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7Li2(0, ±1)分子体系基态振-转能级的全电子计算

王巧霞 王玉敏 马日 闫冰

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7Li2(0, ±1)分子体系基态振-转能级的全电子计算

王巧霞, 王玉敏, 马日, 闫冰

All-electron calculation of ground state vibration-rotation energy levels of 7Li2(0, ±1) molecular systems

Wang Qiao-Xia, Wang Yu-Min, Ma Ri, Yan Bing
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  • 采用单参考与多参考耦合簇理论结合相关一致高斯基组计算研究了7Li2(0, ±1)分子体系的电子基态的势能曲线, 计算考虑了体系所有电子的关联效应与相对论效应, 拟合得到了体系的光谱常数, 并获得了电子基态的振动-转动能级信息. 计算得到的中性与阳离子体系的光谱常数与实验值符合得很好; 对于阴离子体系, 平衡核间距的计算仍需进一步改进, 其他光谱常数符合较好. 计算结果表明, 中性和阳离子体系基态波函数具有明显的单参考组态特点, 而阴离子分子基态应采用多参考组态波函数描述. 对于基态的振动-转动能级, 与现有实验值符合得很好; 尽管各种计算方法对阴离子基态的平衡核间距计算结果仍有差异, 但振动能级间隔的结果相互符合得很好. 本文的研究可为Li2分子体系基态, 尤其是光谱学信息很少的阴离子体系的电子结构与光谱的精确研究提供了有用的光谱信息.
    The investigation of spectroscopic information is important for understanding the mechanisms of molecular photochemical and photophysical reactions. As a prototype to study the electronic structures and spectra of diatomic molecular systems, the vibration-rotational spectra of alkali dimer and its ions have aroused considerable research interest in the last two decades. Single-reference and multi-reference coupled cluster theory in combination with correlation consistent Gaussian basis set are adopted to study the ground-state potential energy curves of 7Li2(0,± 1) molecular systems. The correlation effect and relativistic effect of all the electrons are taken into account in the calculation. And the spectroscopic constants, including the equilibrium internuclear distance Re, the harmonic vibrational frequency ωe, the anharmonic constant ωexe, the equilibrium rotational constant Be, and the dissociation energy De of the molecular system and vibration-rotational energy level information of the ground states are obtained by solving the radial Schrödinger equations. The calculated spectroscopic constants of the neutral and positive ion system accord well with the experimental values; however for the negative ion system, the calculation of equilibrium internuclear distance needs further improving, and other spectroscopic constants are consistent well with the experimental values. The present computational results indicate that the ground state wave functions of neutral and positive ion systems have obvious single reference configuration characteristics, while the ground state of negative ion molecule system should be described with multireference configuration wave functions. The vibration-rotational energy levels of ground state with different theoretical methods are in good agreement with the experimental values. The vibrational-rotational energy levels and spectroscopic constants of neutral and positive ion systems are well reproduced, and some experimental information about spectrum is still lacking. Although the difference among the equilibrium internuclear distances for the ground state of the negative ion, obtained from different theoretical methods are still existent, the results of the vibrational level interval accord well with each other. This study provides useful information about spectrum for accurately investigating the electronic structures and spectra of the ground state of Li2 molecular system and its two isotopic molecules, especially for the negative ion system with little information about spectrum.
      通信作者: 马日, rma@jlu.edu.cn ; 闫冰, yanbing@jlu.edu.cn
    • 基金项目: 国家重点研发计划(批准号: 2017YFA0403300)、国家自然科学基金(批准号: 91750104, 11574114, 11874177)和吉林省自然科学基金(批准号: 20160101332JC)资助的课题.
      Corresponding author: Ma Ri, rma@jlu.edu.cn ; Yan Bing, yanbing@jlu.edu.cn
    • Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0403300), the National Natural Science Foundation of China (Grant Nos. 91750104, 11574114, 11874177), and the Jilin Provincial National Science Foundation, China (Grant No. 20160101332JC).
    [1]

