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BH分子8个Λ-S态和23个Ω态光谱性质的理论研究

邢伟 李胜周 孙金锋 李文涛 朱遵略 刘锋

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BH分子8个Λ-S态和23个Ω态光谱性质的理论研究

邢伟, 李胜周, 孙金锋, 李文涛, 朱遵略, 刘锋

Theoretical study on spectroscopic properties of 8 Λ-S and 23 Ω states for BH molecule

Xing Wei, Li Sheng–Zhou, Sun Jin–Feng, Li Wen–Tao, Zhu Zun–Lüe, Liu Feng
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  • 本文利用内收缩多参考组态相互作用方法计算了BH分子8个低电子态(X1Σ+, a3Π, A1Π, b3Σ, 23Π, 13Σ+, 15Σ和15Π)和在自旋-轨道耦合效应下所产生的23个Ω态的势能曲线、以及${\rm{X}}{}^1\Sigma _{{0^ + }}^ +$, ${{\rm{a}}^3}{\Pi _{{0^ + }}}$, ${{\rm{a}}^3}{\Pi _1}$, ${{\rm{a}}^3}{\Pi _2}$${{\rm{A}}^1}{\Pi _1}$态之间6对跃迁的跃迁偶极矩. 为了获得精确的势能曲线, 计算中修正了单双电子激发、核价相关效应、相对论效应和基组截断带来的误差. 获得的BH分子的光谱和跃迁数据与现有的理论值和实验值符合得很好. 计算结果表明: BH分子的A1Π1(υ' = 0 – 2, J' = 1, +) →$ {\text{X}}{}^1\Sigma _{{0^ + }}^ + $(υ′′ = 0 – 2, J ′′ = 1, –)跃迁具有较大的爱因斯坦A系数和加权的吸收振子强度、高度对角化分布的振动分支比, A1Π1态具有较短的辐射寿命. 另外, ${{\rm{a}}^3}{\Pi _{{0^ + }}}$和a3Π1态对A1Π1(υ' = 0) ↔ $ {\rm X}^1\Sigma _{{0^ + }}^ + $(υ′′ = 0)循环跃迁的影响可以忽略. 因此, 基于A1Π1(υ'= 0—1, J ′ = 1, +) ↔ $ {\rm X}^1\Sigma _{{0^ + }}^ + $(υ′′ = 0—3, J′′ = 1, –)循环跃迁, 我们提出了用一束主冷却激光(λ00 = 432.45 nm)和两束再泵浦激光(λ10 = 479.67 nm和λ21 = 481.40 nm)冷却BH分子的方案, 并评价了冷却效果.
    In this work, the potential energy curves of eight low electronic states (X1Σ+, a3Π, A1Π, b3Σ-, 23Π, 13Σ+, 15Σ-, and 15Π) and twenty-three Ω states of BH molecule, and the transition dipole moments among the $ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $, $ {{\text{a}}^{\text{3}}}{\Pi_{{{\text{0}}^ + }}} $, a3Π1, a3Π2, and A1Π1 states are calculated by using the internally contracted multireference configuration interaction (icMRCI) method. In order to obtain the accurate potential energy curve, the errors caused by single and double electron excitation, core-valence correlation effects, relativistic effects and basis set truncation are corrected. The spectral and transition data of BH molecule are in good agreement with the available theoretical and experimental data. The calculation results show that the A1Π1(υ′ = 0-2, J′ = 1, +) →$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′ = 0-2, J′′ = 1, –) transition has large Einstein A-coefficient, weighted absorption oscillator strength, and highly diagonal vibrational branching ratio Rυ′υ′′, and the excited state A1Π1(υ′ = 0, 1) have short spontaneous radiation lifetimes. Moreover, the effects of $ {{\text{a}}^{\text{3}}}{\Pi_{{{\text{0}}^ + }}} $and a3Π1 states on A1Π1(υ′ = 0) ↔ $ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′ = 0) cycle transition can be ignored. Therefore, according to the A1Π1(υ′ = 0-1, J′ = 1, +) ↔ $ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′ = 0-3, J′′ = 1, –) cycle transition, we propose to apply one main cooling laser (λ00 = 432.45 nm) and two repumping lasers (λ10 = 479.67 nm and λ21 = 481.40 nm) to laser cooling BH molecules, and evaluation of the cooling effect.
      通信作者: 邢伟, wei19820403@163.com
    • 基金项目: 国家自然科学基金(批准号: 61275132, 11274097)、河南省自然科学基金(批准号: 212300410233)、河南省高等学校重点科研项目(批准号: 21A140023)和信阳师范学院南湖学者奖励计划青年项目资助的课题.
      Corresponding author: Xing Wei, wei19820403@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61275132, 11274097), the Natural Science Foundation of Henan Province, China (Grant No. 212300410233), the Key Scientific Research Prgoram of Higher Education of Henan Province, China (Grant No. 21A140023), and the Nanhu Scholars Program for Young Scholars of XYNU, China.
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  • 图 1  BH分子8个Λ-S态的势能曲线

    Fig. 1.  Potential energy curves of 8Λ-S states of the BH molecule.

