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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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出版历程
  • 收稿日期:  2021-08-05
  • 修回日期:  2021-09-17
  • 上网日期:  2022-01-13
  • 刊出日期:  2022-01-20

SbS电子基态及激发态势能曲线和振动能级的理论研究

    基金项目: 国家自然科学基金(批准号: 11804031)资助的课题

摘要: 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.

English Abstract

    • 含硫双原子体系在天体物理学、大气化学、燃烧化学、分子反应动力学等众多领域承担着重要角色, 因此一直是相关领域的关注对象. 硫化锑(SbS)具备优异的稳定性和丰富的元素储存, 因有较大的吸收系数和1.7 eV的带隙宽度, 作为良好的半导体材料和光敏材料得到了广泛应用[1-5], 而且锑基硫族化合物也满足叠层太阳能电池的要求, 有助于提高光电转换效率[6]. Shimauchi和Nishiyama[7]于1968年对SbS自由基的电子结构与发射电子光谱进行了报道, 他们确定了7个电子激发态至基态的电子跃迁谱带的带头波长, 但没有对激发态进行标识. Ω基态的谐振频率分别为480 cm–1和470 cm–1, 而7个激发态的谐振频率介于296—442 cm–1之间. 除此以外, 其他光谱常数目前仍然未知.

      对氮族元素硫化物自由基的研究始于1932年对NS的$ {{\text{B}}^2}{\Sigma ^ + } \to {{\text{X}}^2}\Pi $$ {{\text{A}}^2}\Pi \to {{\text{X}}^2}\Pi $谱带的实验探测[8]. 1951年和1954年, Zeeman等[9,10]分别对这两个谱带进行了实验光谱转动分析. 此后开展的微波谱[11]、紫外与可见光[12-14]实验获得了丰富的电子激发态光谱常数与基态的精细结构常数. 对PS自由基的光谱研究源于对紫外与可见光波段$ {{\text{C}}^2}\Sigma - $$ {{\text{X}}^2}\Pi $$ {{\text{B}}^2}\Pi - {{\text{X}}^2}\Pi $谱带的实验探测. 1955—1979年[15-20], 若干个工作组探测到了这两个谱带的大量谱线, 通过转动分析确定了各电子态的光谱常数. 随后, 该体系的近红外[21]、毫米波[22]与亚毫米波[23]光谱也陆续被探测获得. Shimauchi 研究组[24-28]在1969—1973年对AsS的光谱开展了系列研究, 获得了$ {{\text{A}}^2}{\Pi _{3/2}} - {{\text{X}}^2}{\Pi _{3/2}} $跃迁的大量数据及各电子态的分子常数. 1967年Barrow等[29]首次对BiS的可见光谱进行了探测. Patiño等[30]于1984年研究了BiS的$ {{\text{A}}^2}{\Pi _{1/2}} - {{\text{X}}^2}{\Pi _{1/2}} $谱带高J量子数跃迁的超精细双分裂结构, 确定了$ {{\text{X}}^2}{\Pi _{1/2}} $态的分子常数. 借助傅里叶变换光谱仪, BiS的近红外[31,32]、微波谱[31]和可见光光谱[32]也被探测到, 涉及${\text{X}}{}^2{\Pi _{1/2}}$${\text{X}}{}^2{\Pi _{3/2}}$态的分子常数得以确定.

      在理论研究方面, Hartree-Fock方法(HF)[33]、组态相互作用(CI)[34]、多参考双重激发组态相互作用(MRDCI)[35-37]、密度泛函理论(DFT)[38]、广义价键(GVB)[39]、二阶Møller-Plesset微扰理论(MP2)[39]、完全活性空间-平均耦合对泛函(CAS-ACPF)[40]、单双迭代包括三重激发的耦合簇[CCSD(T)][41,42]及其显关联方法CCSD(T)-F12[43]、Gaussian-3(G3)[44]、多参考组态相互作用(MRCI)[45-52]及Rydberg-Klein-Rees (RKR)[53]等计算方法均被用于确定NS, PS, AsS和BiS等4种含硫双原子体系各电子态的结构参数、光谱常数、振动能级以及跃迁性质等, 将所得计算数据分别与各自的实验数据进行了比较. 并且预测了实验中没有涉及的Λ-S态及Ω激发电子态的特性, 得到了这些态的跃迁偶极矩、弗兰克-康登因子、爱因斯坦系数及自发辐射寿命等数据.

      与对氮族元素硫化物自由基的结构和光谱的众多研究所获得的丰富的数据及结论相比, 对SbS自由基的相关研究明显不足. 除了前文提到的一篇实验研究报道[7]外, 到目前为止还没有相关的理论研究. 因此, 本文对SbS的结构和电子态进行了系统研究, 以填补相关数据的空白.