    Gardet G, Rogemond F, Chermette H 1996 J. Chem. Phys. 105 9933Google Scholar

    [2]

    Barakat B, Bacis R, Carrot F, Churassy S, Crozet P, Martin F, Verges J 1986 Chem. Phys. 102 215Google Scholar

    [3]

    Maniero A M, Acioli P H 2005 Int. J. Quantum Chem. 103 711Google Scholar

    [4]

    Schmidt-Mink I, Müller W, Meyer W 1985 Chem. Phys. 92 263Google Scholar

    [5]

    Bernheim R A, Gold L P, Tipton T 1983 J. Chem. Phys. 78 3635Google Scholar

    [6]

    Hessel M M, Vidal C R 1979 J. Chem. Phys. 70 4439Google Scholar

    [7]

    Bernheim R A, Gold L P, Tipton T, Konowalow D D 1984 Chem. Phys. Lett. 105 201Google Scholar

    [8]

    Blustin P H, Linnett J W 1974 J. Chem. Soc. Faraday Trans. 2 Mol. Chem. Phys. 70 826Google Scholar

    [9]

    Sarkas H W, Arnold S T, Hendricks J H, Slager V L, Bowen K H 1994 Z. Phys. D 29 209Google Scholar

    [10]

    Hogreve H 2000 Eur. Phys. J. D 8 85Google Scholar

    [11]

    Nasiri S, Zahedi M 2017 Comput. Theor. Chem. 1114 106Google Scholar

    [12]

    Brito B G A, Hai G Q, Cândido L 2017 J. Chem. Phys. 146 174306Google Scholar

    [13]

    Rabli D, McCarroll R 2017 Chem. Phys. 487 23Google Scholar

    [14]

    魏长立, 梁桂颖, 刘晓婷, 颜培源, 闫冰 2016 物理学报 65 163101Google Scholar

    Wei C L, Liang G Y, Liu X T, Yan P Y, Yan B 2016 Acta Phys. Sin. 65 163101Google Scholar

    [15]

    Yang X, Xu H, Yan B 2019 Chin. Phys. B 28 348

    [16]

    Zhang L L, Gao S B, Meng Q T, Song Y Z 2015 Chin. Phys. B 24 201

    [17]

    Wei C L, Zhang X M, Ding D J, Yan B 2016 Chin. Phys. B 25 13102Google Scholar

    [18]

    Hampel C, Peterson K A, Werner H J 1992 Chem. Phys. Lett. 190 1Google Scholar

    [19]

    Knowles P J, Hampel C, Werner H 1993 J. Chem. Phys. 99 5219Google Scholar

    [20]

    Werner H J, Knowles P J, G Knizia, et al. http://www. molpro.net. [2019-3-10]

    [21]

    Rolik Z, Szegedy L, Ladjánszki I, Ladóczki B, Kállay M 2013 J. Chem. Phys. 139 094105Google Scholar

    [22]

    Prascher B P, Woon D E, Peterson K A, Dunning T H, Wilson A K 2011 Theor. Chem. Acc. 128 69Google Scholar

    [23]

    Wolf A, Reiher M, Hess B A 2002 J. Chem. Phys. 117 9215Google Scholar

    [24]

    Le Roy R J 2017 J. Quant. Spectrosc. Radiat. Transf. 186 167Google Scholar

    [25]

    Magnier S, Rousseau S, Allouche A R, Hadinger G, Aubert-Frécon M 1999 Chem. Phys. 246 57Google Scholar

  • 图 1  Li2(0, ±1)的基态势能曲线(能量零点取为各自平衡核间距处能量)

    Fig. 1.  Potential energy curves of ground states for Li2(0, ±1) (the energy zero-point is located at respective equilibrium internuclear distance).

    表 1  7Li2 (X1g+)分子的光谱常数

    Table 1.  The spectroscopic constants of 7Li2 (X1g+).