    图 2  BH分子23个Ω态的势能曲线

    Fig. 2.  Potential energy curves of 23 Ω states of the BH molecule.

    图 3  BH分子6对跃迁的跃迁偶极矩曲线

    Fig. 3.  Curves of the transition dipole moments versus internuclear separation of six-pair states of the BH molecule.

    图 4  利用A1Π1(υ′) ↔$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′)跃迁进行激光冷却BH分子的方案. 虚线表示A1Π1(υ′ = 0, 1) →$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′ = 0 –3)跃迁的自发辐射振动分支比(Rυ′υ′′). 红色实线表示激光驱动$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′) → A1Π1 (υ′)跃迁

    Fig. 4.  The proposed laser cooling scheme for the BH using A1Π1(υ′) ↔$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′) transition. The dotted line indicate the spontaneous radiation vibrational branching ratio (Rυ′υ′′) of A1Π1(υ′ = 0, 1) →$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′ = 0 – 3) transition. The red solid line indicate the wavelength (λυ′′υ′) at which the laser drives the $ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′) →A1Π1 (υ′). transition.

    表 1  BH分子前两个离解极限产生的8个Λ-S态的离解关系

    Table 1.  Dissociation relationships of the 8 Λ –S states generated from the first two dissociation asymptotes of the BH molecule

    离解极限Λ-S态能级a/cm–1
    本文实验[30]理论[31]
    B(2Pu) + H(2Sg)X1Σ+, a3Π, A1Π, 13Σ+0.000.000.00
    B(4Pg) + H(2Sg)b3Σ, 15Σ, 23Π, 15Π28907.6628644.99+xb28932.70
    a, 4Pg态能级为4P1/2, 4P3/24P5/2能级的算术平均值减去2P3/22P1/2能级的算术平均值; b, 4P5/2能级外推值的不确定度.
    下载: 导出CSV

    表 2  icMRCI + Q/56 + CV + SR理论水平上BH分子7个Λ-S态的光谱常数

    Table 2.  Spectroscopic parameters of the 7 Λ-S states of BH at level of icMRCI + Q/56 + CV + SR.

    Λ-S态来源Te/cm–1Re/nmωe/cm–1ωexe/cm–1Be/cm–1αe/(102 cm–1)De/eV
    X1Σ+本文00.122952367.2848.778212.039537.09853.7137
    实验[8]00.123222366.7349.338412.025542.1516
    实验[10]02366.7349.339812.025842.1565
    实验[12]02364.6647.709812.025742.15913.6476±0.0037a
    实验[13]00.123222366.7349.340512.025542.1450
    理论[5]00.122902352.044.012.0863.6863
    理论[15]00.12301237946.7912.073.70
    理论[16]00.12312237812.0553.578b
    理论[17]00.1230235948.841.83.6773
    理论[18]00.123272368.4850.695712.11043.053.6580
    理论[19]00.123003.6751
    理论[20]00.122932365.6947.231012.080141.63.6851
    a3Π本文10944.320.118992625.9759.417712.891941.64042.3507
    实验[14]xc0.119002625.1455.784012.893141.56102.3867
    理论[5]10645.00.119002961.0109.612.9042.3806
    理论[15]0.11913265362.7012.872.38
    理论[17]105830.11900262560.445.52.3677
    理论[18]9557.670.119252598.9846.630012.940042.532.3135
    A1Π本文23203.520.122232253.2836.831011.834311.62540.8368
    实验[10]23135.440.12195d2251.4656.572512.2003553.76700.697d
    实验[12]23105.102342.41127.761812.1998653.67360.7786±0.0037a
    理论[5]22997.900.122102404.60147.312.27950.9098
    理论[15]0.122132320136.512.240.71
    理论[16]230610.12235229012.200.73b
    理论[17]231440.12222341129.685.10.8109
    理论[18]22260.890.122672280.2693.623312.22960.830.7536
    理论[19]23099.840.122122343.96128.17812.283674.00.8938
    b3Σ本文38238.630.121642440.8954.447712.250833.67122.5959
    实验[14]xc+27152.750.1216252438.1055.56212.342643.0872.5987
    理论[15]0.12256234548.4512.162.54
    理论[17]377080.1217243057.345.92.5845
    理论[18]36859.520.121992428.3355.40912.28444.312.5403
    23Π本文50730.460.192151273.8920.78964.944713.09571.0467
    理论[15]0.19338142557.044.881.04
    理论[17]502160.1931129538.69.91.0321
    13Σ+本文51738.070.125920.0031
    理论[17]516880.123
    15Σ本文58295.540.16981634.868167.6766.51936192.6410.1093
    理论[17]576740.170152887.3153.20.1084
    a, 文献[11]中的值; b, D0值; c, x表示a3Π态相对于X1Σ+态的Te值; d, 文献[7]中的值.
    下载: 导出CSV