    • 基于完全活性空间自洽场方法[54]构建了CI波函数, 借助包含Davidson修正的多参考组态相互作用(MRCI+Q)方法[55], 计算了SbS前三个离解极限27个Λ-S电子态的能量. 对S原子和Sb原子分别选用aug-cc-pwCV5Z全电子基组[56]与aug-cc-pwCV5 Z-PP标量相对论基组[57], 其中Sb原子的1s—3d电子用相对论有效原子实势ECP28MDF取代. 计算中将Sb原子的4s4p与S原子的1s电子作为芯电子, Sb原子的4d和S原子的2s2p原子轨道作为闭壳层分子轨道, Sb原子的5s5p与S原子的3s3p原子轨道作为活性分子轨道. 以C2v群替代SbS的简并对称性Cv群, 用其不可约表示a1, b1, b2a2表示的双占据闭壳层轨道和活性轨道分别为(4, 2, 2, 1)与(4, 2, 2, 0). 能量点的计算范围是1.7 Å—10.0 Å (1 Å = 0.1 nm), 最小扫描步长为0.05 Å, 每条势能曲线计算了51个数据点.

      在考虑核价相关修正和标量相对论修正后, 通过Murrell-Sorbie(M-S)势能函数[58]拟合单点能得到电子态的势能曲线, 然后通过均方根值(RMS)来评估拟合效果. M-S函数是能够较好地反映双原子体系势能函数的解析表达式之一, 本研究组也已经基于该势能函数研究了NS[59], SCl+[60,61], SCl [60], SF±[62], MgS+[63], SH[64]等若干含硫双原子体系. M-S势能函数定义为:

      $ V(\rho ) = - {D_{\text{e}}}\left(1 + \sum\limits_{i = 1}^{\text{n}} {{a_i}{\rho ^i}} \right)\exp ( - {a_1}\rho ), $

      其中, $ \rho = R - {R_{\text{e}}} $, $ R $$ {R_{\text{e}}} $分别是核间距以及平衡核间距, $ {D_{\text{e}}} $是离解能, $ {a_i} $是拟合参量.

      通过Breit-Pauli算符[65]考虑自旋-轨道耦合(SOC)效应可以计算得到Ω电子态的能量. 在核价相关修正和标量相对论修正的基础上, 将能量点通过最小二乘拟合法得到势能函数, 并计算出各电子态的光谱常数. 以上所有能量计算均基于MOLPRO软件[66]完成. 利用Level程序[67]还计算得出每个电子态的振动能级与转动常数.

      鉴于SbS还没有实验数据可做比较, 本文还计算了PS, AsS, BiS这3种氮族元素硫化物的若干电子态. 采用的方法与计算SbS的方法相同, 均通过MRCI+Q方法进行. 对S原子, N原子和P原子采用aug-cc-pwCV5Z基组[56], 对As原子和Bi原子采用aug-cc-pwCV5Z-PP基组[57], 其中分别包含ECP10MDF和ECP60MDF相对论有效原子实势. 得到了每一种体系第一离解极限的Λ-S电子态及其对应的Ω电子态能量, 进一步计算出每个电子态的光谱常数与振动能级.

    • SbS前三个离解极限相对能量的计算值及对应的电子态如表1所列, 本文计算值与实验值相比, 符合得很好. 例如S原子第一激发态1Dg相对基态3Pg的能量为9346 cm–1, 与实验值[68]相差约1.2%, 而Sb原子第一激发态2Du与基态4Su能量间隔为10022 cm–1, 高于实验值[68]约1.7%. 所有Λ-S电子态势能曲线如图1所示, 其中${{\text{1}}^4}{\Sigma ^ + }$, ${{\text{1}}^6}{\Sigma ^ + }$, $ {1^6}\Pi $, ${2^2}\Delta $, ${3^4}{\Sigma ^ + }$, ${3^4}\Delta $, ${1^4}\Phi $, $3{}^4\Pi $, $4{}^4\Pi $$5{}^4\Pi $为排斥态, 其余电子态均为束缚态.

      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

      表 1  SbS的Λ-S态离解极限

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

      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.

      基态${{\text{X}}^{\text{2}}}\Pi $与第一激发态${1^4}\Pi $Re附近的能量差超过了12800 cm–1, 并且没有其他电子态势能曲线与基态曲线交叉, 表明与其对应的Ω态不会受到其他Ω = 1/2或Ω = 3/2电子态的影响, 其光谱常数也不会有大的变化. 在R = 2.4—3.4 Å, E = 25000—40000 cm–1范围内, 激发态势能曲线产生了复杂的曲线(避免)交叉, 预示了在此范围内对其Ω态的分析将具有很大的挑战性.