    MethodReωe/cm–1ωexe/cm–1Be/cm–1De/eV
    vCCSD(T)/TZa2.6992346.35562.66870.65961.038
    CCSD(T)/TZ2.6770350.56092.71630.67061.046
    CCSD(T)/QZ2.6742351.77842.72380.67201.052
    CCSD(T)/5Z2.6734352.02222.72850.67241.053
    实验b2.6734351.422952.44170.668241.060
    注: a未包含1s轨道电子关联; b激光诱导荧光傅里叶变换谱(LIF FTS)实验PKR拟合值[2,6].
    下载: 导出CSV

    表 2  7Li2 (X1g+)分子的振动能级Gv (J = 0) (单位: cm–1)

    Table 2.  The vibrational levels Gv (J = 0) of 7Li2 (X1g+) (unit in cm–1).

    Vibrational levels本次结果理论a实验b
    0000
    1346.17346.05346.46
    2687.11686.65687.86
    31022.781021.711024.08
    41353.131351.151355.01
    51678.111674.881680.54
    61997.671992.812000.56
    72311.722304.852314.95
    82620.212610.922623.58
    92923.032910.902926.35
    103220.093204.703223.11
    113511.293492.233513.74
    123796.493773.363798.10
    134075.584048.004076.05
    144348.394316.024347.45
    154614.784577.314612.16
    164874.554831.744870.02
    175127.525079.525120.86
    185373.465319.525364.53
    195612.145552.595600.84
    205843.275778.255829.63
    216066.575996.356050.69
    226281.676206.726263.83
    236488.166409.206468.84
    246685.586603.596665.49
    RMS8.68(0.16%)33.93(0.65%)
    注: a FCIPP计算值[3], b LIF FTS实验值[2,6].
    下载: 导出CSV

    表 3  7Li2 (X1g+)分子的各振动能级的转动常数BvDv

    Table 3.  The rotational constants Bv and Dv of 7Li2 (X1g+).

    vBv/cm–1Dv/10-4 cm–1
    Expt.[2,6]This workExpt.[2,6]This work
    00.669070.668820.0987
    10.661960.661710.0991
    20.654790.654530.0996
    30.647540.647280.1002
    40.640190.639950.1007
    50.632750.632520.1014
    60.625210.624990.1021
    70.617540.617330.1028
    80.609740.609540.1037
    90.601800.601600.1046
    100.593680.593480.1056
    110.585400.585180.1068
    120.576920.576670.1080
    130.568220.567930.1093
    140.559180.558920.10970.1108
    150.550000.549610.11190.1123
    160.540550.539950.11430.1138
    170.530610.529900.11460.1152
    180.520440.519390.11800.1165
    190.509920.508340.12150.1175
    200.498850.496670.12460.1181
    210.487260.484290.12650.1185
    220.478450.471090.11820.1187
    230.462460.456980.13400.1190
    240.449130.441830.14010.1200
    下载: 导出CSV

    表 4  7Li2±1分子体系基态的光谱常数

    Table 4.  The spectroscopic constants of ground-state 7Li2±1 systems.

    SpeciesMethodReωe/cm–1ωexe/cm–1Be/cm–1De/eV
    Li2+本次结果a3.0986262.75991.56400.50051.297
    本次结果a23.1337258.82111.54130.48931.279
    本次结果a33.1038262.35481.56690.49881.294
    MPb3.122263.081.29540.49451.2976
    CIc3.099263.760.50061.2945
    DMCd3.11266.21.5930.47531.2965
    实验[5,7]3.11262 ± 21.7 ± 0.50.496 ± 0.0021.2973
    Li2本次结果a3.0265230.64571.58810.52470.850
    本次结果a33.0396231.10242.31150.52010.845
    DMCd3.10235.33.1660.46520.7733
    MRDCIe3.062236.22.420.857
    CCSD(T)f3.00240.73.1660.52380.9085
    实验[10]3.094 ± 0.015232 ± 350.502 ± 0.0050.865 ± 0.022(D0)
    注: a RCCSD(T)/5Z; a2vMRCCSD/TZ + 4s2p(未包含1s的电子关联); a3MRCCSD/TZ + 4s2p(包含1s的电子关联); bmodel potential (MP) method[25]; cconfiguration interaction (CI) with effective core potential[4]; ddiffusion quantum Monte-Carlo (DMC) method[12]; emultireference singly and doubly CI (MRDCI)[11]; f CCSD(T, full)/cc-pv5z[12].
    下载: 导出CSV