    表 3  BH分子23个Ω态的离解关系

    Table 3.  Dissociation relationships of the 23 Ω states of the BH molecule.

    原子态(B + H)Ω态能级/cm–1
    本文实验[30]
    B(2P1/2) + H(2S1/2)0, 0+, 10.000.00
    B(2P3/2) + H(2S1/2)2, 1(2), 0+, 014.57215.287
    B(4P1/2) + H(2S1/2)0, 0+, 128910.6328647.43+x a
    B(4P3/2) + H(2S1/2)2, 1(2), 0+, 028914.6728652.07+x a
    B(4P5/2) + H(2S1/2)3, 2(2), 1(2), 0+, 028921.4128658.40+x a
    a, 4P5/2能级外推值的不确定度.
    下载: 导出CSV

    表 4  利用icMRCI + Q/56 + CV + SR + SOC理论计算获得的17个Ω态的光谱常数

    Table 4.  Spectroscopic parameters obtained by the icMRCI + Q/56 + CV + SR + SOC calculations for the 17 Ω states.

    Ω态Te/cm–1Re/nmωe/cm–1ωexe/cm–1Be/cm–1102αe/cm–1De/eVRe附近主要的Λ–S态/%
    $ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $00.122952367.2848.778312.039537.09853.7138X1Σ+ (100.00)
    ${\text{a} }{}^{\text{3} }{\Pi_{ { {\text{0} }^{{ - } } } }}$10940.360.118992625.9359.416512.891841.64262.3506a3Π (100.00)
    $ {\text{a}}{}^{\text{3}}{\Pi_{{{\text{0}}^ + }}} $10940.370.118992625.9359.419212.891841.64242.3506a3Π (100.00)
    a3Π110944.320.118992625.9759.414012.891941.64032.3513a3Π (100.00)
    a3Π210948.490.118992626.0159.413112.891941.63842.3509a3Π (100.00)
    A1Π123203.520.122232253.2836.831711.833811.70340.9051A1Π (100.00)
    (3)0+第一势阱38244.330.121632438.0844.728112.292538.30411.5501b3Σ (100.00)
    (3)0+第二势阱50725.860.192130.002623Π (100.00)
    (3)138244.350.121632447.6954.293412.316737.61490.8995b3Σ (100.00)
    (4)145758.490.164964850.091293.006.739524.021681.662913Σ+ (100.00)
    ${\text{2} }{}^{\text{3} }{\Pi_{ { {\text{0} }^{ { - } } } } }$50726.070.192141274.0020.84504.944703.096111.046623Π (100.00)
    (4)0+50726.510.188602344.5477.797616.561629.69761.0478b3Σ (99.82), 23Π (0.18)
    (5)150728.050.188632531.33412.6715.2041561.47521.0476b3Σ (99.92), 23Π (0.08)
    23Π250734.850.192151273.8620.79034.944713.095201.046723Π (100.00)
    ${\text{1} }{}^{\text{3} }{\Sigma}_{ { {\text{0} }^{{ - } } } }^ +$51738.080.125920.003113Σ+ (100.00)
    ${\text{1} }{}^{\text{5} }{\Sigma}_{ { {\text{0} }^{{ - } } } }^{{ - } }$58295.530.16981634.857167.6536.51872192.4710.109615Σ (100.00)
    ${\text{1} }{}^{\text{5} }{\Sigma}_{\text{2} }^{{ - } }$58295.550.16981634.862167.6606.51884192.5020.109615Σ (100.00)
    ${\text{1} }{}^{\text{5} }{\Sigma}_{\text{2} }^{{ - } }$58295.570.16981634.867167.6696.51902192.5500.109515Σ (100.00)
    下载: 导出CSV