      束缚态完整的光谱常数列于表2. 需要说明的是, 本文所得电子激发态的谐振频率总体上与文献[7]的数据(介于296—442 cm–1之间)是相符的, 但是由于文献[7]没有标识电子态, 因此无法与其数据进行比较. 拟合的RMS值均较小, 表明拟合质量较高. 基态${{\text{X}}^{\text{2}}}\Pi $主要由15σαβxαβyαβxα电子组态构成, 相比激发态其势阱最深, 但Re最小. 第一激发态${1^4}\Pi $通过7πy→8πy电子迁移形成, 虽然其Re与第二、第三激发态${{\text{2}}^{\text{2}}}\Pi $${{\text{3}}^{\text{2}}}\Pi $Re非常接近, 但均与基态相差超过9%, 因此可预测这几个低激发态至基态跃迁的弗兰克-康登因子偏小. ${{\text{2}}^{\text{2}}}\Pi $${{\text{3}}^{\text{2}}}\Pi $均呈现多组态特征, 贡献最大的电子组态分别由自旋取向不同的电子保持自旋方向性, 并从7πy迁移至8πy轨道而形成. ${1^4}{\Sigma ^ - }$的主要电子组态为15σαxαβyαβxαyα, 所占权重为83%. 8π→16σ的电子迁移形成${{\text{1}}^{\text{2}}}{\Sigma ^ + }$电子态. 除个别电子态以外, 大多数电子态均表现出较明显的多参考特性.

      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)

      表 2  SbS的Λ-S态光谱常数

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

      表3汇总了氮族元素硫化物自由基的光谱常数. 通过比较, 发现该系列硫化物基态${{\text{X}}^{\text{2}}}\Pi $的光谱常数体现了同族元素代换后的渐变规律性. 随着氮族元素核电荷数的增加, Re逐渐变大, 这源于氮族元素np3价电子的弥散性渐强, 而氮族元素与S原子之间的化学键减弱则导致谐振频率ωe逐渐减小.

      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.

      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.

    • 由于SbS电子态数量多且曲线(避免)交叉复杂, 本文仅对基态及部分低激发Ω态计算与讨论, 其势能曲线如图2所示. 计算涉及的Ω态离解极限, 即S原子3P2,1,0原子态能级间隔与实验数据[68]吻合很好, 第二、第三离解极限的计算值与实验值相差约为 3.6%和5.6% (见表4). 各电子态的光谱常数列于表5. 其中, 仅有Ω基态的谐振频率有实验值[7]可做比较, 本文计算值与实验值相符很好. 各势能曲线拟合的RMS值也比较令人满意.

      图  2  SbS的Ω态势能曲线

      Figure 2.  Potential energy curves of 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

      表 4  SbS自由基Ω态的离解极限

      Table 4.  Dissociation relationships 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

      表 5  SbS自由基的Ω态光谱常数

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

      在SOC作用下, Λ-S基态${{\text{X}}^{\text{2}}}\Pi $分裂为X(1/2)与X(3/2), 其中前者能量更低, 并且根据二者间能量差可预计其自旋-轨道耦合常数约为2025 cm–1. ${1^4}\Pi $分裂为2(1/2), 3(1/2), 2(3/2)和1(5/2), 裂距较小, 两相邻Ω态间的裂距只有基态裂距的11%. $2{}^2\Pi $分裂为裂距约700 cm–1的3(3/2)和4(1/2)电子态. 与${1^4}{\Sigma ^ - }$${{\text{3}}^{\text{2}}}\Pi $对应的Ω态势能曲线在约2.25 Å处产生了避免交叉. 对比表2的Λ-S态及表5中对应Ω态的数据, 发现光谱常数的变化不大, 证实了本文的预测. 以Re为例, Ω基态X(1/2)与X(3/2)相比, Λ-S基态${{\text{X}}^{\text{2}}}\Pi $的变化分别为0.02%和0.01%, 在表中所列电子态中是最小的, 因此可预测这两个态之间的跃迁会有较大的弗兰克-康登因子. Re变化率最大的态是6(1/2)和5(3/2), 不过二者也分别只比${1^4}{\Sigma ^ - }$减小了0.46%和0.52%. 从总体上看, SOC效应对这些电子态光谱常数的影响较小. 此外, 由于Ω基态与激发态Re相差达到了0.2 Å, 表明这些Ω态间跃迁的弗兰克-康登因子均较小.

      表6列出了氮族元素硫化物自由基Ω基态的光谱常数, 由图6可见, 本文计算值与实验值非常相符. 以BiS为例, X(1/2)与X(3/2)态Re的计算值均只与实验值[31,32]相差小于0.2%, ωe则分别高估了5%和2%左右. 计算值与实验值的一致性, 从侧面证明本文对SbS的计算结果具有很高的精度.