    表 5  Li2± 基态振动能级间隔G (v + 1)–G (v) (单位: cm–1)

    Table 5.  The vibration energy spacing G (v + 1)–G (v) of ground-state Li2± (unit in cm–1)).

    vLi2+Li2
    理论a理论b理论c本次结果理论c本次结果
    0259.51260259.74259.74227.53228.64
    1256.30257256.54256.54222.71223.96
    2253.11254253.35253.35217.93219.69
    3249.95251250.19250.19213.21216.12
    4246.81248247.04247.04208.54213.32
    5243.68244243.92243.92203.95211.08
    6240.57241240.81240.81199.42208.91
    7237.49236237.72237.72194.97206.46
    8234.41235234.65234.65190.61203.52
    9231.35232231.59231.59186.34200.06
    10228.31228228.55228.55182.16196.15
    11225.28226225.51225.51178.08191.88
    12222.26222222.50222.50174.12187.33
    13219.24220219.48219.48170.26182.59
    14216.24216216.48216.48166.53177.72
    15213.24214213.48213.48162.92172.77
    16210.25210210.50210.50159.45167.78
    17207.26207207.50207.50156.11162.77
    18204.28205204.53204.53152.91157.79
    19201.30201201.55201.55149.87152.82
    注: a CCSD(T, FULL)/aug-cc-Pcvqz[12]; b MP[25]; c DMC[12].
    下载: 导出CSV

    表 6  7Li2± 基态分子的各振动能级的转动常数BvDv

    Table 6.  The vibrational levels Bv and Dv of 7Li2±.

    vBv/cm–1Dv/10-4 cm–1
    Li2+Li2Li2+Li2-
    00.497760.520210.072230.10558
    10.492350.511290.071680.10438
    20.486980.502140.071140.10106
    30.481640.492260.070620.09317
    40.476350.481060.070110.07966
    50.471090.468240.069610.06296
    60.465860.454070.069120.04741
    70.460670.439200.068650.03586
    80.455510.424260.068190.02862
    90.450370.409690.067750.02462
    100.445270.395710.067320.02265
    110.440190.382380.066900.02180
    120.435130.369710.066490.02155
    130.430090.357660.066110.02159
    140.425070.346170.065730.02177
    150.420070.335200.065370.02201
    160.415080.324690.065030.02226
    170.410100.314610.064700.02252
    180.405140.304920.064390.02276
    190.400180.295580.064100.02300
    200.395220.286560.063820.02324
    210.390260.277840.063560.02347
    220.385310.269390.063320.02370
    230.380350.261200.063100.02392
    240.375380.253240.062900.02416
    下载: 导出CSV

    表 7  Li2分子的同位素体系的振动能级与转动常数

    Table 7.  The vibrational levels and rotational constants for isotope molecules of Li2.

    vG(v)/cm–1Bv/cm–1Dv/10-4 cm–1
    6Li7Li6Li26Li7Li6Li26Li7Li6Li2
    0000.724310.779780.11580.13429
    13603730.716290.770820.116350.13495
    27147410.708190.761760.116950.13568
    3106311020.700010.752600.117610.13647
    4140614570.691730.743330.118320.13735
    5174318050.683330.733920.119110.13832
    6207421480.674800.724360.119990.13939
    7240024840.666130.714620.120950.14058
    8271928130.657290.704690.122010.14189
    9303231350.648270.694530.123180.14335
    10333834510.639040.684120.124480.14496
    11363937600.629580.673430.125910.14673
    12393240620.619860.662420.127470.14863
    13421943560.609840.651040.129130.15062
    14450046430.599490.639240.130880.15262
    15477349220.588750.626950.132620.1545
    16503851930.577560.614070.134260.1561
    17529754560.565840.600520.135670.15725
    18554757100.553520.586170.136710.15786
    19578959560.540480.570890.137330.15794
    20602361920.526620.554560.137550.15775
    21624964180.511820.537030.137570.15778
    22646566330.495960.518150.13780.15879
    23667168380.478900.497760.138860.16187
    24686670310.460510.475640.141620.16834
    下载: 导出CSV
  • [1]

