975.60473.60.11965.72517.90.12145.42
    2826.20.11905.66817.00.11895.75881.00.12046.22
    31170.20.11835.851157.70.11825.861230.60.11946.24
    41510.20.11775.911494.90.11755.911571.70.11865.89
    51846.60.11715.661828.60.11695.821909.20.11795.87
    2(1/2)3(1/2)$1{}^4\Pi $
    0170.10.11064.55170.30.11064.55160.20.11114.73
    1514.30.11024.55514.00.11014.56499.20.11044.56
    2856.30.10974.56855.50.10964.57838.70.10994.63
    31196.00.10924.571194.70.10914.581176.20.10944.65
    41533.50.10874.581531.60.10864.591511.40.10894.67
    51868.70.10824.581866.20.10814.601844.20.10844.69
    2(3/2)1(5/2)
    0168.80.11084.56170.40.11054.57
    1513.40.11034.57513.20.11004.58
    2855.60.10984.58853.60.10954.58
    31195.50.10934.591191.70.10904.60
    41533.00.10884.601527.50.10854.61
    51868.20.10834.611860.80.10804.62
    下载: 导出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).

    vGvBv107DvGvBv107DvvGvBv108Dv
    PS X(1/2)PS X(3/2)AsS X(3/2)
    0368.40.295501.91368.20.295511.9131952.30.181087.90
    0.29649 a1.85 a0.29695 a1.9 a0.18116(8) b8.6(5) b
    11101.30.293941.921100.80.293941.9242501.20.180247.93
    0.29469 a1.7 a0.29543 a1.8 a0.18033(4) b8.7(8) b
    21828.20.292371.921827.20.292371.9253046.00.179397.93
    0.29333 a1.9 a0.29385 a2.0 a0.17950(4) b8.8(7) b
    32549.00.290781.922547.60.290781.9263587.00.178537.89
    0.29161 a1.85 a0.29223 a1.95 a0.17865(5) b9.1(9) b
    43264.00.289181.923262.20.289171.9374124.10.177657.85
    0.29015 a1.9 a0.29065 a1.8 a0.17782(4) b9.7(8) b
    53973.20.287561.933971.00.287551.93
    0.28855 a2.0 a0.28933 a1.8 aBiS X(1/2)
    64676.70.285951.944674.00.285941.940213.90.113443.19
    0.28710 a1.9 a0.28740 a2.0 a0.112764(5) c3.34(4) c
    75374.20.284341.955371.00.284321.951641.00.113023.19
    0.28653 a1.7 a21065.60.112603.19
    86065.70.282731.966061.90.282711.9631488.00.112183.20
    0.28416 a2.0 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.
    下载: 导出CSV
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