    表 5  A1Π1(υ′, J′ = 1, +) → $ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′, J′′ = 1, –)跃迁的跃迁波数(${\tilde v} $)、爱因斯坦A系数(Aυ′υ′′)、振动分支比(Rυ′υ′′)、波长(λυ′υ′′)、加权的吸收振子强度(gfυ′υ′′)

    Table 5.  The transition wavenumber (${\tilde v} $), Einstein A-coefficients (Aυ′υ′′), vibrational branching ratios (Rυ′υ′′), wavelength (λυ′υ′′), and weighted absorption oscillator strengths (gfυ′υ′′) for the A1Π1(υ′, J′ = 1, +) → $ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′, J′′ = 1, –) transitions.

    υ′–υ${\tilde v}/$cm–1Aυ′υ′′/sRυ′υ′′λυ′υ′′/nmgfυ′υ′′ υ′–υ${\tilde v} $/cm–1Aυ′υ′′/sRυ′υ′′λυ′υ′′/nmgfυ′υ′′
    0-023140.447.98×1060.9912432.450.0067 1-025243.779.61×1040.0138396.426.78×10–4
    0-120862.556.67×1040.0083479.676.89×10–41-122965.886.80×1060.9777435.740.0580
    0-218684.363.86×1034.79×10–4535.594.97×10–51-220787.694.72×1040.0068481.404.91×10–4
    0-316602.974.43×1015.50×10–6602.737.22×10–71-318706.301.13×1040.0016534.961.45×10–4
    0-414612.081.752.17×10–7684.853.69×10–81-416715.407.15×1011.03×10–5598.681.15×10–6
    2-027090.981.76×1033.10×10–4369.391.08×10–53-028588.601.08×1032.66×10–4350.045.95×10–6
    2-124813.094.31×1050.0759403.300.00323-126310.721.89×1034.66×10–4380.341.23×10–5
    2-222634.905.22×1060.9192442.110.04583-224132.531.16×1060.2858414.670.0090
    2-320553.511.38×1032.43×10–4486.881.47×10–53-322051.132.80×1060.6887453.810.0259
    2-418562.622.46×1040.0043539.103.21×10–43-420060.244.31×1040.0106498.854.82×10–4
    2-516658.641.50×1012.64×10–6600.722.43×10–73-518156.265.40×1040.1330551.177.37×10–4
    下载: 导出CSV

    表 7  a3Π1(υ′, J′ = 1, +) →$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′, J′′ = 1, –)跃迁的跃迁波数(${\tilde v} $)、爱因斯坦A系数(Aυ′υ′′)、振动分支比(Rυ′υ′′)、波长(λυ′υ′′)、加权的吸收振子强度(gfυ′υ′′)

    Table 7.  The transition wavenumber (${\tilde v} $), Einstein A-coefficients(Aυ′υ′′), vibrational branching ratios (Rυ′υ′′), wavelength (λυ′υ′′), and weighted absorption oscillator strengths (gfυ′υ′′) for the a3Π1(υ′, J′ = 1, +) →$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′, J′′ = 1, –).

    υ′–υ${\tilde v} $/cm–1Aυ′υ′′/sRυ′υ′′λυ′υ′′/nmgfυ′υ′′ υ′–υ${\tilde v} $/cm–1Aυ′υ′′/sRυ′υ′′λυ′υ′′/nmgfυ′υ′′
    0-011039.580.12780.9615906.484.72×10–9 1-013546.430.00810.0607738.731.98×10–10
    0-18761.690.00500.03741142.142.91×10–101-111268.540.11480.8613888.064.07×10–9
    0-26583.501.48×10–40.00111520.031.54×10–111-29090.350.00990.07391100.855.36×10–10
    0-34502.113.00×10–62.25×10–52222.766.65×10–131-37008.965.33×10–40.00401427.764.88×10–11
    0-42511.213.32×10–82.50×10–73984.982.37×10–141-45018.071.86×10–51.39×10–41994.223.32×10–12
    2-015928.882.81×10–52.12×10–4628.244.98×10–133-018182.601.94×10–61.47×10–5550.372.63×10–14
    2-113651.000.01520.1142733.073.66×10–103-115904.715.54×10–54.22×10–4629.199.84×10–13
    2-211472.810.10230.7703872.253.49×10–93-213726.520.02110.1607729.045.04×10–10
    2-39391.410.01410.10591065.567.17×10–103-311645.130.09120.6945859.343.03×10–9
    2-47400.520.00120.00891352.229.71×10–113-49654.230.01680.12771036.558.09×10–10
    下载: 导出CSV