    Gardet G, Rogemond F, Chermette H 1996 J. Chem. Phys. 105 9933Google Scholar

    [2]

    Barakat B, Bacis R, Carrot F, Churassy S, Crozet P, Martin F, Verges J 1986 Chem. Phys. 102 215Google Scholar

    [3]

    Maniero A M, Acioli P H 2005 Int. J. Quantum Chem. 103 711Google Scholar

    [4]

    Schmidt-Mink I, Müller W, Meyer W 1985 Chem. Phys. 92 263Google Scholar

    [5]

    Bernheim R A, Gold L P, Tipton T 1983 J. Chem. Phys. 78 3635Google Scholar

    [6]

    Hessel M M, Vidal C R 1979 J. Chem. Phys. 70 4439Google Scholar

    [7]

    Bernheim R A, Gold L P, Tipton T, Konowalow D D 1984 Chem. Phys. Lett. 105 201Google Scholar

    [8]

    Blustin P H, Linnett J W 1974 J. Chem. Soc. Faraday Trans. 2 Mol. Chem. Phys. 70 826Google Scholar

    [9]

    Sarkas H W, Arnold S T, Hendricks J H, Slager V L, Bowen K H 1994 Z. Phys. D 29 209Google Scholar

    [10]

    Hogreve H 2000 Eur. Phys. J. D 8 85Google Scholar

    [11]

    Nasiri S, Zahedi M 2017 Comput. Theor. Chem. 1114 106Google Scholar

    [12]

    Brito B G A, Hai G Q, Cândido L 2017 J. Chem. Phys. 146 174306Google Scholar

    [13]

    Rabli D, McCarroll R 2017 Chem. Phys. 487 23Google Scholar

    [14]

    魏长立, 梁桂颖, 刘晓婷, 颜培源, 闫冰 2016 物理学报 65 163101Google Scholar

    Wei C L, Liang G Y, Liu X T, Yan P Y, Yan B 2016 Acta Phys. Sin. 65 163101Google Scholar

    [15]

    Yang X, Xu H, Yan B 2019 Chin. Phys. B 28 348

    [16]

    Zhang L L, Gao S B, Meng Q T, Song Y Z 2015 Chin. Phys. B 24 201

    [17]

    Wei C L, Zhang X M, Ding D J, Yan B 2016 Chin. Phys. B 25 13102Google Scholar

    [18]

    Hampel C, Peterson K A, Werner H J 1992 Chem. Phys. Lett. 190 1Google Scholar

    [19]

    Knowles P J, Hampel C, Werner H 1993 J. Chem. Phys. 99 5219Google Scholar

    [20]

    Werner H J, Knowles P J, G Knizia, et al. http://www. molpro.net. [2019-3-10]

    [21]

    Rolik Z, Szegedy L, Ladjánszki I, Ladóczki B, Kállay M 2013 J. Chem. Phys. 139 094105Google Scholar

    [22]

    Prascher B P, Woon D E, Peterson K A, Dunning T H, Wilson A K 2011 Theor. Chem. Acc. 128 69Google Scholar

    [23]

    Wolf A, Reiher M, Hess B A 2002 J. Chem. Phys. 117 9215Google Scholar

    [24]

    Le Roy R J 2017 J. Quant. Spectrosc. Radiat. Transf. 186 167Google Scholar

    [25]

    Magnier S, Rousseau S, Allouche A R, Hadinger G, Aubert-Frécon M 1999 Chem. Phys. 246 57Google Scholar

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出版历程
  • 收稿日期:  2019-03-13
  • 修回日期:  2019-04-10
  • 上网日期:  2019-06-01
  • 刊出日期:  2019-06-05

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