      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.

      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.

    • 通过求解核运动的径向薛定谔方程, 得到了SbS的${\text{X}}{}^2\Pi $, $1{}^4\Pi $, ${2^2}\Pi $, ${3^2}\Pi $, ${1^4}{\Sigma ^ - }$电子态及其对应Ω态的全部振动态. 表7列出了v = 0—5的振动能级、转动常数和离心畸变常数. 受SOC效应影响, Ω态中6(1/2)和5(3/2)的振动能级相比Λ-S态均降低了15%左右, 是这些低激发态中变化最大的. 该现象源于这两个态分别与5(1/2)和4(3/2)在Re附近产生曲线避免交叉, 使得6(1/2)和5(3/2)的势能曲线在Re处相比${1^4}{\Sigma ^ - }$Λ-S态的绝对能量降低了约300 cm–1. 总体上看, SOC效应对SbS四重态, 如$1{}^4\Pi $${1^4}{\Sigma ^ - }$影响相对更为显著, 而对二重态的影响则不明显.

      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

      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).

      为证明本文计算结果的准确性, 对验证计算并已获得光谱常数的PS, AsS和BiS进行了振动分析, 计算数据及相应实验结果列于表8可见, 本文计算得到的PS自由基X(1/2)与X(3/2)的转动常数及离心畸变常数与实验值[19]符合得非常好, 其中偏差最大的是X(3/2)态v = 7的转动常数(约0.8%), 其他能级转动常数与实验值的偏差均在0.5%左右. 对于AsS, X(3/2)态v = 3—7能级的转动常数与实验值[25]相差不到0.1%. 对于BiS来讲, 只有X(1/2)的振动能级有实验值[29], 计算值高估了实验值约0.6%.

      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.

      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).

    • 借助Level程序计算了若干Ω激发态至基态振动跃迁的爱因斯坦系数$ {A_{v'J'v''J''}} $及跃迁频率$ {v_{v'J'v''J''}} $. 通过(2)式计算了跃迁强度$ {I_{v'J'v''J''}} $, 式中$J' $是上态转动量子数, $ {E_{v''J''}} $是下态能量, Q(T)是对应温度T的配分函数, h, c, k是基本常量.

      $ {I_{v'J'v''J''}} {=} \dfrac{{(2J' {+} 1)\exp \left( - \dfrac{{hc{E_{v''J''}}}}{{kT}}\right)}}{{8{\text{π }}cv_{v'J'v''J''}^2Q}} \times {A_{v'J'v''J''}} . $

      图3(a)(c)所示, 在所有计算的谱带中, 2(1/2)→X(1/2)的$ v' \to v'' = 0, 1, 2 $跃迁强度相对更大, 主要分布在540—750 nm之间. 4(1/2)→X(1/2)与5(1/2)→X(1/2)谱带则主要位于400—550 nm波段, 其中前者除$ v' \to v'' = 0 $外跃迁强度均较小, 而后者$v' = 0, 1, 2, 3, 4 \to v''=0$ 跃迁则分布较密集. 6(1/2)→X(1/2)跃迁的最强谱带位于430 nm附近, $ v' \to v'' = 0, 1, 2 $跃迁的强度随$ v'' $的增加而渐大. 以上4个激发态至Ω基态的跃迁均位于可见光区域.

      图  3  SbS的振动谱带

      Figure 3.  Vibrational transition bands of SbS.

      图3(d)绘制了X(3/2)→X(1/2)跃迁的$ \Delta v = $$ - 1, {\text{ }}0, {\text{ }}1 $谱带(仅绘制出$ v' \leqslant 15 $). 3个谱带均位于中红外波段, 其分布与位于近红外波段的BiS相应谱带分布(文献[31], 图2)非常相似. 强度最大的$ \Delta v = 0 $谱带位于$ \Delta v = - 1 $$\Delta v = 1$谱带间, $ \Delta v = 1 $谱带的强度最小, 在3个谱带中位于长波长一端. 以上数据与结论均能够对SbS的光谱探测提供理论支持和数据支撑.

    • 通过MRCI+Q方法计算了SbS电子基态及低激发态的电子结构, 得到了能量最低的三个Λ-S离解极限所有的电子态及部分Ω态的势能曲线. 通过离解极限处的能量计算所得Sb原子与S原子的能级与实验值相符很好. 计算了各电子态的光谱常数、振动能级, 模拟了Ω激发态至基态的振动光谱, 为后续开展光谱探测提供了参考依据. 本文还对PS, AsS, BiS的电子态进行了验证计算, 所得的光谱常数和振动能级均与已有的实验结果相符, 间接证明本文SbS计算结果的可信度.

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