    表 6  $ {{\text{a}}^{\text{3}}}{\Pi_{{{\text{0}}^ + }}} $(υ′, J′ = 0, + ) →$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′, J′′ = 1, –)跃迁的跃迁波数(${\tilde v} $)、爱因斯坦A系数(Aυ′υ′′)、振动分支比(Rυ′υ′′)、波长(λυ′υ′′)、加权的吸收振子强度(gfυ′υ′′)

    Table 6.  The transition wavenumber(${\tilde v} $), Einstein A-coefficients(Aυ′υ′′), vibrational branching ratios (Rυ′υ′′), wavelength (λυ′υ′′), and weighted absorption oscillator strengths (gfυ′υ′′) for the $ {{\text{a}}^{\text{3}}}{\Pi_{{{\text{0}}^ + }}} $(υ′, J′ = 0, + ) →$ {\text{X}}{}^{\text{1}}{\Sigma}_{{{\text{0}}^ + }}^ + $(υ′′, J′′ = 1, –) transitions.

    υ′–υ${\tilde v} $/cm–1Aυ′υ′′/sRυ′υ′′λυ′υ′′/nmgfυ′υ′′ υ′–υ${\tilde v} $/cm–1Aυ′υ′′/sRυ′υ′′λυ′υ′′/nmgfυ′υ′′
    0-011039.100.18780.8913906.522.31×10–9 1-013546.355.67×10–40.0030738.734.63×10–12
    0-18761.220.02160.10271142.214.22×10–101-111268.460.14410.7666888.061.70×10–9
    0-26583.030.00120.00581520.144.24×10–111-29090.270.03910.20821100.867.10×10–10
    0-34501.634.60×10–52.18×10–42223.003.40×10–121-37008.880.00390.02091427.781.20×10–10
    0-42510.749.71×10–74.61×10–63985.722.31×10–131-45017.982.33×10–40.00121994.251.39×10–11
    2-015929.213.36×10–40.0020628.221.98×10–123-018183.371.76×10–61.12×10–5550.347.97×10–15
    2-113651.320.00230.0142733.051.84×10–113-115905.489.50×10–40.0061629.165.63×10–12
    2-211473.130.10810.6354872.221.23×10–93-213727.290.00500.0320728.993.99×10–11
    2-39391.740.05070.29821065.528.62×10–103-311645.900.08170.5216859.289.03×10–10
    2-47400.840.00800.04681352.162.18×10–103-49655.010.05420.34641036.478.72×10–10
    下载: 导出CSV

    表 8  A1Π1(υ′, J′ = 1, +), $ {{\text{a}}^{\text{3}}}{\Pi _{{0^ + }}} $(υ′, J′ = 0, + )和a3Π1(υ′, J′ = 1, +)态的辐射寿命(τυ)

    Table 8.  Spontaneous radiative lifetimes(τυ′) for the A1Π1(υ′, J′ = 1, +), $ {{\text{a}}^{\text{3}}}{\Pi _{{0^ + }}} $(υ′, J′ = 0, +)和a3Π1(υ′, J′ = 1, +) transitions

    υ$ {\text{a}}{}^{\text{3}}{\Pi_{{{\text{0}}^ + }}} $/s a3Π1/s A1Π1/ns
    总和/ns$ {\text{A}}{}^{\text{1}}{\Pi_{\text{1}}}{\text{ - }}{{\text{X}}^{\text{1}}}{\Sigma}_{{{\text{0}}^ + }}^ + $/ns$ {\text{A}}{}^{\text{1}}{\Pi_{\text{1}}} $-$ {\text{a}}{}^{\text{3}}{\Pi_{{{\text{0}}^ + }}} $/sA1Π1– a3Π1/sA1Π1– a3Π2/s
    04.75 7.52 124.18124.182.71111.48177.04
    15.327.50143.86143.863.0390.08116.30
    25.887.53176.12176.123.5883.05192.36
    36.397.61246.20246.204.7793.55255.19
    46.857.78
    57.278.09
    下载: 导出CSV
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  • 收稿日期:  2022-01-07
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